CN109951711A - A kind of EZW data compression method based on random adjusting thresholds - Google Patents
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Abstract
The invention discloses a kind of EZW data compression methods based on random adjusting thresholds, this method includes the steps that it is wavelet transformation, quantization, coding that wavelet coding is carried out to image, decoding process is in contrast, when to image scanning coding, initial threshold is calculated first, then EZW coding is carried out, EZW coding judge that the method for the threshold size of wavelet coefficient importance goes to encode digital picture using random adjustment, specific practice be in threshold value every time divided by 2 when add positive random number in an adjustable extent to divisor 2.The present invention adjusts the threshold value for judging wavelet coefficient importance at random, allow threshold value in a small range random value, image is set to improve compression ratio while guaranteeing also proper mass, for same picture, threshold value is taken to be encoded at random in different ranges, compression ratio increases, and the compression image restoring effect being distorted is preferable, although Y-PSNR has a degree of decline, influence little.
Description
Technical field
The present invention relates to a kind of EZW data compression methods based on random adjusting thresholds, belong to distributed generation resource and through transport
Row control technology field.
Background technique
The information of picture showing has the feature it is clear that intuitive, clear, can show well it is seen that
Information.However the information content that image includes is very big, so that image information occupies very big memory space, increases acquisition of information
Cost, is nowadays the epoch of network high-speed development, and a large amount of information redundancy is no longer satisfied people to acquisition information rate
Requirement.Under such environment of times, compression of images becomes the important directions that people solve the problems, such as.Such as remote sensing images, medicine
The fields such as image, weather nephogram, DTV have a wide range of applications.Can inevitably exist in the compression process of image and lose
Very, the image compression encoding method based on wavelet transformation can not only eliminate the statistical redundancy in image data well, and
The profile and detailed information of image can also be all reacted well.EZW can be controlled according to the requirement of picture quality and compression ratio and be compiled
Decoding process, with the increase for receiving bit, the details of reconstructed image is more, and quality can become better and better.But a large amount of scanning
The time of coding will be increased, this will necessarily also reduce code efficiency.
Multistage tree set partitioning sequence (Set Partitioning in Hierarchical Threes, SPIHT) is calculated
The concept of spatial orientation tree, non-direct descendant's set L (i, j) and all descendants's set D (i, j), more effective earth's surface is utilized in method
Coefficient construction is shown, code efficiency ratio EZW, which has, significantly to be improved.But in low bit-rate scenarios, it is extensive to will lead to decoding
Multiple image fault degree is higher.Improved spiht algorithm eliminates 3 ordered lists in spiht algorithm, it is easier to hardware
It realizes.But compression quality is declined, signal-to-noise ratio can be declined.
Summary of the invention
The technical problem to be solved by the present invention is a kind of EZW data compression method based on random adjusting thresholds is provided, with
Solve above-mentioned problems of the prior art.
The technical scheme adopted by the invention is as follows:
A kind of EZW data compression method based on random adjusting thresholds, this method include carrying out wavelet coding to image
Step is wavelet transformation, quantization, coding, and decoding process in contrast, when encoding to image scanning, calculates initial threshold first,
Then EZW coding is carried out, the iterative process of encryption algorithm is as follows:
1) judge whether the absolute coefficient on path is greater than threshold value T, turn the 2) step if it is greater than T, otherwise turn the 5) step;
2) judge whether coefficient is positive on path, be to turn the 3) step, no turn the 4) step;
3) it just will judge that the coefficient on position replaces with 0, be designated as P, turn the 6) step;
4) it just will judge that the coefficient on position replaces with 0, be designated as N, turn the 6) step;
5) if it is isolated zero, IZ is marked;If it is zerotree root, then number in this position is replaced with 0, mark ZTR, turned
6) step;
6) position that P, N is marked is encoded in order, if absolute coefficient is if on the section [T, T+T/2]
Be encoded to 0, if absolute coefficient is encoded to 1 if on the section [T+T/2,2T], by T used in current iteration, flag sequence,
Coded sequence saves in case when decoding is used, and finally turns the 7) step;
7) threshold value T is replaced with into T/2, if T is greater than or equal to the minimum threshold of setting, turns the 1) step, otherwise terminate.
