CN105551066A - Transform domain down-sampling technology-based low-resolution image compression method - Google Patents

Abstract

The invention provides a transform domain down-sampling technology-based low-resolution image compression method. According to the method, the encoding quality of a part of the pixels in an image is improved in the compression encoding process of the image through a down-sampling technology of transform domains; and the pixel points are used for forming a high-quality low-resolution image so as to satisfy the display output demand, so that the construction of the high-quality low-resolution image is completed while the image is encoded. Compared with the traditional method, the method has the advantages that high-quality pixel points are provided for the output of the low-resolution images in the image compression process, the defect that the traditional method is relatively bad in low-resolution compressed image quality as the compression and low-resolution output are asynchronously realized is overcome, and the efficient uniformity of the image compression and low-resolution output is realized.

Description

A kind of low-resolution image compression method based on transform domain down-sampling technology

Technical field

The invention belongs to image code domain, relate generally to the compress technique of digital picture.

Background technology

The low resolution of image realizes mainly in order to adapt to the display demand of low-resolution display devices.In actual applications, generally need to carry out compression coding to original image and wait resolution reconstruction, then reduce the resolution of compressed images, this demand can be met.And the acquisition of low-resolution image, be normally achieved by carrying out spatial domain down-sampling to the image after compression.Therefore, high-quality compressed image is very important to acquisition later stage high-quality low-resolution image.In order to realize high-quality compressed image in early stage, classic method often needs to realize by improving encoder bit rate, will reduce overall code efficiency like this.Therefore, how under the condition of bandwidth sum limited storage space, realizing the display of the low resolution, compressed image of high-quality effect, is the large problem that New Image coding techniques research field needs to solve.

The low resolved reconstruction in traditional ground for compressed image, needs to realize in two steps, and the first step compresses image, second step be to compression after image carry out the spatial domain down-sampling of pixel in horizontal direction and vertical direction, to reduce the resolution of image.When using traditional jpeg image coding standard to compress image, the quality of each pixel in the compressed image of gained is suitable, when carrying out low resolution display, display quality cannot improve further because being subject to the constraint of coding quality, therefore the low of compressed images low resolution display translation efficiency is caused, see list of references " JPEG (JointPhotographicExpertsGroup): ISO/IECIS10918 – 1/ITU-TRecommendationT.81, DigitalCompressionandCodingofContinuous-ToneStillImage, 1993 ".If the compression coding of image and low resolution display translation can be combined, the efficiency of the low resolution display translation of compressed image so greatly will be improved.

Summary of the invention

The object of this invention is to provide a kind of novel low-resolution image compression method based on transform domain down-sampling technology, transform domain down-sampling technology and image low resolution display translation mainly combine by this method, while carrying out compressed encoding to whole image, the display for low resolution provides high-quality reconstruction image.Compared with traditional method, the present invention is in the process of compression of images, and the image for low resolution exports and provides high-quality pixel, overcomes the shortcoming that classic method exports because of substep realization compression and low resolution and causes low resolution compressed image second-rate.

Content of the present invention for convenience of description, first do following term definition:

Definition 1, the method for image block in traditional jpeg image compression standard

Traditional image block method is according to the method for in Joint Photographic Experts Group, image being carried out to piecemeal, original image is divided into the equidimension image block of multiple non-overlapping copies, specific descriptions process is see " JPEG (JointPhotographicExpertsGroup): ISO/IECIS10918 – 1/ITU-TRecommendationT.81; DigitalCompressionandCodingofContinuous-ToneStillImage, 1993 ";

Definition 2, the method for traditional calculating discrete cosine transformation matrix

The method of traditional calculating discrete cosine transformation matrix is the definition according to discrete cosine transformation matrix, calculate each element in transformation matrix, thus produce the discrete cosine transformation matrix of arbitrary size as required, specific descriptions process is see document " digital video coding techniques principle ", Gao Wen, Zhao Debin, Ma Siwei work, Science Press;

Definition 3, traditional matrix K ronecker multiplication

Traditional matrix K ronecker multiplication is expressed as wherein, represent Kronecker multiplication operator, the matrix of A to be size be m × n, and

The matrix of B to be size be p × q, the matrix of C to be size be mp × nq,

Specific descriptions process is see document " matrix analysis and application (the 2nd edition) ", and a prominent personage is outstanding, publishing house of Tsing-Hua University;

Definition 4, traditional matrix transpose operation

Traditional matrix transpose is that the row of matrix A is changed into corresponding row, and the new matrix obtained is called and is denoted as A by the transposed matrix of A ^t, the matrix transpose operation of symbol T representing matrix; Specific descriptions process is see document " matrix analysis and application (the 2nd edition) ", and a prominent personage is outstanding, publishing house of Tsing-Hua University;

Definition 5, traditional vectorial filling algorithm based on discrete cosine transform

Traditional vectorial filling algorithm based on discrete cosine transform utilizes a part of component of discrete cosine transformation matrix and original input vector, by calculating corresponding Filling power, carries out data replacement to another part component; Concrete steps are see document " Arbitrarily-shapedtransformcodingbasedonanewpaddingtechn ique ";

Definition 6, traditional one-dimensional discrete cosine transform method

Traditional one-dimensional discrete cosine transform method utilizes discrete cosine transformation matrix premultiplication line of input vector, thus obtain the coefficient vector after converting, specific descriptions process is see document " digital video coding techniques principle ", and Gao Wen, Zhao Debin, Ma Siwei are outstanding, Science Press;

Definition 7, the quantization method in traditional jpeg image compression standard

Quantization method in traditional jpeg image compression standard is divided by corresponding with each element quantized in form for each element in matrix of coefficients after transition coding, then to the floor operation that each result obtained rounds up, thus the matrix of coefficients of quantification is obtained; Specific descriptions process is see " JPEG (JointPhotographicExpertsGroup): ISO/IECIS10918 – 1/ITU-TRecommendationT.81; DigitalCompressionandCodingofContinuous-ToneStillImage, 1993 ";

Definition 8, the quantification method in traditional jpeg image compression standard

Quantification method in traditional jpeg image compression standard is multiplied corresponding with each element quantized in form for each element quantized in rear matrix of coefficients, thus obtains the matrix of coefficients of inverse quantization; Specific descriptions process is see " JPEG (JointPhotographicExpertsGroup): ISO/IECIS10918 – 1/ITU-TRecommendationT.81; DigitalCompressionandCodingofContinuous-ToneStillImage, 1993 ";

Definition 9, the coding method in traditional jpeg image compression standard

Coding method in traditional jpeg image compression standard mainly comprises carries out transition coding, quantification and entropy code and calculation code bit number to each image block; Specific descriptions process is see " JPEG (JointPhotographicExpertsGroup): ISO/IECIS10918 – 1/ITU-TRecommendationT.81; DigitalCompressionandCodingofContinuous-ToneStillImage, 1993 ";

Definition 10, the coding/decoding method in traditional jpeg image compression standard

Coding/decoding method in traditional jpeg image compression standard mainly comprises and carries out inverse transformation and inverse quantization to each image block; Specific descriptions process is see " JPEG (JointPhotographicExpertsGroup): ISO/IECIS10918 – 1/ITU-TRecommendationT.81; DigitalCompressionandCodingofContinuous-ToneStillImage, 1993 ";

Definition 11, traditional 2-D discrete cosine inverse transform method

Traditional 2-D discrete cosine inverse transform method completes in two steps, the first step, utilizes the inverse matrix premultiplication input matrix of discrete cosine transformation matrix, obtains a matrix; Second step, with the inverse matrix right matrix taking advantage of the first step to obtain again of discrete cosine transformation matrix transposed matrix, thus obtains the matrix after inverse transformation; Specific descriptions process is see document " digital video coding techniques principle ", and Gao Wen, Zhao Debin, Ma Siwei are outstanding, Science Press;

