CN108632610A - A kind of colour image compression method based on interpolation reconstruction - Google Patents

A kind of colour image compression method based on interpolation reconstruction Download PDF

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CN108632610A
CN108632610A CN201810349273.5A CN201810349273A CN108632610A CN 108632610 A CN108632610 A CN 108632610A CN 201810349273 A CN201810349273 A CN 201810349273A CN 108632610 A CN108632610 A CN 108632610A
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朱树元
何志应
王岩
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University of Electronic Science and Technology of China
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    • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
    • H04N19/129—Scanning of coding units, e.g. zig-zag scan of transform coefficients or flexible macroblock ordering [FMO]
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    • H04N19/12—Selection from among a plurality of transforms or standards, e.g. selection between discrete cosine transform [DCT] and sub-band transform or selection between H.263 and H.264
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Abstract

The invention belongs to Image Compression fields, provide a kind of colour image compression method based on interpolation reconstruction, to overcome the problems, such as the down-sampling interpolation reconstruction distortion of chromatic component in conventional color image compression coding technology it is apparent this.Compression method of the present invention utilizes the sef-adapting filter compressed based on interpolation proposed to be filtered chromatic component, while substantially saving code check, more prior informations are provided for the interpolation reconstruction of decoding end chromatic component, interpolation quality is high, and the RGB color image color fidelity finally synthesized is high；At the same time, the present invention has been effectively saved encoder bit rate, and then improves the code efficiency of coloured image entirety.

Description

A kind of colour image compression method based on interpolation reconstruction
Technical field
The invention belongs to Image Compression fields, and in particular to a kind of color image compression side based on interpolation reconstruction Method.
Background technology
Important carrier of the coloured image as multimedia messages has many advantages, such as intuitive and easy to understand, vivid, meets The mankind are remembered as a kind of means of high-efficiency information communication for the cognitive style of information.In the present of information industry rapid development It, Color Image Processing and transmission technology by feat of the characteristics of capable of storing and transmitting the image of high quality with lower data volume, Have become the key technology of network information transmission.
Since color image data itself has the characteristics that data volume is big, in order to promote code efficiency, color image compression The method of coding is typically that original image is transformed into the spaces YUY from rgb space, according to different application scenarios and practical need It asks, compressed encoding is carried out by different sample formats.Since human eye is more sensitive to the luminance information Y of coloured image, and coloration Information Cb, Cr is insensitive, therefore in the compressed encoding to coloured image, typically carries out down-sampling coding to chromatic component, To achieve the purpose that save code check, common sample format has YCbCr 4:2:0、YCbCr 4:2:2、YCbCr 4:1:1, such as text It offers：“BT.601-7:Studio encoding parameters of digital television for standard 4: 3and wide scre en 16:9aspect ratios, 2011 ".
However, traditional colour image compression method based on chrominance space down-sampling is by simply inserting in decoding end Value-based algorithm rebuilds chromatic component, and interpolation algorithm is often limited to all many conditions such as prior information deficiency, is unable to get more high-quality The interpolation image of amount；Therefore, although traditional colour image compression method has higher compression ratio, compressed RGB figures As being commonly present color distortion, especially for coloury high fidelity visual, there are apparent quality degradations for compression image.
Invention content
It is an object of the invention to provide a kind of novel coloured image based on interpolation reconstruction in view of the above technical problems Compression method, to overcome the down-sampling interpolation reconstruction of chromatic component in conventional color image compression coding technology be distorted it is apparent this One problem, the compression method utilize the sef-adapting filter compressed based on interpolation proposed to be filtered place to chromatic component Reason provides more prior informations while substantially saving code check for the interpolation reconstruction of decoding end chromatic component, whole to make The compression coding efficiency for opening coloured image improves；Compared with traditional color image compression coding, the present invention is to chromatic component The quality higher of interpolation reconstruction, code check are lower, and the code efficiency of coloured image entirety is obviously improved.