Initial threshold:
In formula: CmaxIndicate greatest coefficient absolute value.
It is evaluated after end-of-encode using parameter peak signal-to-noise ratio and compression ratio:
Parameter peak signal-to-noise ratio (PSNR) is defined as follows:
Wherein MSE () indicates the mean square deviation of certain color component, and if k is 3 in RGB mode, i.e. red, green, blue is three-component
The sum of mean square deviation, k is 1 in grayscale mode;
The calculation formula of compression ratio (CR) are as follows:
CR=(1-Nz) × 100% (20)
Wherein,NEZ: zero number;NWC: wavelet coefficient number.
If matrix of wavelet coefficients isSubscript 1 indicates coefficient when this is encoded for the 1st EZW, and 1 table epicycle of subscript is not
The matrix of coding, subscript p, q indicate that this matrix has p row q column, and each element is in matrixI, j value range be respectively [1,
P], [1, q], define operator abs () when acting on a matrix, expression takes absolute value to each element of matrix, have:
Defining operator sign () is to take symbolic operation to element each in matrix, is had
Threshold value is T when the 1st wheel coding1, definition operator subb (, T) and it is that each element subtracts T in matrix, have
It is to make threshold value divided by 2 for the decoded information transmitted when first round coding to decoder
For the threshold value of next round coding.
When updating threshold value every time divided by 2 in cataloged procedure, to 2 plus random number within one 0 to 1, specifically with formula (25)
Mode adjusts threshold value:
Beneficial effects of the present invention: compared with prior art, the present invention adjusts the threshold for judging wavelet coefficient importance at random
Value allows threshold value in a small range random value, image is made to improve compression ratio while guaranteeing also proper mass, schemes for same
Piece takes threshold value to be encoded at random in different ranges, and compression ratio increases, and the compression image restoring effect being distorted
Preferably, it although Y-PSNR has a degree of decline, influences little.
Detailed description of the invention
Fig. 1 is subspace relational graph;
Fig. 2 is decomposition and reconstruction procedure chart;
Fig. 3 is Embedded zero-tree wavelet scanning sequency figure;
Fig. 4 is EZW coding flow chart;
Fig. 5 is original image to be processed;
Fig. 6 is algorithm coding decoding process figure;
Fig. 7 is experimental result picture after processing picture.
Specific embodiment
With reference to the accompanying drawing and the present invention is described further in specific embodiment.
Embedded zero-tree wavelet principle: multiresolution analysis and wavelet transformation, if x ∈ R, f:x → R and ψk(x): x → R is
The function system of linear independence, then f (x) may be expressed as:
Wherein, akIt is expansion coefficient, V is referred to as function system { ψk(x) } at space:
For example, with integer translation and real number two-value scale, quadractically integrable function ψkForm expanded function set { ψj,k
(x) }:
The small echo positive inverse transform formula difference of one-dimensional functions is as follows:
Wherein CψMeet admissible condition, formula (3) is the process for seeking expansion coefficient, and formula (4) is to ask in function space
A function.If function system { ψj,kIt (x) } is with integer translation and real number two-value scale, quadractically integrable function ψk∈L2(R) group
At expanded function set.In wavelet transformation, take
ψj,k(x)=2j/2ψ(2jx-k) (5)
Wherein, ψ (x) ∈ L2(R), j, k ∈ Z, if assigning a specified value, such as j=j to the j in formula (5)0, expansion collection
Conjunction will be { ψj,k(x) } a subset, and without crossing over L2(R), a sub-spaces V can be indicatedj0:
It can define as a result, and represent any j, the generalized expression-form of the span subspace on k are as follows:
VjSize increase with j, have and change lesser variable or Detailfunction may include in subspace, this is more
The Fundamentals of Mathematics of resolution analysis.
As x ∈ RnWhen, principles above and representation method can analogize.The case where when image data is n=2, when image
When data are considered as separable two-dimensional discrete data, it may be expressed as:
φ (x, y)=φ (x) φ (y) (8)
Wherein φ (x) is unidimensional scale function, and defining ψ (x) is wavelet function, then can establish two-dimensional wavelet transformation basis
Three two-dimentional wavelets:
Scaling function φ (x) can regard low-pass filter as, and wavelet function ψ (x) is the high-pass filter of same layer.And letter
Manifold is L2(R2) under orthonormal basis, indicate are as follows:
{ψl j,m,n(x, y) }={ 2jψl(x-2jm,y-2jn)} (10)
Wherein, j >=0, l=1,2,3, j, l, m, n be integer.