Definition 12, traditional bicubic interpolation method

Traditional bicubic interpolation method is interpolation method the most frequently used in two-dimensional space, and in this interpolation method, the value at point (u, v) place can be obtained by the weighted mean of 16 points nearest in rectangular node around it; Specific descriptions process is see document " Cubicconvolutioninterpolationfordigitalimageprocessing ";

Definition 13, the method for image block composograph in traditional jpeg image compression standard

The method of traditional image block composograph carries out not overlapping each other combination with the method for synthesizing complete image with image block according in jpeg image compression standard, specific descriptions process is see " JPEG (JointPhotographicExpertsGroup): ISO/IECIS10918 – 1/ITU-TRecommendationT.81; DigitalCompressionandCodingofContinuous-ToneStillImage, 1993 ";

The invention provides a kind of low-resolution image compression method based on transform domain down-sampling technology, it comprises the following steps:

Step 1, the pre-service of image

Be the image of W × H by size, in jpeg image compression standard traditionally, the method for image block is divided into N=(W × H)/16 ²individual non-overlapping copies, size is the square image blocks of 16 × 16, is designated as B ₁, B ₂..., B _i..., B _n, here, the width of W representative image, the height of H representative image, total number of image block after N representative image divides, the index of i representative image block, i ∈ 1,2 ..., N}.

Step 2, the generation of index matrix

256 natural numbers 1,2 ..., 256 press from small to large, and order is from top to bottom put by column, and producing a size is the index matrix of 16 × 16, is designated as I:

Element in I is designated as I (x, y), and here, x represents the horizontal ordinate of index matrix I interior element, and y represents the ordinate of index matrix I interior element, x and y is natural number, and 1≤x≤16,1≤y≤16.

Step 3, the generation of column index vector

First, define 2 column index subvectors, be designated as respectively here, the row vector of 1 × 64, x is odd number, and y is odd number, and 1≤x≤16,1≤y≤16}, namely , I (15,1) I (1,3) I (3,3) ..., I (15,3),, I (1,15) I (3,15) ..., I (15,15)]=[13 ... 153335 ..., 47 ..., 225227 ..., 239]; the row vector of 1 × 192, be odd number when x with y is different, and 1≤x≤16,1≤y≤16}, namely , I (16,1) I (1,2) I (2,2) ..., I (16,2),, I (2,15) I (4,15),, I (16,15) I (1,16) I (2,16) ..., I (16,16)]=[24,, 161718 ... 32 ..., 226228,, 240241242 ... 256], wherein, I is the index matrix produced in step 2, x represents the horizontal ordinate of index matrix I interior element, and y represents the ordinate of index matrix I interior element, x and y is natural number;

Then, will form the column index vector of 1 × 256 according to order from left to right, be designated as i (15, 1) I (1, 3) I (3, 3), I (15, 3), I (1, 15) I (3, 15), I (15, 15) I (2, 1) I (4, 1), I (16, 1) I (1, 2) I (2, 2), I (16, 2), I (2, 15) I (4, 15), I (16, 15) I (1, 16) I (2, 16), I (16, 16)]=[13, 153335, 47, 225227, 23924, 161718, 32, 226228, 240241242, 256], here, I is the index matrix produced in step 2.

Step 4, the generation of line index vector

First, define 3 line index subvectors, be designated as respectively here, be a size be the row vector of 1 × 64, 1≤x≤8,1≤y≤8}, namely , I (8,1) I (1,2) I (2,2) ..., I (8,2),, I (1,8) I (2,8) ..., I (8,8)]=[12 ... 81718 ..., 24 ..., 113114 ..., 120]; be a size be the row vector of 1 × 64, 9≤x≤16,1≤y≤8}, namely , I (16,1) I (9,2) I (10,2) ..., I (16,2),, I (9,8) I (10,8) ..., I (16,8)]=[910 ... 162526 ..., 32 ..., 121122 ..., 128]; be a size be the row vector of 1 × 128, 1≤x≤16,9≤y≤16}, namely , I (16,9) I (1,10) I (2,10),, I (16,10) ..., I (1,16) I (2,16) ..., I (16,16)]=[129130,, 144145146 ..., 160 ... 241242 ..., 256], wherein, I is the index matrix produced in step 2, and x represents the horizontal ordinate of index matrix I interior element, and y represents the ordinate of index matrix I interior element, x and y is natural number;

Then, will form according to order from left to right the line index vector that a size is 1 × 256, be designated as =[I (1, 1) I (2, 1), I (8, 1) I (1, 2) I (2, 2), I (8, 2), I (1, 8) I (2, 8), I (8, 8) I (9, 1) I (10, 1), I (16, 1) I (9, 2) I (10, 2), I (16, 2), I (9, 8) I (10, 8), I (16, 8) I (1, 9) I (2, 9), I (16, 9) I (1, 10) I (2, 10), I (16, 10), I (1, 16) I (2, 16), I (16, 16)]=[12, 81718, 24, 113114, 120910, 162526, 32, 121122, 128129130, 144145146, 160, 241242, 256], here, I is the index matrix produced in step 2.

Step 5, the generation of transformation matrix

First, the method for calculating discrete cosine transformation matrix traditionally, producing a size is the discrete cosine transformation matrix of 16 × 16, is designated as C;

Secondly, brought into by discrete cosine transformation matrix C in traditional matrix K ronecker multiplication, producing a size is the transformation matrix of 256 × 256, is designated as D, and here, symbol represent the Kronecker multiplication operator in traditional matrix K ronecker multiplication.

Step 6, the row of adjustment transformation matrix

The column index vector that step 3 is produced each element be designated as here, l represents the index of middle element, l is natural number, 1≤l≤256;

Forming a new size by all column vectors in matrix D is the transformation matrix of 256 × 256, and be designated as E, step is:

1st time, get of matrix D individual column vector, the 1st row of generator matrix E; The l time, get of matrix D individual column vector, the l row of generator matrix E; 256th time, get of matrix D individual column vector, the 256th row of generator matrix E,

Namely

Here, e _m,nrepresent the element in matrix E, m represents the horizontal ordinate of index matrix E interior element, and n represents the ordinate of index matrix E interior element, m and n is natural number, 1≤m≤256,1≤n≤256.

Step 7, the row of adjustment transformation matrix

The line index vector that step 4 is produced each element be designated as here, l represents the index of middle element, l is natural number, 1≤l≤256;

All row vectors in the matrix E produced by step 6 form a new transformation matrix, and be designated as F, step is as follows: the 1st time, with the of matrix E 1st row of individual row vector generator matrix F; The l time, with of matrix E the l of individual row vector generator matrix F is capable; 256th time, with of matrix E 256th row of individual row vector generator matrix F,

Namely

Here, f _p,qrepresent the element in matrix F, p represents the horizontal ordinate of index matrix F interior element, and q represents the ordinate of index matrix F interior element, p and q is natural number, 1≤p≤256,1≤q≤256.