To achieve the above object, the technical solution adopted by the present invention is：
In order to facilitate description present disclosure, following term definition is done first：
Define 1：RGB and the YCbCr color space changover method of standard
The conversion formula of RGB-YCbCr is：
Y=0.257*R+0.504*G+0.098*B+16
Cb=-0.148*R-0.291*G+0.439*B+128
Cr=0.439*R-0.368*G-0.071*B+128
YCbCr-RGB conversion formulas：
R=1.164* (Y-16)+1.596* (Cr-128)
G=1.164* (Y-16) -0.813* (Cr-128) -0.392* (Cb-128)
B=1.164* (Y-16)+2.017* (Cb-128)；
Define 2：Two-dimension discrete cosine transform
According to discrete cosine transformation matrix, image block is transformed into transform domain from pixel domain, obtains transform coefficient matrix；
Define 3：Bicubic interpolation methods
The pixel (x, y) that interpolation is needed to each takes 4 × 4 neighborhood point (x near iti,yj) (i, j=0,1,2, 3) interpolation calculation, is carried out as follows：
W is interpolation coefficient matrix, and f (x, y) is the pixel value of pixel (x, y)；
Define 4：Traditional Kronecker multiplication
Traditional Kronecker multiplication is expressed asWherein,Indicating Kronecker multiplication operators, A is Size is the matrix of m × n, and：
B is the matrix that size is p × q, and C is the matrix that size is mp × nq,
Define 5：l1Norm constraint
l1Norm refers to the sum of each element absolute value, also referred to as Lasso regularization in vector；If using l1Model As soon as number carrys out regularization parameter vector X, the most elements for being desirable to X are all 0, that is, parameter X is allowed to be sparse；
Define 6：Iteratively faster threshold value convergence algorithm
Iteratively faster threshold value contraction algorithm (A fast iterative shrinkage-thresholding Algorithm) it is a kind of l declining thought based on gradient1Norm optimization method, compared with traditional gradient descent method, iteration The selection of correcting mode is more reasonable in the process, and convergence rate is faster；
Define 7：Soft Thresholding for Signal operates
Soft Thresholding for Signal operation is that iteratively faster threshold value contraction algorithm declines the most important improvement of thought for gradient, can be effective Choose more suitable next iteration sequence in ground so that entire iterative algorithm is rapidly restrained；
Define 8：The Zig-Zag scanning sequencies of image encoding transform coefficients
The scanning sequency of one 8 × 8 transform coefficient matrix is as follows：
The size of numerical value represents the sequencing of Zig-Zag scannings in matrix.
A kind of colour image compression method based on interpolation reconstruction provided by the invention, which is characterized in that including following step Suddenly：
Step 1, color space is converted：
Using RGB-YCbCr image color space conversion methods, the coloured image of input is converted to from rgb space YCbCr images obtain luminance component image Y and chromatic component Cb, Cr；
Step 2, two-dimension discrete cosine transform (dct transform) is carried out to luminance component Y：
Luminance component Y is divided into N=(W × H)/82A non-overlapping copies, the square image blocks that size is 8 × 8, to each Image block carries out 2-D discrete cosine variation, obtains the transform coefficient matrix of N number of luminance component Y；Wherein, W indicates the width of image Degree, H indicate the height of image；
Step 3, chromatic component Cb, Cr are filtered respectively using the sef-adapting filter compressed based on interpolation：
Chromatic component Cb, Cr are divided into M=(W × H)/162A non-overlapping copies, the square-shaped image that size is 16 × 16 Block；For one 16 × 16 image block, corresponding 64 pixels of odd-numbered line odd column, referred to as retention point are chosen, and will Its coordinate record is denoted as Ω；Then, image block is arranged by row and is converted to vector x, corresponding retention point x in xΩIt indicates；
Interpolating matrix is set as H (interpolating matrix is determined by bicubic interpolation methods), then the vector of interpolation reconstructionTable It is shown as：
In order to make the vector of reconstructionIt is as identical with original image vector x as possible, two Norm minimums of its difference are enabled, are obtained Retain point set after optimization
