CN102316324B - Image coding prediction method based on local minimum entropy - Google Patents

Abstract

The invention relates to an image coding prediction method based on local minimum entropy. The method is especially suitable for compression processing of a static image. The method is characterized by: carrying out wavelet transformation and wavelet coefficient quantification to the image; selecting a wavelet coefficient which has a strong correlation with a bit to be coded as a prediction coefficient; defining an importance state function, an importance state direction weighting function and an importance state and a function of the prediction coefficient; taking reduction of entropy as a discrimination criteria, establishing a local optimum prediction model so as to classify data of the bit to be coded. By using the prediction model established in the invention, high efficient predictive coding of the wavelet coefficient can be realized. An experiment result shows that under a same compression ratio, objective quality of the recovery image can be effectively raised compared with a static image compression standard JPEG 2000.

Description

A kind of image coded prediction method based on local minimum entropy

Technical field

The present invention relates to a kind of coded prediction method that is applicable to the still image compression, relating in particular to a kind of reduction amplitude with entropy comes the contraposition data to predict classification as foundation, thereby approach the image coded prediction method of wavelet coefficient high-order conditional entropy, belong to the Image Compression field.

Background technology

In recent ten years, be used widely in the still image compression based on the image compression algorithm of wavelet transformation, be considered to present compression performance the best way.Its compression process mainly comprises preliminary treatment, wavelet transformation, quantification, four steps of entropy coding, as shown in Figure 1.Wherein, entropy coding is encoded to it according to the probability that data occur, and can remove the statistical redundancy between data, thereby finishes the representing of original image information with minimum data volume, is the crucial and assurance that realizes image compression.

Entropy coding method commonly used has Run-Length Coding, Huffman encoding and arithmetic coding.By two kinds of entropy coding methods wherein being combined (among the still image compression international standard JPEG Run-Length Coding and Huffman encoding in conjunction with), (among the still image compression international standard JPEG2000 context being predicted and the arithmetic coding combination) perhaps combines Predicting Technique and entropy coding, can remove the redundancy between the conversion coefficient better, improve the efficient of entropy coding.Wherein, Predicting Technique utilizes Given information to infer unknown message, thereby reduces the uncertainty of unknown message, the feasible high-order conditional entropy that can approach information source, the raising that finally brings code efficiency.

The predictive coding of wavelet coefficient normally scans the wavelet coefficient bit data based on bit plane and encodes, because more be conducive to excavate the correlation between the wavelet coefficient on this level, thereby fully removes the redundancy between coefficient, improves compression efficiency.The Bit-Plane Encoding Forecasting Methodology of wavelet coefficient comprises C/B, EBCOT (being adopted by JPEG2000), PCAS etc., these class methods are utilized the correlation between wavelet coefficient, value condition according to selected predictive coefficient, predict the probability distribution of current position to be encoded, the tangible position to be encoded of probability distribution difference is divided into different class (be conducive to reach littler condition entropy), the close position to be encoded of probability distribution is classified as similar (avoiding the context dilution), make the high-order condition entropy that sorted bit data correspondence is littler, thereby be conducive to improve the efficient of follow-up arithmetic coding.But still there is the problem and shortage of following several respects in these class methods:

(1) do not take full advantage of correlation between the wavelet coefficient, during predictive coding, correlation between the wavelet coefficient mainly is presented as amplitude, direction, area coherence, and existing method has only been utilized wherein one or both, and is comprehensive and abundant inadequately to the utilization of correlation.

(2) design anticipation function or when setting up forecast model, overemphasized the predicting function (as PCAS) of directional characteristic (as EBCOT) or the single coefficient of coefficient, and in fact there is dependency relation current position to be encoded with its a plurality of coefficients on every side, and therefore existing method fails to bring into play the integrated forecasting effect of a plurality of coefficients.

(3) foundation of forecast model mainly relies on experience or statistics, not from the demand of follow-up entropy coding, thereby make the different probability do not distinguish position to be encoded well distribute, fail effectively to approach the high-order entropy of information source, influenced the compression efficiency of image.