Step 8, is converted into column vector by each image block

First, image block B step 1 produced _iin each row, according to order from left to right, to take out successively, and according to first row, secondary series ..., the 16 row, from top to bottom put order composition a size be the column vector of 256 × 1, be designated as namely here, x _jrepresent column vector in element, j is the subscript index of middle element, j is natural number, 1≤j≤256; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Then, will in element x ₁, x ₃, x ₅, x ₇, x ₉, x ₁₁, x ₁₃, x ₁₅, x ₃₃, x ₃₅, x ₃₇, x ₃₉, x ₄₁, x ₄₃, x ₄₅, x ₄₇, x ₆₅, x ₆₇, x ₆₉, x ₇₁, x ₇₃, x ₇₅, x ₇₇, x ₇₉, x ₉₇, x ₉₉, x ₁₀₁, x ₁₀₃, x ₁₀₅, x ₁₀₇, x ₁₀₉, x ₁₁₁, x ₁₂₉, x ₁₃₁, x ₁₃₃, x ₁₃₅, x1 ₃₇, x ₁₃₉, x ₁₄₁, x ₁₄₃, x ₁₆₁, x ₁₆₃, x ₁₆₅, x ₁₆₇, x ₁₆₉, x ₁₇₁, x ₁₇₃, x ₁₇₅, x ₁₉₃, x ₁₉₅, x ₁₉₇, x ₁₉₉, x ₂₀₁, x ₂₀₃, x ₂₀₅, x ₂₀₇, x ₂₂₅, x ₂₂₇, x ₂₂₉, x ₂₃₁, x ₂₃₃, x ₂₃₅, x ₂₃₇and x ₂₃₉, generating a size is in accordance with the order from top to bottom the column vector of 64 × 1, is designated as that is: here, x _krepresent column vector in element, k is the subscript index of middle element, k is natural number, 1≤k≤256; X' _jrepresent column vector in element, j is the subscript index of middle element, j is natural number, 1≤j≤64; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 9, fills the generation of vector

By the column vector produced in the transformation matrix F produced in step 7 and step 8 substitute into traditional based in the vectorial filling algorithm of discrete cosine transform, obtain the filling column vector that a size is 192 × 1, be designated as that is:

here, x " _krepresent column vector in element, k is the subscript index of middle element, k is natural number, 1≤k≤192; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 10, the generation of intermediate vector

By the column vector produced in step 8 with the column vector produced in step 9 forming a size is in accordance with the order from top to bottom the column vector of 256 × 1, is designated as that is:

Namely

Here, y _lrepresent column vector in element, l is the subscript index of middle element, l is natural number, 1≤l≤256; X' _jrepresent the column vector produced in step 8 in element, j is the subscript index of middle element, j is natural number, 1≤j≤64; X " _krepresent the column vector produced in step 9 in element, k is the subscript index of middle element, k is natural number, 1≤k≤192; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 11, the generation of coefficient vector

By traditional one-dimensional discrete cosine transform method to the intermediate vector produced in step 10 carry out discrete cosine transform, obtain coefficient vector namely here, z _jrepresent column vector in element, j is the subscript index of middle element, j is natural number, 1≤j≤256; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 12, the generation of matrix of coefficients

Definition size be 8 × 8 matrix of coefficients be B' _i, use the 1 to 8 element z ₁~ z ₈generate B' in accordance with the order from top to bottom _ithe 1st row; With the 9 to 16 element z ₉~ z ₁₆generate B' in accordance with the order from top to bottom _ithe 2nd row; With the 17 to 24 element z ₁₇~ z ₂₄generate B' in accordance with the order from top to bottom _ithe 3rd row; With the 25 to 32 element z ₂₅~ z ₃₂generate B' in accordance with the order from top to bottom _ithe 4th row; With the 33 to 40 element z ₃₃~ z ₄₀generate B' in accordance with the order from top to bottom _ithe 5th row; With the 41 to 48 element z ₄₁~ z ₄₈generate B' in accordance with the order from top to bottom _ithe 6th row; With the 49 to 56 element z ₄₉~ z ₅₆generate B' in accordance with the order from top to bottom _ithe 7th row; With the 57 to 64 first z ₅₇~ z ₆₄element generates B' in accordance with the order from top to bottom _ithe 8th row;

Namely $B_i^{\′}=\left[\begin{array}{cccc}{\mathrm{\β}}_{1,1}& {\mathrm{\β}}_{1,2}& \mathrm{...}& {\mathrm{\β}}_{1,n}\\ {\mathrm{\β}}_{2,1}& {\mathrm{\β}}_{2,2}& \mathrm{...}& {\mathrm{\β}}_{2,n}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\mathrm{\β}}_{m,1}& {\mathrm{\β}}_{m,2}& \mathrm{...}& {\mathrm{\β}}_{m,n}\end{array}\right]=\left[\begin{array}{cccc}{z}_1& z_9& \mathrm{...}& z_{57}\\ z_2& z_{10}& \mathrm{...}& z_{58}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ z_8& z_{16}& \mathrm{...}& z_{64}\end{array}\right],$

Here, β _m,nb' _iin element, m represent matrix B ' _ithe horizontal ordinate of interior element, n represent matrix B ' _ithe ordinate of interior element, m and n is natural number, 1≤m≤8,1≤n≤8; z ₁, z ₂..., z ₆₄represent the column vector produced in step 11 in 64 elements; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 13, encodes to matrix of coefficients

With the quantization method in traditional jpeg image compression standard to the matrix of coefficients B' produced in step 12 _iquantize, by the matrix of coefficients obtained after quantification, be designated as

Here, be in element, m represents matrix the horizontal ordinate of interior element, n represents matrix the ordinate of interior element, m and n is natural number, 1≤m≤8,1≤n≤8;

With the quantification method pair in traditional jpeg image compression standard carry out inverse quantization, obtain the matrix of coefficients B after inverse quantization " _i,

Here, β " _m,nb " _iin element, m represents matrix B " _ithe horizontal ordinate of interior element, n represents matrix B " _ithe ordinate of interior element, m and n is natural number, 1≤m≤8,1≤n≤8; Here, the index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 14, decodes to matrix of coefficients

First, define the full null matrix that a size is 16 × 16, be designated as

${\hat{B}}_i=\left[\begin{array}{cccc}0& 0& \mathrm{...}& 0\\ 0& 0& \mathrm{...}& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ 0& 0& \mathrm{...}& 0\end{array}\right];$

Secondly, the matrix B that step 13 is obtained " _ithe 1st column element take out successively, and put into matrix successively 1 to 8 row of the 1st row; By matrix B " _ithe 2nd column element take out successively, and put into matrix successively 1 to 8 row of the 2nd row; By matrix B " _ithe 3rd column element take out successively, and put into matrix successively 1 to 8 row of the 3rd row; By matrix B " _ithe 4th column element take out successively, and put into matrix successively 1 to 8 row of the 4th row; By matrix B " _ithe 5th column element take out successively, and put into matrix successively 1 to 8 row of the 5th row; By matrix B " _ithe 6th column element take out successively, and put into matrix successively 1 to 8 row of the 6th row; By matrix B " _ithe 7th column element take out successively, and put into matrix successively 1 to 8 row of the 7th row; By matrix B " _ithe 8th column element take out successively, and put into matrix successively 1 to 8 row of the 8th row; By amended matrix be designated as

Here, be in element, p represents matrix the horizontal ordinate of interior element, q represents matrix the ordinate of interior element, p and q is natural number, 1≤p≤16,1≤q≤16; β " _m,nb " _iin element, m represents matrix B " _ithe horizontal ordinate of interior element, n represents matrix B " _ithe ordinate of interior element, m and n is natural number, 1≤m≤8,1≤n≤8; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Finally, with traditional 2-D discrete cosine inverse transform method to matrix carry out 2-D discrete cosine inverse transformation, obtain the picture element matrix that size is 16 × 16, be designated as b _i:

Here, α _m,nb _iin element, m represents matrix b _ithe horizontal ordinate of interior element, n represents matrix b _ithe ordinate of interior element, m and n is natural number, 1≤m≤16,1≤n≤16; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 15, the correction of decoded image blocks

To the picture element matrix b produced in step 14 _i, carry out interpolation by traditional bicubic interpolation method to the pixel be positioned on (u, v) position, here, u is b _ithe horizontal ordinate of interior pixel, v is b _ithe ordinate of interior pixel, u and v is natural number, and is odd number when u with v is different, 1≤u≤16,1≤v≤16; Interpolation image block matrix will be obtained, be designated as b ' _i:

Here, α ' _m,nb ' _iin element, m represents matrix b ' _ithe horizontal ordinate of interior element, n represents matrix b ' _ithe ordinate of interior element, m and n is natural number, 1≤m≤16,1≤n≤16; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 16, the spatial domain down-sampling of image block

First, define a size be the full null graph of 8 × 8 as block matrix, be designated as

Here, the index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Then, the matrix b ' step 15 obtained _iin the element of the upper all odd-numbered lines of the 1st row take out one by one, put into successively the 1st row; By b ' _iin the element of the upper all odd-numbered lines of the 3rd row take out one by one, put into successively the 2nd row; By b ' _iin the element of the upper all odd-numbered lines of the 5th row take out one by one, put into successively the 3rd row; By b ' _iin the element of the upper all odd-numbered lines of the 7th row take out one by one, put into successively the 4th row; By b ' _iin the element of the upper all odd-numbered lines of the 9th row take out one by one, put into successively the 5th row; By b ' _iin the element of the upper all odd-numbered lines of the 11st row take out one by one, put into successively the 6th row; By b ' _iin the element of the upper all odd-numbered lines of the 13rd row take out one by one, put into successively the 7th row; By b ' _iin the element of the upper all odd-numbered lines of the 15th row take out one by one, put into successively the 7th row; Obtain image block

${\hat{b}}_i^{\′}=\left[\begin{array}{cccc}{\mathrm{\α}}_{1,1}^{\′}& {\mathrm{\α}}_{1,3}^{\′}& \mathrm{...}& {\mathrm{\α}}_{1,15}^{\′}\\ {\mathrm{\α}}_{3,1}^{\′}& {\mathrm{\α}}_{3,3}^{\′}& \mathrm{...}& {\mathrm{\α}}_{3,15}^{\′}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\mathrm{\α}}_{15,1}^{\′}& {\mathrm{\α}}_{15,3}^{\′}& \mathrm{...}& {\mathrm{\α}}_{15,15}^{\′}\end{array}\right];$

Here, α ' _m,nb ' _iin element, m represents matrix b ' _ithe horizontal ordinate of interior element, n represents matrix b ' _ithe ordinate of interior element, m and n is odd number, and 1≤m≤16,1≤n≤16; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 17, builds high-definition picture

For the interpolation image block matrix b ' produced in step 15 _i, adopt the method for image block composograph in traditional jpeg image compression standard, producing size is the image of W × H, is designated as here, W represents the width of input picture in step 1, and H represents the height of input picture in step 1, the index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block.

Step 18, builds low-resolution image

With the image block produced in step 16 the method of image block composograph in jpeg image compression standard traditionally, produces the image that size is (W/2) × (H/2), is designated as here, W represents the width of input picture in step 1, and H represents the height of input picture in step 1, the index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block.

Ultimate principle of the present invention: the down-sampling technology utilizing transform domain, in the compression encoding process of image, improves the coding quality of part pixel in image, and forms high-quality low-resolution image to meet the demand of display translation with these pixels.While image is encoded, complete the structure of high-quality low-resolution image.

Essence of the present invention is: in order to meet the display demand of high-quality low resolution, compressed image, the coding method of the down-sampling technology based on transform domain is applied in Image Coding by the present invention, improve the quality of part pixel in compressed image, thus achieve the high-quality coding of low resolution output image.

Innovative point of the present invention: the low resolution that the down-sampling technology of transform domain is applied to compressed image by the present invention is encoded and in display, image compression encoding and low resolution rebuild and combine, achieve the display of efficient compressed image low resolution.

Advantage of the present invention: the compression of image and low resolution display translation are combined, based on the compressed encoding of image, for the display of high-quality low resolution provides guarantee, and achieves the efficient unification of compression of images and low resolution display translation.

Accompanying drawing explanation

Fig. 1 is realization flow of the present invention;

Fig. 2 is the PSNR value that the coding method of application different images obtains under same-code code check.

Embodiment

The present invention mainly adopts the mode of emulation experiment to verify the feasibility of this system model, and institute is in steps all through experimental verification, and for realizing the compression of images based on transform domain down-sampling technology, concrete implementation step is as follows:

Step 1, the pre-service of image

Width W=16 of setting image ^m, height H=16 of image ⁿ, m and n is natural number here, and in jpeg image compression standard traditionally, the method for image block is divided into N=(W × H)/16 ²individual non-overlapping copies, size is the square image blocks of 16 × 16, is designated as B ₁, B ₂..., B _n, here, total number of image block after N representative image divides, the index of i representative image block, i ∈ 1,2 ..., N};

Step 2, the generation of index matrix

256 natural numbers 1,2 ..., 256 press from small to large, and order is from top to bottom put by column, and producing a size is the index matrix of 16 × 16, is designated as I:

Element in I is designated as I (x, y), and here, x represents the horizontal ordinate of index matrix I interior element, and y represents the ordinate of index matrix I interior element, x and y is natural number, and 1≤x≤16,1≤y≤16.

Step 3, the generation of column index vector

First, define 2 column index subvectors, be designated as respectively here, the row vector of 1 × 64, x is odd number, and y is odd number, and 1≤x≤16,1≤y≤16}, namely , I (15,1) I (1,3) I (3,3) ..., I (15,3),, I (1,15) I (3,15) ..., I (15,15)]=[13 ... 153335 ..., 47 ..., 225227 ..., 239]; the row vector of 1 × 192, be odd number when x with y is different, and 1≤x≤16,1≤y≤16}, namely , I (16,1) I (1,2) I (2,2) ..., I (16,2),, I (2,15) I (4,15),, I (16,15) I (1,16) I (2,16) ..., I (16,16)]=[24,, 161718 ... 32 ..., 226228,, 240241242 ... 256], wherein, I is the index matrix produced in step 2, x represents the horizontal ordinate of index matrix I interior element, and y represents the ordinate of index matrix I interior element, x and y is natural number;

Then, will with form the column index vector of 1 × 256 according to order from left to right, be designated as i (15, 1) I (1, 3) I (3, 3), I (15, 3), I (1, 15) I (3, 15), I (15, 15) I (2, 1) I (4, 1), I (16, 1) I (1, 2) I (2, 2), I (16, 2), I (2, 15) I (4, 15), I (16, 15) I (1, 16) I (2, 16), I (16, 16)]=[13, 153335, 47, 225227, 23924, 161718, 32, 226228, 240241242, 256], here, I is the index matrix produced in step 2.