It is one 256 obtained by traditional Kronecker multiplication by two 16 × 16 dct transform Matrix Cs to set T × 256 transformation matrix：Wherein, symbolIndicate traditional Kronecker operators；Choose the inverse matrix T of T-1In 64 respective coordinates Ω row, form the matrix Λ that new dimension is 64 × 256, then xΩ=Λ X, X indicate coefficient to Amount, accordingly converts formula (2) to：
In order to make coefficient vector X rarefactions, l is added to formula (3)1Norm constraint is to get to target equation：
Wherein, | | | |2Indicate two norms, | | | |1Indicate a norm；
Above-mentioned target equation optimal solution is solved by iteratively faster threshold value convergence algorithmIt is reduced into 16 × 16 change Change coefficient matrix；Since the coefficient pressure in iterative process by transform coefficient matrix in addition to the position Π of 8 × 8 pieces of the upper left corner is set to 0, Therefore down-sampling is done to transform coefficient matrix, only retains the transform coefficient matrix of 8 × 8 size of the upper left corner, be used for subsequent compression Coding；
To each 16 × 16 image block of Cb, Cr component carry out it is above-mentioned be filtered, obtain M Cb, Cr component Transform coefficient matrix；
Further, above-mentioned target equation optimal solutionCalculating process it is as follows：
A) it initializes：
If X(0)=X(1)=T-1X, X(0)Indicate initial value, the X of coefficient vector X(1)Indicate the first time iteration of coefficient vector X Value；Default intermediate variable t0=t1=1, t0Indicate initial value, the t of intermediate variable t1Indicate the first time iteration of intermediate variable t Value；
B) iteration successively is carried out according to following iterative formula：
Assuming that X(i+1)In corresponding one 16 × 16 transformation coefficient square, 8 × 8 pieces of the upper left corner Coordinate set be Π；If coefficient vector X(i+1)Position coordinates be not belonging to Π, then force set to 0；
Wherein, i indicates that iterations, λ, L are predetermined constant, and soft () indicates Soft Thresholding for Signal operation；
C) work as iteration errorReach default maximum iteration less than pre-determined threshold or iterations, Then stop iteration, exports optimal coefficient vector
Step 4, the transform coefficient matrix compressed encoding of component Y, Cb, Cr are obtained into encoding code stream：
Quantification treatment is carried out to each transform coefficient matrix of component Y, component Cb, component Cr respectively, is encoded using image The Zig-Zag scanning sequencies of transformation coefficient are ranked up, and carry out entropy coding later, obtain compressed encoding code stream；
Step 5, encoding code stream is decoded, obtains Y, Cb, Cr picture content：
Encoding code stream is decoded to obtain N number of component Y quantized transform coefficient matrixes, M component Cb, Cr quantization transform coefficient square Battle array；
Inverse quantization, inverse transformation processing are carried out to each component Y quantized transform coefficient matrixes, obtain decoded N number of Y-component Image block, and it is spliced into Y-component image；
To each component Cb, Cr quantized transform coefficient matrix, coefficient 0 is first used to be filled with the quantization transform of 16 × 16 sizes Coefficient matrix, then inverse quantization, inverse transformation processing are carried out, decoded M Cb, Cr component image block is obtained, and be spliced into Cb, Cr Component image；
Step 6, interpolation reconstruction Cb, Cr component images：
Using the retention point chosen in advance based on the sef-adapting filter that interpolation is compressed to Cb, Cr component image into row interpolation It rebuilds, obtains high quality Cb, Cr component image；
Step 7, color space converts：
Finally obtained Y, Cb, Cr component image is converted into RGB by YCbCr-RGB image color space conversion methods Image completes color image compression.
From operation principle, the present invention proposes a kind of sef-adapting filter based on interpolation compressed encoding, to coloration point Amount is filtered so that chromatic component has more prior informations, the coloration of interpolation reconstruction in decoding end interpolation reconstruction Component and original chrominance components error are smaller, and the RGB color image color fidelity finally synthesized is high；At the same time, the filtering Device is effectively reducing the quantity for the transformation coefficient for needing to encode, and makes transformation coefficient rarefaction, has been effectively saved coding Code check, and then improve the code efficiency of entire coloured image.