In the Bit-Plane Encoding of wavelet coefficient, the effect of prediction depends primarily on the foundation of structure and the disaggregated model of anticipation function.The present invention selects relevant wavelet coefficient as predictive coefficient comprehensively, structure dependency prediction function comes the prediction effect of comprehensive a plurality of coefficients, and according to the size of its predicting function, adopt progressively screening method, as criterion, set up a kind of disaggregated model of local optimum with effective reduction of entropy, fully remove statistical redundancy, the different probability of effectively having distinguished position to be encoded distributes, and the high-order conditional entropy of having approached wavelet coefficient, has finally realized wavelet coefficient is efficiently compressed.

Summary of the invention

At aforesaid problem, the present invention adopts technical scheme as described below:

A kind of image coded prediction method based on local minimum entropy is characterized in that, may further comprise the steps:

Step 1: image is carried out wavelet transformation and wavelet coefficient quantification, with each wavelet coefficient binary number representation, scanning wavelet coefficient bit plane; Choose with the stronger coefficient of position to be encoded correlation as predictive coefficient, comprise that the neighbour occupies coefficient, neighbours' coefficient far away, paternal number and father neighbours' coefficient;

Step 2: for occupying predictive coefficient with the strongest neighbour of position to be encoded correlation, the function of three kinds of predictive coefficients of structure, embody the multiple correlation of itself and coefficient to be encoded, the function of described predictive coefficient comprises important character state function, significance state weighted direction function, significance state and function;

Step 3: for the more weak predictive coefficient of other and position to be encoded correlation, comprise neighbours far away, father, father neighbours' predictive coefficient, according to its dependency relation with to be encoded, choose above-mentioned a kind of function expression form respectively and construct its anticipation function;

Step 4: according to the reduction amplitude of entropy, the multiple dependency prediction function of having constructed is screened, set up a kind of forecast model based on local minimum entropy, according to the actual value of predictive coefficient the wavelet coefficient bit data is predicted as some classification.

In the described step 1, it is 8 coefficient N around the current position to be encoded that the neighbour occupies coefficient ₀～N ₇, neighbours' coefficient far away occupies peripheral 16 the coefficient FN of coefficient for the neighbour ₀～FN ₁₅Described paternal number is the FACTOR P of the low one-level frequency band correspondence position in current position to be encoded, and 8 neighbours that father neighbours' coefficient enclosed for paternal several weeks occupy FACTOR P N ₀～PN ₇

In the described step 2, the significance state anticipation function be used for distinguishing described predictive coefficient important at the upper strata bit plane, when the anterior layer bit plane important or unimportant these three kinds of states also, its expression formula is defined as follows:

$S(M_i,p)=\left\{\begin{array}{cc}K& 2^p\&le;M_i\\ 1& 2^{p-1}\&le;M_i<2^p\\ 0& M_i<2^{p-1}\end{array}\right.$

Wherein, M _iRepresent described predictive coefficient N _iAmplitude, 0≤i≤7 wherein, p represents the current bit plane number of plies of encoding, S (M _i, p) functional value is represented described predictive coefficient in the significance state value when the anterior layer bit plane, and K is ratio parameter (positive integer greater than 1), and described bit plane is the bit plane of wavelet coefficient.

In the described step 2, significance state weighted direction anticipation function is the important character state function weighted sum to described predictive coefficient, and assigns weight for each predictive coefficient according to the size of predictive coefficient and current position to be encoded correlation:

$f_1\left(M\right)=\underset{i=0}{\overset{7}{\mathrm{\&Sigma;}}}{w}_{i}S(M_i,p)$

F wherein ₁(M) the weighted direction anticipation function value of the described predictive coefficient of expression, w _iThe weight of representing described predictive coefficient, S (M _i, p) be the significance state anticipation function.

In the described step 2, significance state and function are used for distinguishing the important number of described predictive coefficient not simultaneously to the influence of probability distribution, and its expression formula is defined as follows:

$f_2\left(M\right)=\underset{i=0}{\overset{7}{\mathrm{\&Sigma;}}}\mathrm{\&sigma;}\left(M_i\right)$

F wherein ₂(M) the anticipation function value of the described predictive coefficient of expression, σ (M _i) represent described predictive coefficient at the importance discriminant value of bit plane p, whether important on the present bit plane in order to distinguish this predictive coefficient, be defined as follows:

${\mathrm{\&sigma;}}_3\left(M_i\right)=\left\{\begin{array}{cc}1& S(M_i,p)\&NotEqual;0\\ 0& S(M_i,p)=0\end{array}\right.$

S (M wherein _i, p) be the significance state anticipation function.