Step 4, the generation of line index vector

First, define 3 line index subvectors, be designated as respectively here, be a size be the row vector of 1 × 64, namely , I (8,1) I (1,2) I (2,2) ..., I (8,2),, I (1,8) I (2,8) ..., I (8,8)]=[12 ... 81718 ..., 24 ..., 113114 ..., 120]; be a size be the row vector of 1 × 64, namely , I (16,1) I (9,2) I (10,2) ..., I (16,2),, I (9,8) I (10,8) ..., I (16,8)]=[910 ... 162526 ..., 32 ..., 121122 ..., 128]; be a size be the row vector of 1 × 128, namely , I (16,9) I (1,10) I (2,10),, I (16,10) ..., I (1,16) I (2,16) ..., I (16,16)]=[129130,, 144145146 ..., 160 ... 241242 ..., 256], wherein, I is the index matrix produced in step 2, and x represents the horizontal ordinate of index matrix I interior element, and y represents the ordinate of index matrix I interior element, x and y is natural number;

Then, will form according to order from left to right the line index vector that a size is 1 × 256, be designated as =[I (1, 1) I (2, 1), I (8, 1) I (1, 2) I (2, 2), I (8, 2), I (1, 8) I (2, 8), I (8, 8) I (9, 1) I (10, 1), I (16, 1) I (9, 2) I (10, 2), I (16, 2), I (9, 8) I (10, 8), I (16, 8) I (1, 9) I (2, 9), I (16, 9) I (1, 10) I (2, 10), I (16, 10), I (1, 16) I (2, 16), I (16, 16)]=[12, 81718, 24, 113114, 120910, 162526, 32, 121122, 128129130, 144145146, 160, 241242, 256], here, I is the index matrix produced in step 2.

Step 5, the generation of transformation matrix

First, the method for calculating discrete cosine transformation matrix traditionally, producing a size is the discrete cosine transformation matrix of 16 × 16, is designated as C;

Secondly, brought into by discrete cosine transformation matrix C in traditional matrix K ronecker multiplication, producing a size is the transformation matrix of 256 × 256, is designated as D, and here, symbol represent the Kronecker multiplication operator in traditional matrix K ronecker multiplication.

Step 6, the row of adjustment transformation matrix

The column index vector that step 3 is produced each element be designated as here, l represents the index of middle element, l is natural number, 1≤l≤256;

Forming a new size by all column vectors in matrix D is the transformation matrix of 256 × 256, and be designated as E, step is: the 1st time, gets of matrix D individual column vector, the 1st row of generator matrix E; The l time, get of matrix D individual column vector, the l row of generator matrix E; 256th time, get of matrix D individual column vector, the 256th row of generator matrix E,

Namely

Here, e _m,nrepresent the element in matrix E, m represents the horizontal ordinate of index matrix E interior element, and n represents the ordinate of index matrix E interior element, m and n is natural number, 1≤m≤256,1≤n≤256.

Step 7, the row of adjustment transformation matrix

The line index vector that step 4 is produced each element be designated as here, l represents the index of middle element, l is natural number, 1≤l≤256;

All row vectors in the matrix E produced by step 6 form a new transformation matrix, and be designated as F, step is as follows:

1st time, with of matrix E 1st row of individual row vector generator matrix F; The l time, with of matrix E the l of individual row vector generator matrix F is capable; 256th time, with of matrix E 256th row of individual row vector generator matrix F,

Namely

Here, f _p,qrepresent the element in matrix F, p represents the horizontal ordinate of index matrix F interior element, and q represents the ordinate of index matrix F interior element, p and q is natural number, 1≤p≤256,1≤q≤256.

Step 8, is converted into column vector by each image block

First, image block B step 1 produced _iin each row, according to order from left to right, to take out successively, and according to first row, secondary series ..., the 16 row, from top to bottom put order composition a size be the column vector of 256 × 1, be designated as namely here, x _jrepresent column vector in element, j is the subscript index of middle element, j is natural number, 1≤j≤256; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Then, will in element x ₁, x ₃, x ₅, x ₇, x ₉, x ₁₁, x ₁₃, x ₁₅, x ₃₃, x ₃₅, x ₃₇, x ₃₉, x ₄₁, x ₄₃, x ₄₅, x ₄₇, x ₆₅, x ₆₇, x ₆₉, x ₇₁, x ₇₃, x ₇₅, x ₇₇, x ₇₉, x ₉₇, x ₉₉, x ₁₀₁, x ₁₀₃, x ₁₀₅, x ₁₀₇, x ₁₀₉, x ₁₁₁, x ₁₂₉, x ₁₃₁, x ₁₃₃, x ₁₃₅, x1 ₃₇, x ₁₃₉, x ₁₄₁, x ₁₄₃, x ₁₆₁, x ₁₆₃, x ₁₆₅, x ₁₆₇, x ₁₆₉, x ₁₇₁, x ₁₇₃, x ₁₇₅, x ₁₉₃, x ₁₉₅, x ₁₉₇, x ₁₉₉, x ₂₀₁, x ₂₀₃, x ₂₀₅, x ₂₀₇, x ₂₂₅, x ₂₂₇, x ₂₂₉, x ₂₃₁, x ₂₃₃, x ₂₃₅, x ₂₃₇and x ₂₃₉, generating a size is in accordance with the order from top to bottom the column vector of 64 × 1, is designated as that is: here, x _krepresent column vector in element, k is the subscript index of middle element, k is natural number, 1≤k≤256; X' _jrepresent column vector in element, j is the subscript index of middle element, j is natural number, 1≤j≤64; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 9, fills the generation of vector

By the column vector produced in the transformation matrix F produced in step 7 and step 8 substitute into traditional based in the vectorial filling algorithm of discrete cosine transform, obtain the filling column vector that a size is 192 × 1, be designated as that is: here, x " _krepresent column vector in element, k is the subscript index of middle element, k is natural number, 1≤k≤192; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 10, the generation of intermediate vector

By the column vector produced in step 8 with the column vector produced in step 9 forming a size is in accordance with the order from top to bottom the column vector of 256 × 1, is designated as that is:

Namely

Here, y _lrepresent column vector in element, l is the subscript index of middle element, l is natural number, 1≤l≤256; X' _jrepresent the column vector produced in step 8 in element, j is the subscript index of middle element, j is natural number, 1≤j≤64; X " _krepresent the column vector produced in step 9 in element, k is the subscript index of middle element, k is natural number, 1≤k≤192; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 11, the generation of coefficient vector

By traditional one-dimensional discrete cosine transform method to the intermediate vector produced in step 10 carry out discrete cosine transform, obtain coefficient vector namely here, z _jrepresent column vector in element, j is the subscript index of middle element, j is natural number, 1≤j≤256; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 12, the generation of matrix of coefficients

Definition size be 8 × 8 matrix of coefficients be B' _i, use the 1 to 8 element z ₁~ z ₈generate B' in accordance with the order from top to bottom _ithe 1st row; With the 9 to 16 element z ₉~ z ₁₆generate B' in accordance with the order from top to bottom _ithe 2nd row; With the 17 to 24 element z ₁₇~ z ₂₄generate B' in accordance with the order from top to bottom _ithe 3rd row; With the 25 to 32 element z ₂₅~ z ₃₂generate B' in accordance with the order from top to bottom _ithe 4th row; With the 33 to 40 element z ₃₃~ z ₄₀generate B' in accordance with the order from top to bottom _ithe 5th row; With the 41 to 48 element z ₄₁~ z ₄₈generate B' in accordance with the order from top to bottom _ithe 6th row; With the 49 to 56 element z ₄₉~ z ₅₆generate B' in accordance with the order from top to bottom _ithe 7th row; With the 57 to 64 first z ₅₇~ z ₆₄element generates B' in accordance with the order from top to bottom _ithe 8th row;