The beneficial effects of the present invention are：
The present invention provides a kind of colour image compression method based on interpolation reconstruction, for tradition based on JPEG's YCbCr4:2:The color image compression technological color problem of dtmf distortion DTMF of 0 format, the adaptive-filtering of the interpolation compression based on the present invention Device is filtered chromatic component, and more prior informations, interpolation matter are utilized during chromatic component interpolation reconstruction Amount is high, and the RGB color image color fidelity finally synthesized is high；At the same time, the present invention has been effectively saved encoder bit rate, into And improve the code efficiency of coloured image entirety.
Description of the drawings
Fig. 1 is that the present invention is based on the flow diagrams of the colour image compression method of interpolation reconstruction.
Fig. 2 uses coloured image by emulation in the embodiment of the present invention：(a)Airplane；(b)Peppers.
Specific implementation mode
The present invention is described in further details with reference to the accompanying drawings and examples.
A kind of colour image compression method based on interpolation reconstruction is provided in the present embodiment, as shown in Figure 1；The present embodiment is adopted The feasibility of the present invention is verified with the mode of emulation experiment, all steps all pass through experimental verification；Image used in experiment It is natural number that width, which is W=16 × m, is highly H=16 × n, m and n；
The above-mentioned colour image compression method based on interpolation reconstruction, specific implementation step are as follows：
Step 1, color space is converted
Using the RGB-YCbCr image color space conversion methods of standard, the coloured image of input is converted from rgb space For YCbCr images, luminance component image Y and chromatic component Cb, Cr are obtained；
Step 2, two-dimension discrete cosine transform (dct transform) is carried out to luminance component Y
Luminance component Y is divided into N=(W × H)/82A non-overlapping copies, the square image blocks that size is 8 × 8 carry out two Long-lost cosine code is tieed up, the transform coefficient matrix of luminance component Y is obtained；Here, the width of W representative images, the height of H representative images Degree；
Step 3, chromatic component Cb, Cr are filtered using the sef-adapting filter compressed based on interpolation
Chromatic component Cb, Cr are divided into M=(W × H)/162A non-overlapping copies, the square-shaped image that size is 16 × 16 Block chooses corresponding 64 pixels of odd-numbered line odd column, referred to as retention point, and will for one 16 × 16 image block Its coordinate record gets off, and is denoted as Ω；Later, image block is arranged by row and is converted to vector x, corresponding retention point x in xΩTable Show；Assuming that interpolating matrix is H (interpolating matrix is determined by bicubic interpolation methods), then the vector of interpolation reconstructionIt can indicate For：
In order to make the vector of reconstructionAs identical with original image vector x as possible, we enable two Norm minimums of its difference, It obtains：
Assuming that T is one 256 obtained by traditional Kronecker multiplication by two 16 × 16 dct transform Matrix Cs × 256 transformation matrix, i.e.,:Here symbolRepresent traditional Kronecker operators.Choose the inverse square of T Battle array T-1In 64 respective coordinates Ω row, form the matrix Λ that new dimension is 64 × 256, then xΩ=Λ X, accordingly can will be public Formula (2) is converted into：
In order to make coefficient vector X rarefactions, l is added to formula (3)1Norm constraint obtains：
The target equation can seek optimal solution by improved iteratively faster threshold value convergence algorithm.Specific algorithm steps are as follows institute Show：
A) it initializes：
If X(0)=X(1)=T-1X, and t0=t1=1.
B) iteration：
1)
2)
3)Soft represents Soft Thresholding for Signal operation；
4)
5) assume X(i+1)In corresponding one 16 × 16 transformation coefficient square, the coordinate that 8 × 8 pieces of the upper left corner is Π.If Coefficient Xk (i+1)Position coordinates k be not belonging to Π, then force be set to 0；
6) i=i+1；
7) work as iteration errorReach preset maximum iteration less than thresholding or iterations, then Stop iteration, obtains final X；If being unsatisfactory for condition, step 1) is returned to.