In the described step 4, adopt greedy algorithm to screen anticipation function, its distinguishing rule is that choosing of certain anticipation function can make the entropy of its corresponding prediction classification reduce amplitude greater than pre-set threshold.

The present invention is under offline mode, select with the strong coefficient of position to be encoded correlation as predictive coefficient, construct the multiple anticipation function that can embody different correlations, set up forecast model from the angle that improves follow-up entropy-coding efficiency, current position to be encoded is divided into some classes; Actual value according to predictive coefficient in the line compression process calculates predicted value, corresponding arithmetic encoder is sent in current position to be encoded carry out the entropy coding, has realized the efficient predictive coding to wavelet coefficient.Experimental result shows, compares with still image compression standard JPEG 2000 under identical compression ratio, has effectively improved the objective quality that recovers image.

Description of drawings

The present invention is further illustrated below in conjunction with the drawings and specific embodiments.

Fig. 1 is based on the compression/de-compression flow chart of the method for compressing image of wavelet transformation.

Fig. 2 is the basic flow sheet of a kind of image coded prediction method based on local minimum entropy of the present invention.

Fig. 3 (a) is depicted as 3 grades of pyramid wavelet decomposition schematic diagrames, and Fig. 3 (b) is father and son and the neighborhood schematic diagram between wavelet coefficient, and Fig. 3 (c) has provided selected predictive coefficient set.

Embodiment

Basic ideas of the present invention are: under offline mode, utilize a plurality of predictive coefficients of selecting, construct the dependency prediction function, and set up forecast model based on local minimum entropy; During line compression, calculate predicted value according to forecast model, corresponding arithmetic encoder is sent in position to be encoded encode, realize the compression to wavelet coefficient.

Below, with reference to each implementation step of image coded prediction method of the present invention shown in Figure 2, the present invention will be described in detail.

Step 1: image is carried out wavelet transformation and wavelet coefficient quantification, with each wavelet coefficient binary number representation, scanning wavelet coefficient bit plane; Choose with the stronger coefficient of position to be encoded correlation as predictive coefficient, comprise that the neighbour occupies coefficient, neighbours' coefficient far away, paternal number and father neighbours' coefficient.

Image is carried out wavelet transformation, and the wavelet coefficient that generates is quantized.Basic principle according to wavelet transformation, the amplitude size of wavelet coefficient has represented it to recovering the significance level of picture quality influence, under given bit rate, priority encoding significant coefficient (coefficient that amplitude is big) can improve the quality of recovering image, but, sequential encoding meeting in strict accordance with order of magnitude increases a large amount of positional informations, introduces the thought of Bit-Plane Encoding for this reason.So-called bit plane refers to wavelet coefficient is represented with binary form, and at this moment, the plane that the identical bits of all coefficients is formed just is called a bit plane.Therefore, the process of Bit-Plane Encoding is exactly along bit plane order from high to low, successively all bit data in each bit plane of scanning encoding.Adopt this mode, make the bigger coefficient of amplitude preferentially obtain coding naturally, thereby avoided the positional information expense dexterously.

The selection of predictive coefficient is the empty localization property frequently according to wavelet transformation, quaternary tree decomposition texture when wavelet transformation is applied to image compression becomes several frequency bands to picture breakdown, carries out obtaining behind wavelet transformation four frequency band LL of the first order for piece image ₁, LH ₁, HL ₁And HH ₁, successively to low frequency LL at different levels _kDecompose four frequency bands that obtain thicker one-level, i.e. the tower decomposition of small echo is depicted as 3 grades of wavelet decomposition schematic diagrames as Fig. 3 (a).The corresponding same spatial domain of the coefficient of frequency band same position not at the same level image block, adjacent frequency coefficient is generated by adjacent spatial domain image block, and it is relevant relevant with neighbours more than to be called the father and son, shown in Fig. 3 (b).For guaranteeing the comprehensive of tolerance, above-mentioned correlation is expanded, shown in Fig. 3 (c), neighbours' coefficient is subdivided into the neighbour occupies coefficient N ₀～N ₇With neighbours' coefficient FN far away ₀～FN ₁₅, 8 neighbours that enclose paternal several weeks are occupied coefficient are defined as father neighbours' FACTOR P N ₀～PN ₇Above all coefficients all are chosen to be predictive coefficient, thus the correlation between the full use wavelet coefficient.According to present known experimental result, the correlation power of predictive coefficient and coefficient to be encoded is followed successively by: 8 neighbours' coefficient＞paternal number＞single father neighbours' coefficient＞single neighbours' coefficients far away, the predicting function of the coefficient correspondence that correlation is more strong is also more big.