Namely $B_i^{\′}=\left[\begin{array}{cccc}{\mathrm{\β}}_{1,1}& {\mathrm{\β}}_{1,2}& \mathrm{...}& {\mathrm{\β}}_{1,n}\\ {\mathrm{\β}}_{2,1}& {\mathrm{\β}}_{2,2}& \mathrm{...}& {\mathrm{\β}}_{2,n}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\mathrm{\β}}_{m,1}& {\mathrm{\β}}_{m,2}& \mathrm{...}& {\mathrm{\β}}_{m,n}\end{array}\right]=\left[\begin{array}{cccc}{z}_1& z_9& \mathrm{...}& z_{57}\\ z_2& z_{10}& \mathrm{...}& z_{58}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ z_8& z_{16}& \mathrm{...}& z_{64}\end{array}\right],$

Here, β _m,nb' _iin element, m represent matrix B ' _ithe horizontal ordinate of interior element, n represent matrix B ' _ithe ordinate of interior element, m and n is natural number, 1≤m≤8,1≤n≤8; z ₁, z ₂..., z ₆₄represent the column vector produced in step 11 in 64 elements; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 13, encodes to matrix of coefficients

With the quantization method in traditional jpeg image compression standard to the matrix of coefficients B' produced in step 12 _iquantize, by the matrix of coefficients obtained after quantification, be designated as

Here, be in element, m represents matrix the horizontal ordinate of interior element, n represents matrix the ordinate of interior element, m and n is natural number, 1≤m≤8,1≤n≤8; With the quantification method pair in traditional jpeg image compression standard carry out inverse quantization, obtain the matrix of coefficients B after inverse quantization " _i,

Here, β " _m,nb " _iin element, m represents matrix B " _ithe horizontal ordinate of interior element, n represents matrix B " _ithe ordinate of interior element, m and n is natural number, 1≤m≤8,1≤n≤8; Here, the index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 14, decodes to matrix of coefficients

First, define the full null matrix that a size is 16 × 16, be designated as

${\hat{B}}_i=\left[\begin{array}{cccc}0& 0& \mathrm{...}& 0\\ 0& 0& \mathrm{...}& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ 0& 0& \mathrm{...}& 0\end{array}\right];$

Secondly, the matrix B that step 13 is obtained " _ithe 1st column element take out successively, and put into matrix successively 1 to 8 row of the 1st row; By matrix B " _ithe 2nd column element take out successively, and put into matrix successively 1 to 8 row of the 2nd row; By matrix B " _ithe 3rd column element take out successively, and put into matrix successively 1 to 8 row of the 3rd row; By matrix B " _ithe 4th column element take out successively, and put into matrix successively 1 to 8 row of the 4th row; By matrix B " _ithe 5th column element take out successively, and put into matrix successively 1 to 8 row of the 5th row; By matrix B " _ithe 6th column element take out successively, and put into matrix successively 1 to 8 row of the 6th row; By matrix B " _ithe 7th column element take out successively, and put into matrix successively 1 to 8 row of the 7th row; By matrix B " _ithe 8th column element take out successively, and put into matrix successively 1 to 8 row of the 8th row; By amended matrix be designated as

Here, be in element, p represents matrix the horizontal ordinate of interior element, q represents matrix the ordinate of interior element, p and q is natural number, 1≤p≤16,1≤q≤16; β " _m,nb " _iin element, m represents matrix B " _ithe horizontal ordinate of interior element, n represents matrix B " _ithe ordinate of interior element, m and n is natural number, 1≤m≤8,1≤n≤8; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Finally, with traditional 2-D discrete cosine inverse transform method to matrix carry out 2-D discrete cosine inverse transformation, obtain the picture element matrix that size is 16 × 16, be designated as b _i:

Here, α _m,nb _iin element, m represents matrix b _ithe horizontal ordinate of interior element, n represents matrix b _ithe ordinate of interior element, m and n is natural number, 1≤m≤16,1≤n≤16; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 15, the correction of decoded image blocks

To the picture element matrix b produced in step 14 _i, carry out interpolation by traditional bicubic interpolation method to the pixel be positioned on (u, v) position, here, u is b _ithe horizontal ordinate of interior pixel, v is b _ithe ordinate of interior pixel, u and v is natural number, and is odd number when u with v is different, 1≤u≤16,1≤v≤16; Interpolation image block matrix will be obtained, be designated as b ' _i:

Here, α ' _m,nb ' _iin element, m represents matrix b ' _ithe horizontal ordinate of interior element, n represents matrix b ' _ithe ordinate of interior element, m and n is natural number, 1≤m≤16,1≤n≤16; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 16, the spatial domain down-sampling of image block

First, define a size be the full null graph of 8 × 8 as block matrix, be designated as

Here, the index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Then, the matrix b ' step 15 obtained _iin the element of the upper all odd-numbered lines of the 1st row take out one by one, put into successively the 1st row; By b ' _iin the element of the upper all odd-numbered lines of the 3rd row take out one by one, put into successively the 2nd row; By b ' _iin the element of the upper all odd-numbered lines of the 5th row take out one by one, put into successively the 3rd row; By b ' _iin the element of the upper all odd-numbered lines of the 7th row take out one by one, put into successively the 4th row; By b ' _iin the element of the upper all odd-numbered lines of the 9th row take out one by one, put into successively the 5th row; By b ' _iin the element of the upper all odd-numbered lines of the 11st row take out one by one, put into successively the 6th row; By b ' _iin the element of the upper all odd-numbered lines of the 13rd row take out one by one, put into successively the 7th row; By b ' _iin the element of the upper all odd-numbered lines of the 15th row take out one by one, put into successively the 7th row; Obtain image block

${\hat{b}}_i^{\′}=\left[\begin{array}{cccc}{\mathrm{\α}}_{1,1}^{\′}& {\mathrm{\α}}_{1,3}^{\′}& \mathrm{...}& {\mathrm{\α}}_{1,15}^{\′}\\ {\mathrm{\α}}_{3,1}^{\′}& {\mathrm{\α}}_{3,3}^{\′}& \mathrm{...}& {\mathrm{\α}}_{3,15}^{\′}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\mathrm{\α}}_{15,1}^{\′}& {\mathrm{\α}}_{15,3}^{\′}& \mathrm{...}& {\mathrm{\α}}_{15,15}^{\′}\end{array}\right];$

Here, α ' _m,nb ' _iin element, m represents matrix b ' _ithe horizontal ordinate of interior element, n represents matrix b ' _ithe ordinate of interior element, m and n is odd number, and 1≤m≤16,1≤n≤16; The index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block;

Step 17, builds high-definition picture

For the interpolation image block matrix b ' produced in step 15 _i, adopt the method for image block composograph in traditional jpeg image compression standard, producing size is the image of W × H, is designated as here, W represents the width of input picture in step 1, and H represents the height of input picture in step 1, the index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block.

Step 18, builds low-resolution image

With the image block produced in step 16 the method of image block composograph in jpeg image compression standard traditionally, produces the image that size is (W/2) × (H/2), is designated as here, W represents the width of input picture in step 1, and H represents the height of input picture in step 1, the index of i representative image block, i ∈ 1,2 ..., N}, N represent total number that image in step 1 divides rear image block.

Embodiment being applied to Lena and Barbara two width resolution is in the classical legend of 512 × 512, accompanying drawing 2 is under different encoder bit rates, different images is applied to the Y-PSNR (peaksignaltonoiseratio, PSNR) obtained after different method for compressing image carries out Code And Decode.Clearly, the method in the present invention has obvious performance boost than existing methods.