C) coefficient vector after output optimization
For the coefficient vector after the optimization of outputIt is reduced into 16 × 16 transform coefficient matrix.Due to iteration The coefficient pressure by transform coefficient matrix in addition to the position Π of 8 × 8 pieces of the upper left corner is set to 0 in the process, therefore by transform coefficient matrix Down-sampling is done, the transform coefficient matrix of 8 × 8 size of the upper left corner is only retained, is used for subsequent compressed encoding；
To each 16 × 16 image block of Cb, Cr component carry out it is above-mentioned be filtered, obtain the transformation of Cb, Cr component Coefficient matrix.
Step 4, the transform coefficient matrix compressed encoding of Y, Cb, Cr are obtained into encoding code stream
The transform coefficient matrix of Y-component, Cb components, Cr components is subjected to quantification treatment, using image encoding transform coefficients Zig-Zag scanning sequencies be ranked up, carry out entropy coding later, obtain compressed encoding code stream；
Step 5, encoding code stream is decoded, obtains Y, Cb, Cr picture content
Quantization parameter in encoding code stream is placed on transformation according to the Zig-Zag scanning sequencies of image encoding transform coefficients In coefficient matrix, the quantized transform coefficient matrix of Y, Cb, Cr component is obtained；
The processing such as inverse quantization, inverse transformation are carried out to the quantized transform coefficient matrix of Y-component, obtain decoded Y component map Picture；
To the quantized transform coefficient matrix of Cb, Cr component, it is first filled with to the transformation coefficient of 16 × 16 sizes with coefficient 0 Matrix, then the processing such as inverse quantization, inverse transformation are carried out, obtain decoded Cb, Cr component image；
Step 6, interpolation reconstruction Cb, Cr components
Using the sef-adapting filter retention point chosen in advance of filter compressed based on interpolation to Cb, Cr component into row interpolation weight It builds, obtains higher Cb, Cr component of quality；Specific method is：Cb, Cr component are divided into the image block that size is 16 × 16, and It is converted into vectorThe retention point chosen in filtering is extracted, vector is obtainedThe then interpolation mistake of Cb, Cr component Journey is expressed as：
It willIt is reduced into matrix, you can Cb, Cr the component image block rebuild, and image block is formed into Cb, Cr image Component；
Step 7, color space converts
Finally obtained Y, Cb, Cr component is converted into RGB figures by YCbCr-RGB image color space conversion methods Picture completes color image compression.
In the classical legend for being 512 × 512 applied to Airplane and two width resolution ratio of Peppers by embodiment, such as Fig. 2 It is shown；Under different encoder bit rates, after being coded and decoded using different colour image compression methods to different images Obtained Y-PSNR (peak signal to noise ratio, PSNR) is as shown in the table；It is obvious that the method for the present invention The coloured image of compression has higher code efficiency and quality.
The above description is merely a specific embodiment, any feature disclosed in this specification, except non-specifically Narration, can be replaced by other alternative features that are equivalent or have similar purpose；Disclosed all features or all sides Method or in the process the step of, other than mutually exclusive feature and/or step, can be combined in any way.