In each layer of transformation, image is broken down into the image of four a quarter sizes, by original image and one
Make two times of interval samplings by the direction x and y after wavelet basis inner product to generate.First layer (j=1) Wavelet transformation can be write as:
Variation for subsequent level (j > 1), in four identical interval sampling filtering operations of each layer of progress.
Shown in the small echo positive inverse transform formula of two-dimensional discrete data such as formula (12), formula (13):
In upper two formula, i Changing Times table level, vertical, diagonal value,It defines in scale j0
The approximation of upper f (x, y),Coefficient attached horizontal, vertical, diagonal details.
It is mainly concerned with the decomposition application of scaling function and wavelet function in the multiresolution analysis of image data, original is believed
Number (function) first according to scaling function at the function subspace (V) under each resolution ratio, the signal of these subspaces is provided
One approximation of original signal, in addition again by wavelet function at the difference section (W) of subspace under adjacent resolution ratio,
The detail section of original signal is provided, relationship is as shown in Figure 1, expression formula is shown in formula (16)
From V0V is decomposed step by step1、W2, then arrive V2、W2, it is (15), (16) with the expression formula that Mallat algorithm is realized:
Its restructuring procedure are as follows:
Specific decomposable process and restructuring procedure are as shown in Figure 2.
A kind of EZW data compression method based on random adjusting thresholds, this method include carrying out wavelet coding to image
Step be wavelet transformation, quantization, coding, decoding process in contrast, image pass through wavelet transformation after, low frequency sub-band data
It is worth bigger.Embedded encoded in EZW is exactly accurately to control code rate according to the precedence of this information importance level.Right
During original signal decomposition analysis, the signal in the space V is to obtain the approximate signal under thick scale by low-pass filter (L)
It is empty then further to obtain W under thin scale by high-pass filter (H) when to analyze a certain part signal details for part
Between middle detail section signal.For one-dimensional, an original signal can be decomposed into LL1、HL1、LH1、HH1Four parts.It is embedding
During entering formula Embedded Zerotree Wavelet, using Z-shaped sequential scan.As shown in figure 3, being calculated first just when being encoded to image scanning
Then beginning threshold value carries out EZW coding, the iterative process of encryption algorithm is as follows:
1) judge whether the absolute coefficient on path is greater than threshold value T, turn the 2) step if it is greater than T, otherwise turn the 5) step;
2) judge whether coefficient is positive on path, be to turn the 3) step, no turn the 4) step;
3) it just will judge that the coefficient on position replaces with 0, be designated as P, turn the 6) step;
4) it just will judge that the coefficient on position replaces with 0, be designated as N, turn the 6) step;
5) if it is isolated zero, IZ is marked;If it is zerotree root, then number in this position is replaced with 0, mark ZTR, turned
6) step;
6) position that P, N is marked is encoded in order, if absolute coefficient is if on the section [T, T+T/2]
Be encoded to 0, if absolute coefficient is encoded to 1 if on the section [T+T/2,2T], by T used in current iteration, flag sequence,
Coded sequence saves in case when decoding is used, and finally turns the 7) step;
7) threshold value T is replaced with into T/2, if T is greater than or equal to the minimum threshold of setting, turns the 1) step, otherwise terminate.
It is as shown in Figure 4 that EZW encodes flow chart.
Initial threshold:
In formula: CmaxIndicate greatest coefficient absolute value.
Pass through comparison treated picture effect, Y-PSNR (PSNR), bit rate (BitRate) after end-of-encode
Rate and compression ratio (CR) carry out judging improved reasonability and validity.Because the small range of threshold value increases, it is contemplated that coding
Data amount check can be reduced, thus compression ratio can increase, and parameter peak signal-to-noise ratio and compression ratio are used after end-of-encode
It is evaluated:
Parameter peak signal-to-noise ratio (PSNR) is defined as follows:
Wherein MSE () indicates the mean square deviation of certain color component, and if k is 3 in RGB mode, i.e. red, green, blue is three-component
The sum of mean square deviation, k is 1 in grayscale mode;
The calculation formula of compression ratio (CR) are as follows:
CR=(1-Nz) × 100% (20)
Wherein,NEZ: zero number;NWC: wavelet coefficient number.