Claims (1)

1., based on a low-resolution image compression method for transform domain down-sampling technology, it is characterized in that it comprises the following steps:

Step 1; The pre-service of image

Be the image of W × H by size, in jpeg image compression standard traditionally, the method for image block is divided into N=(W × H)/16 ²individual non-overlapping copies; Size is the square image blocks of 16 × 16; Be designated as B ₁; B ₂; B _i; B _n; Here; The width of W representative image; The height of H representative image; Total number of image block after N representative image divides; The index of i representative image block; I ∈ { 1; 2; N};

Step 2; The generation of index matrix

256 natural numbers 1; 2; 256 press from small to large; Order is from top to bottom put by column; Producing a size is the index matrix of 16 × 16; Be designated as I:

Element in I is designated as I (x, y); Here; X represents the horizontal ordinate of index matrix I interior element; Y represents the ordinate of index matrix I interior element; X and y is natural number; And 1≤x≤16; 1≤y≤16;

Step 3; The generation of column index vector

First; Define 2 column index subvectors; Be designated as respectively here; it is the row vector of 1 × 64; for odd number; Y is odd number; And 1≤x≤16,1≤y≤16}; Namely it is the row vector of 1 × 192; it is odd number time different with y; And 1≤x≤16,1≤y≤16}; Namely wherein, I is the index matrix produced in step 2; X represents the horizontal ordinate of index matrix I interior element; Y represents the ordinate of index matrix I interior element; X and y is natural number;

Then; Will with the column index vector of one 1 × 256 is formed according to order from left to right; Be designated as here; I is the index matrix produced in step 2;

Step 4; The generation of line index vector

First; Define 3 line index subvectors; Be designated as respectively here; be a size be the row vector of 1 × 64; namely be a size be the row vector of 1 × 64; namely be a size be the row vector of 1 × 128; namely wherein, I is the index matrix produced in step 2; X represents the horizontal ordinate of index matrix I interior element; Y represents the ordinate of index matrix I interior element; X and y is natural number;

Then; Will the line index vector that a size is 1 × 256 is formed according to order from left to right; Be designated as here; I is the index matrix produced in step 2;

Step 5; The generation of transformation matrix

First; The method of calculating discrete cosine transformation matrix traditionally; Producing a size is the discrete cosine transformation matrix of 16 × 16; Be designated as C;

Secondly; Discrete cosine transformation matrix C is brought in traditional matrix K ronecker multiplication; Producing a size is the transformation matrix of 256 × 256; Be designated as D; And here; Symbol represent the Kronecker multiplication operator in traditional matrix K ronecker multiplication;

Step 6; The row of adjustment transformation matrix

The column index vector that step 3 is produced each element be designated as here; L represents the index of middle element, l is natural number; 1≤l≤256;

Forming a new size by all column vectors in matrix D is the transformation matrix of 256 × 256; Be designated as E; Step is: the 1st time; Get of matrix D individual column vector; 1st row of generator matrix E; The l time; Get of matrix D individual column vector, the l row of generator matrix E; 256th time; Get of matrix D individual column vector; 256th row of generator matrix E;

Namely

Here; e _m,nrepresent the element in matrix E; M represents the horizontal ordinate of index matrix E interior element; N represents the ordinate of index matrix E interior element; M and n is natural number; 1≤m≤256,1≤n≤256;

Step 7; The row of adjustment transformation matrix

The line index vector that step 4 is produced each element be designated as here; L represents the index of middle element, l is natural number; 1≤l≤256;

All row vectors in the matrix E produced by step 6 form a new transformation matrix; Be designated as F; Step is as follows:

1st time; With of matrix E 1st row of individual row vector generator matrix F; The l time; With of matrix E the l of individual row vector generator matrix F is capable; 256th time; With of matrix E 256th row of individual row vector generator matrix F,

Namely

Here; f _p,qrepresent the element in matrix F; P represents the horizontal ordinate of index matrix F interior element; Q represents the ordinate of index matrix F interior element; P and q is natural number; 1≤p≤256,1≤q≤256;

Step 8; Each image block is converted into column vector

First; The image block B that step 1 is produced _iin each row; According to order from left to right; Take out successively; And according to first row; Secondary series; 16 row; From top to bottom put order composition a size be the column vector of 256 × 1; Be designated as namely here; x _jrepresent column vector in element; J is the subscript index of middle element; J is natural number; 1≤j≤256; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Then; Will in element x ₁, x ₃, x ₅, x ₇, x ₉, x ₁₁, x ₁₃, x ₁₅, x ₃₃, x ₃₅, x ₃₇, x ₃₉, x ₄₁, x ₄₃, x ₄₅, x ₄₇, x ₆₅, x ₆₇, x ₆₉, x ₇₁, x ₇₃, x ₇₅, x ₇₇, x ₇₉, x ₉₇, x ₉₉, x ₁₀₁, x ₁₀₃, x ₁₀₅, x ₁₀₇, x ₁₀₉, x ₁₁₁, x ₁₂₉, x ₁₃₁, x ₁₃₃, x ₁₃₅, x1 ₃₇, x ₁₃₉, x ₁₄₁, x ₁₄₃, x ₁₆₁, x ₁₆₃, x ₁₆₅, x ₁₆₇, x ₁₆₉, x ₁₇₁, x ₁₇₃, x ₁₇₅, x ₁₉₃, x ₁₉₅, x ₁₉₇, x ₁₉₉, x ₂₀₁, x ₂₀₃, x ₂₀₅, x ₂₀₇, x ₂₂₅, x ₂₂₇, x ₂₂₉, x ₂₃₁, x ₂₃₃, x ₂₃₅, x ₂₃₇and x ₂₃₉; Generating a size is in accordance with the order from top to bottom the column vector of 64 × 1; Be designated as that is: here; x _krepresent column vector in element; K is the subscript index of middle element; K is natural number; 1≤k≤256; X' _jrepresent column vector in element; J is the subscript index of middle element; J is natural number; 1≤j≤64; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 9; Fill the generation of vector

By the column vector produced in the transformation matrix F produced in step 7 and step 8 substitute into traditional based in the vectorial filling algorithm of discrete cosine transform; Obtain the filling column vector that a size is 192 × 1; Be designated as that is: here; X " _krepresent column vector in element; K is the subscript index of middle element; K is natural number; 1≤k≤192; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 10; The generation of intermediate vector

By the column vector produced in step 8 with the column vector produced in step 9 forming a size is in accordance with the order from top to bottom the column vector of 256 × 1; Be designated as that is:

Namely

Here; y _lrepresent column vector in element; L is the subscript index of middle element; L is natural number; 1≤l≤256; X' _jrepresent the column vector produced in step 8 in element; J is the subscript index of middle element; J is natural number; 1≤j≤64; X " _krepresent the column vector produced in step 9 in element; K is the subscript index of middle element; K is natural number; 1≤k≤192; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 11; The generation of coefficient vector

By traditional one-dimensional discrete cosine transform method to the intermediate vector produced in step 10 carry out discrete cosine transform; Obtain coefficient vector namely here; z _jrepresent column vector in element; J is the subscript index of middle element; J is natural number; 1≤j≤256; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block; Symbol T represents traditional matrix transpose operation;

Step 12; The generation of matrix of coefficients

Definition size be 8 × 8 matrix of coefficients be B' _i; With the 1 to 8 element z ₁~ z ₈generate B' in accordance with the order from top to bottom _ithe 1st row; With the 9 to 16 element z ₉~ z ₁₆generate B' in accordance with the order from top to bottom _ithe 2nd row; With the 17 to 24 element z ₁₇~ z ₂₄generate B' in accordance with the order from top to bottom _ithe 3rd row; With the 25 to 32 element z ₂₅~ z ₃₂generate B' in accordance with the order from top to bottom _ithe 4th row; With the 33 to 40 element z ₃₃~ z ₄₀generate B' in accordance with the order from top to bottom _ithe 5th row; With the 41 to 48 element z ₄₁~ z ₄₈generate B' in accordance with the order from top to bottom _ithe 6th row; With the 49 to 56 element z ₄₉~ z ₅₆generate B' in accordance with the order from top to bottom _ithe 7th row; With the 57 to 64 first z ₅₇~ z ₆₄element generates B' in accordance with the order from top to bottom _ithe 8th row;