Claims (2)

1. a kind of colour image compression method based on interpolation reconstruction, which is characterized in that include the following steps：
Step 1, color space is converted：
Using RGB-YCbCr image color space conversion methods, the coloured image of input is converted into YCbCr figures from rgb space Picture obtains luminance component image Y and chromatic component Cb, Cr；
Step 2, two-dimension discrete cosine transform is carried out to luminance component Y：
Luminance component Y is divided into N=(W × H)/82A non-overlapping copies, the square image blocks that size is 8 × 8, to each image Block carries out 2-D discrete cosine variation, obtains the transform coefficient matrix of N number of luminance component Y；Wherein, W indicates width, the H of image Indicate the height of image；
Step 3, chromatic component Cb, Cr are filtered respectively using the sef-adapting filter compressed based on interpolation：
Chromatic component Cb, Cr are divided into M=(W × H)/162A non-overlapping copies, the square image blocks that size is 16 × 16；For One 16 × 16 image block chooses corresponding 64 pixels of odd-numbered line odd column, referred to as retention point, and its coordinate is remembered It records, be denoted as Ω；Then, image block is arranged by row and is converted to vector x, corresponding retention point x in xΩIt indicates；
Interpolating matrix is set as H, then the vector of interpolation reconstructionIt is expressed as：
And then it obtains retaining point setOptimization method：
Setting T is obtained by traditional Kronecker multiplication by two 16 × 16 dct transform Matrix Cs one 256 × 256 transformation matrix：Wherein, symbolIndicate traditional Kronecker operators；Choose the inverse matrix T of T-1 In 64 respective coordinates Ω row, form the matrix Λ that new dimension is 64 × 256, then xΩ=Λ X, X indicate coefficient vector；
Convert above-mentioned optimization method to following target equation accordingly：
Wherein, | | | |2Indicate two norms, | | | |1Indicate a norm；
Above-mentioned target equation optimal solution is solved by iteratively faster threshold value convergence algorithmIt is reduced into 16 × 16 transformation series Matrix number, and down-sampling is done to transform coefficient matrix, retain the transform coefficient matrix of 8 × 8 size of the upper left corner；
To each 16 × 16 image block of Cb, Cr component carry out it is above-mentioned be filtered, obtain the transformation of M Cb, Cr component Coefficient matrix；
Step 4, the transform coefficient matrix compressed encoding of component Y, Cb, Cr are obtained into encoding code stream：
Quantification treatment is carried out to each transform coefficient matrix of component Y, component Cb, component Cr respectively, using image transcoding, coding transform The Zig-Zag scanning sequencies of coefficient are ranked up, and carry out entropy coding later, obtain compressed encoding code stream；
Step 5, encoding code stream is decoded, obtains Y, Cb, Cr picture content：
Encoding code stream is decoded to obtain N number of component Y quantized transform coefficient matrixes, M component Cb, Cr quantized transform coefficient matrix；
Inverse quantization, inverse transformation processing are carried out to each component Y quantized transform coefficient matrixes, obtain decoded N number of Y-component image Block, and it is spliced into Y-component image；
To each component Cb, Cr quantized transform coefficient matrix, coefficient 0 is first used to be filled with the quantization transform coefficient of 16 × 16 sizes Matrix, then inverse quantization, inverse transformation processing are carried out, decoded M Cb, Cr component image block is obtained, and be spliced into Cb, Cr component Image；
Step 6, interpolation reconstruction Cb, Cr component images：
Using the retention point chosen in advance based on the sef-adapting filter that interpolation is compressed to Cb, Cr component image into row interpolation weight It builds, obtains high quality Cb, Cr component image；
Step 7, color space converts：
Finally obtained Y, Cb, Cr component image is converted into RGB figures by YCbCr-RGB image color space conversion methods Picture completes color image compression.
2. by the colour image compression method based on interpolation reconstruction described in claim 1, which is characterized in that mesh in the step 3 Mark equation optimal solutionCalculating process it is as follows：
A) it initializes：
If X(0)=X(1)=T-1X, X(0)Indicate initial value, the X of coefficient vector X(1)Indicate the first time iterative value of coefficient vector X； Default intermediate variable t0=t1=1, t0Indicate initial value, the t of intermediate variable t1Indicate the first time iterative value of intermediate variable t；
B) iteration successively is carried out according to following iterative formula：
If coefficient vector X(i+1)Position coordinates be not belonging to Π, then force set to 0；
Wherein, i indicates that iterations, λ, L are predetermined constant, and soft () indicates Soft Thresholding for Signal operation；Π indicate one 16 × In 16 transformation coefficient square, the coordinate set that 8 × 8 piece of the upper left corner；
C) work as iteration errorReach default maximum iteration less than pre-determined threshold or iterations, then stops Only iteration exports optimal coefficient vector
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