If by formula (12), (13), (15), the resulting wavelet coefficient of (16) principle wavelet systems that format forms as shown in Figure 3
Matrix number isCoefficient when subscript 1 indicates this for the 1st EZW coding, the 1 uncoded matrix of table epicycle of subscript, subscript p,
Q indicates that this matrix has p row q column, and each element is in matrixI, j value range is respectively [1, p], [1, q], defines operator
When abs () acts on a matrix, expression takes absolute value to each element of matrix, has:
Defining operator sign () is to take symbolic operation to element each in matrix, is had
Threshold value is T when the 1st wheel coding1, definition operator subb (, T) and it is that each element subtracts T in matrix, have
It is to make threshold value divided by 2 for the decoded information transmitted when first round coding to decoder
For the threshold value of next round coding.
When updating threshold value every time divided by 2 in cataloged procedure, to 2 plus random number within one 0 to 1, specifically with formula (25)
Mode adjusts threshold value:
In formula: α is the value (take respectively 0,0.1,0.5,1,1.5) of the control range multiplied to random number; rand
() is the random number for 0 to 1 range asked.
Experimental verification:
Used data original image in experimentation as shown in figure 5, it is passed through respectively Embedded Zerotree Wavelet Coding with
And proposed innovatory algorithm is encoded.Algorithm flow is as shown in Figure 6:
Comparison Y-PSNR (PSNR), bit rate (BitRate) rate and compression ratio (CR) obtain experimental data such as table 1
It is shown.
1 experimental result of table
It can be seen that from upper table result when α increase, CR increases, but BitRate and PSNR is being reduced, in order to accept or reject
Suitable factor-alpha defines a validity function S here:
S=100BitRate × λ+PSNR × ρ+CR × σ, (+σ=1 λ+ρ) (26)
Wherein λ, ρ, σ are respectively the proportionality coefficient that parameter BitRate, PSNR, CR are multiplied, and size corresponds to parameters
The shared significance level in performance evaluation, three proportionality coefficients and be 1.When S value maximum, it is believed that effect at this time is to enable
People is most satisfied, and the S value corresponding to different α values is listed in last column of table 1.Treated, and image effect is as shown in Figure 7.
From experimental data and treated image comparison, as a result, it has been found that, compressed image can restore substantially.As α=0,
The processing of data, that is, EZW method as a result, with α increase, the image fault finally restored is bigger, while PSNR is presented by a small margin
Decline, but because of the change of α value, threshold value can become larger in a certain range, cause the coefficient for being labeled as zero more, i.e. NEZValue increase
Greatly, so that CR be made to be in significantly increase trend.But from the point of view of overall effect, although CR increase, compression effectiveness institute it is impacted compared with
It is small, and the image being reduced still remains the main feature of original image, and distortion less, is illustrated in method of the invention
In, the α value that passage capacity evaluation function is chosen not only can effectively improve compression ratio, moreover it is possible to guarantee final compression effectiveness.This
Outside, since the mentioned method of the present invention is for data compression, so the demand to compression ratio increase is bigger, therefore in the present invention
Validity function in the multiplied proportionality coefficient σ value of CR value it is bigger, λ, ρ, σ distinguish value 0.3,0.3,0.4, last comprehensive
Energy evaluation function judgement, as α=0.1, effect is best.In conclusion by adding a α when each scanning updates threshold value
The method of random number can guarantee compression effectiveness while improving compression ratio in (0,1) range again, and compressing data has preferably
Effect.
Conclusion: reducing distortion while improving compression ratio as far as possible, we attempt to carry out in the selection of threshold value related
Processing.Main method is based on embedded system toolchain (EZW) algorithm, to the threshold value in its cataloged procedure in a certain range
Interior random value is encoded, and effect is best when obtaining α=0.1 according to experimental result.Although PSNR has certain decline, from
From the point of view of image effect, distortion is little.Therefore the reasonability and validity for showing proposed method herein, are suitable for engineer application
In.