Namely $B_i^{\′}=\left[\begin{array}{cccc}{\mathrm{\β}}_{1,1}& {\mathrm{\β}}_{1,2}& ...& {\mathrm{\β}}_{1,n}\\ {\mathrm{\β}}_{2,1}& {\mathrm{\β}}_{2,2}& ...& {\mathrm{\β}}_{2,n}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\mathrm{\β}}_{m,1}& {\mathrm{\β}}_{m,2}& ...& {\mathrm{\β}}_{m,n}\end{array}\right]=\left[\begin{array}{cccc}{z}_1& z_9& ...& z_{57}\\ z_2& z_{10}& ...& z_{58}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ z_8& z_{16}& ...& z_{64}\end{array}\right];$

Here; β _m,nb' _iin element; M represent matrix B ' _ithe horizontal ordinate of interior element; N represent matrix B ' _ithe ordinate of interior element; M and n is natural number; 1≤m≤8; 1≤n≤8; z ₁; z ₂; z ₆₄represent the column vector produced in step 11 in 64 elements; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block;

Step 13; Matrix of coefficients is encoded

With the quantization method in traditional jpeg image compression standard to the matrix of coefficients B' produced in step 12 _iquantize; By the matrix of coefficients obtained after quantification; Be designated as

Here; be in element; M represents matrix the horizontal ordinate of interior element; N represents matrix the ordinate of interior element; M and n is natural number; 1≤m≤8; 1≤n≤8;

With the quantification method pair in traditional jpeg image compression standard carry out inverse quantization; Obtain the matrix of coefficients B after inverse quantization " _i;

Here; β " _m,nb " _iin element; M represents matrix B " _ithe horizontal ordinate of interior element; N represents matrix B " _ithe ordinate of interior element; M and n is natural number; 1≤m≤8; 1≤n≤8; Here; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block;

Step 14; Matrix of coefficients is decoded

First; Define the full null matrix that a size is 16 × 16; Be designated as

${\hat{B}}_i=\left[\begin{array}{cccc}0& 0& ...& 0\\ 0& 0& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ 0& 0& ...& 0\end{array}\right];$

Secondly; The matrix B that step 13 is obtained " _ithe 1st column element take out successively; And put into matrix successively 1 to 8 row of the 1st row; By matrix B " _ithe 2nd column element take out successively; And put into matrix successively 1 to 8 row of the 2nd row; By matrix B " _ithe 3rd column element take out successively; And put into matrix successively 1 to 8 row of the 3rd row; By matrix B " _ithe 4th column element take out successively; And put into matrix successively 1 to 8 row of the 4th row; By matrix B " _ithe 5th column element take out successively; And put into matrix successively 1 to 8 row of the 5th row; By matrix B " _ithe 6th column element take out successively; And put into matrix successively 1 to 8 row of the 6th row; By matrix B " _ithe 7th column element take out successively; And put into matrix successively 1 to 8 row of the 7th row; By matrix B " _ithe 8th column element take out successively; And put into matrix successively 1 to 8 row of the 8th row; By amended matrix be designated as

Here; be in element; P represents matrix the horizontal ordinate of interior element; Q represents matrix the ordinate of interior element; P and q is natural number; 1≤p≤16; 1≤q≤16; β " _m,nb " _iin element; M represents matrix B " _ithe horizontal ordinate of interior element; N represents matrix B " _ithe ordinate of interior element; M and n is natural number; 1≤m≤8; 1≤n≤8; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block;

Finally; With traditional 2-D discrete cosine inverse transform method to matrix carry out 2-D discrete cosine inverse transformation; Obtain the picture element matrix that size is 16 × 16; Be designated as b _i:

Here; α _m,nb _iin element; M represents matrix b _ithe horizontal ordinate of interior element; N represents matrix b _ithe ordinate of interior element; M and n is natural number; 1≤m≤16; 1≤n≤16; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block;

Step 15; The correction of decoded image blocks

To the picture element matrix b produced in step 14 _i; By traditional bicubic interpolation method, interpolation is carried out to the pixel be positioned on (u, v) position; Here; U is b _ithe horizontal ordinate of interior pixel; V is b _ithe ordinate of interior pixel; U and v is natural number; And be odd number when u with v is different; 1≤u≤16,1≤v≤16; Interpolation image block matrix will be obtained; Be designated as b ' _i:

Here; α ' _m,nb ' _iin element; M represents matrix b ' _ithe horizontal ordinate of interior element; N represents matrix b ' _ithe ordinate of interior element; M and n is natural number; 1≤m≤16; 1≤n≤16; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block;

Step 16; The spatial domain down-sampling of image block

First; Defining a size is that the full null graph of 8 × 8 is as block matrix; Be designated as

Here; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block;

Then; The matrix b ' that step 15 is obtained _iin the element of the upper all odd-numbered lines of the 1st row take out one by one; Put into successively the 1st row; By b ' _iin the element of the upper all odd-numbered lines of the 3rd row take out one by one; Put into successively the 2nd row; By b ' _iin the element of the upper all odd-numbered lines of the 5th row take out one by one; Put into successively the 3rd row; By b ' _iin the element of the upper all odd-numbered lines of the 7th row take out one by one; Put into successively the 4th row; By b ' _iin the element of the upper all odd-numbered lines of the 9th row take out one by one; Put into successively the 5th row; By b ' _iin the element of the upper all odd-numbered lines of the 11st row take out one by one; Put into successively the 6th row; By b ' _iin the element of the upper all odd-numbered lines of the 13rd row take out one by one; Put into successively the 7th row; By b ' _iin the element of the upper all odd-numbered lines of the 15th row take out one by one; Put into successively the 7th row; Obtain image block

${\hat{b}}_i^{\′}=\left[\begin{array}{cccc}{\mathrm{\α}}_{1,1}^{\′}& {\mathrm{\α}}_{1,3}^{\′}& ...& {\mathrm{\α}}_{1,15}^{\′}\\ {\mathrm{\α}}_{3,1}^{\′}& {\mathrm{\α}}_{3,3}^{\′}& ...& {\mathrm{\α}}_{3,15}^{\′}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\mathrm{\α}}_{15,1}^{\′}& {\mathrm{\α}}_{15,3}^{\′}& ...& {\mathrm{\α}}_{15,15}^{\′}\end{array}\right];$

Here; α ' _m,nb ' _iin element; M represents matrix b ' _ithe horizontal ordinate of interior element; N represents matrix b ' _ithe ordinate of interior element; M and n is odd number; And 1≤m≤16; 1≤n≤16; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block;

Step 17; Build high-definition picture

For the interpolation image block matrix b ' produced in step 15 _i; Adopt the method for image block composograph in traditional jpeg image compression standard; Producing size is the image of W × H; Be designated as here; W represents the width of input picture in step 1; H represents the height of input picture in step 1; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block;

Step 18; Build low-resolution image

With the image block produced in step 16 the method of image block composograph in jpeg image compression standard traditionally; Produce the image that size is (W/2) × (H/2); Be designated as here; W represents the width of input picture in step 1; H represents the height of input picture in step 1; The index of i representative image block; I ∈ { 1; 2; N}; N represents total number that image in step 1 divides rear image block.