The present invention can be realized reduces distortion as far as possible while improving compression ratio, proposes the random EZW for changing threshold value
Algorithm.Main means are based on Embedded Zerotree Wavelet Coding (EZW) algorithm, and random adjustment judges the threshold of wavelet coefficient importance
Value allows threshold value in a small range random value, image is made to improve compression ratio while guaranteeing also proper mass.Because of threshold value conduct
The value for judging node importance, during entire coding and decoding, the effect compressed and restored to final image centainly has
Crucial influence.Algorithmic code is used in actual treatment, for same picture, taken at random in different ranges threshold value into
Row coding, the experimental results showed that compression ratio increases, and the compression image restoring effect being distorted is preferable, although peak value noise
Than there is a degree of decline, but influence little.It is compared finally by analysis, it was demonstrated that the actual effect of mentioned innovatory algorithm,
And a performance evaluating deg function is defined to be accepted or rejected the multiplied factor of random number to reach certain promising result.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Within protection scope of the present invention, therefore, protection scope of the present invention should be based on the protection scope of the described claims lid.
Claims (5)
1. a kind of EZW data compression method based on random adjusting thresholds, it is characterised in that: this method includes small to image progress
The step of wave encodes is wavelet transformation, quantization, coding, and decoding process in contrast, when encoding to image scanning, calculates just first
Then beginning threshold value carries out EZW coding, the iterative process of encryption algorithm is as follows:
1) judge whether the absolute coefficient on path is greater than threshold value T, turn the 2) step if it is greater than T, otherwise turn the 5) step;
2) judge whether coefficient is positive on path, be to turn the 3) step, no turn the 4) step;
3) it just will judge that the coefficient on position replaces with 0, be designated as P, turn the 6) step;
4) it just will judge that the coefficient on position replaces with 0, be designated as N, turn the 6) step;
5) if it is isolated zero, IZ is marked;If it is zerotree root, then number in this position is replaced with 0, mark ZTR, turns the 6)
Step;
6) position that P, N is marked is encoded in order, if absolute coefficient is encoded to if on the section [T, T+T/2]
0, if absolute coefficient is encoded to 1 if on the section [T+T/2,2T], by T used in current iteration, flag sequence, code sequence
Column save in case when decoding is used, and finally turn the 7) step;
7) threshold value T is replaced with into T/2, if T is greater than or equal to the minimum threshold of setting, turns the 1) step, otherwise terminate.
2. a kind of EZW data compression method based on random adjusting thresholds according to claim 1, it is characterised in that: just
Beginning threshold value:
In formula: CmaxIndicate greatest coefficient absolute value.
3. a kind of EZW data compression method based on random adjusting thresholds according to claim 1, it is characterised in that: compile
It is evaluated after code using parameter peak signal-to-noise ratio and compression ratio:
Parameter peak signal-to-noise ratio is defined as follows:
Wherein MSE () indicates the mean square deviation of certain color component, and if k is 3 in RGB mode, i.e., red, green, blue is three-component square
The sum of difference, k is 1 in grayscale mode;
The calculation formula of compression ratio are as follows:
CR=(1-Nz) × 100% (20)
Wherein,NEZ: zero number;NWC: wavelet coefficient number.
4. a kind of EZW data compression method based on random adjusting thresholds according to claim 2, it is characterised in that: set
Matrix of wavelet coefficients isCoefficient when subscript 1 indicates this for the 1st EZW coding, the 1 uncoded matrix of table epicycle of subscript,
Subscript p, q indicates that this matrix has p row q column, and each element is in matrixI, j value range is respectively [1, p], [1, q], definition
When operator abs () acts on a matrix, expression takes absolute value to each element of matrix, has:
Defining operator sign () is to take symbolic operation to element each in matrix, is had
Threshold value is T when the 1st wheel coding1, definition operator subb (, T) and it is that each element subtracts T in matrix, have
It is under being used as threshold value divided by 2 for the decoded information transmitted when first round coding to decoder
The threshold value of one wheel coding.
5. a kind of EZW data compression method based on random adjusting thresholds according to claim 4, it is characterised in that: compile
When updating threshold value divided by 2 every time during code, to 2 plus random number within one 0 to 1, threshold specifically is adjusted in a manner of formula (25)
Value:
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