Treat the process that bits of coded is predicted, utilize the correlation between the wavelet coefficient exactly, the different probability of distinguishing position to be encoded distributes, and therefore, the foundation of forecast model should embody the various correlations between wavelet coefficient:

(1) amplitude correlation

The spatial coherence of image shows as the close of neighbor gray scale and changes, and the amplitude size of wavelet coefficient has reflected the severe degree of spatial domain variation of image grayscale, be between the grey scale pixel value of spatial domain correlation at the imbody of frequency domain, therefore, the close of amplitude between wavelet coefficient or some specific magnitude relationship are called the amplitude correlation.For example, from the level of wavelet coefficient bit plane, if paternal number is when anterior layer bit plane also unimportant (amplitude is worth less than certain), also the probability of inessential (amplitude is worth less than this) is very big for the subsystem number so; And for the adjacent wavelet coefficient in position, they become important in succession at adjacent several bit planes usually.

(2) directional dependency

In image compression, two-dimensional wavelet transformation is separable, carries out conversion along level and vertical direction respectively, thereby the frequency band of formation level, vertical and three directions in diagonal angle reflects that respectively image is in the feature of different directions.Be example with the HL frequency band, the corresponding horizontal high pass of this frequency band, vertical low pass filters, what mainly describe is the information of vertical direction in the image, therefore, in this frequency band, correlation is stronger between the wavelet coefficient of vertical direction, and wavelet coefficient is called directional dependency along the stronger characteristic of correlation between a certain direction wavelet coefficient in certain frequency band.

(3) area coherence

The neighbor pixel that gray value is close in the image has constituted the connected region of image, and this is the embodiment of image space correlation.Still have certain this correlation between the wavelet coefficient after the decomposition, for this reason, the character that adjacent wavelet coefficient is formed the connected region similar to former figure owing to value is close is called area coherence.From the level of bit plane, adjacent wavelet coefficient becomes important at close several bit planes, and the significant coefficient around certain coefficient is more many, and its important probability is also just more big.

The present invention is based on above three kinds of correlations, by setting up a plurality of anticipation functions these correlations are carried out full use, thereby lay the foundation for the foundation of subsequent prediction model.

Step 2: for occupying predictive coefficient with the strongest neighbour of position to be encoded correlation, the function of three kinds of predictive coefficients of structure, embody the multiple correlation of itself and coefficient to be encoded, comprise important character state function, significance state weighted direction function, significance state and function.

(1) important character state function

In order to take full advantage of the amplitude correlation between the wavelet coefficient, distinguish described predictive coefficient important at the upper strata bit plane, when the anterior layer bit plane important or unimportant these three kinds of states also, give described predictive coefficient three kinds of different values, to represent the significance state value of described predictive coefficient, its formula is defined as follows:

$S(M_i,p)=\left\{\begin{array}{cc}K& 2^p\&le;M_i\\ 1& 2^{p-1}\&le;M_i<2^p\\ 0& M_i<2^{p-1}\end{array}\right.$

Wherein, M _iRepresent corresponding described predictive coefficient N _iAmplitude, 0≤i≤7 wherein, p represents the current bit plane number of plies of encoding, S (M _i, p) the described predictive coefficient of expression is in the significance state value when the anterior layer bit plane, and K is ratio parameter (positive integer greater than 1).Experiment shows, to same predictive coefficient, the upper strata bit plane important when more important than present bit plane predicting function more obvious, therefore, S (M _i, p) the more big coefficient N that shows _iImportance degree more high.The setting of parameter K is in order to increase the flexibility of construction of function, by adjusting the value of K, can change the importance degree difference of different bit plane levels, for the structure of more complicated anticipation function brings convenience.

(2) significance state weighted direction function

Significance state weighted direction function is on the basis of important character state function, embodies the anticipation function of the cumulative effects of the directional dependency between coefficient in the frequency band and different directions importance emphatically.For comprehensive 8 neighbours occupy the predicting function of coefficient, the present invention adopts the form of linear weighted function summation expression formula to construct significance state weighted direction function f ₁(M), embodying formula is defined as

$f_1\left(M\right)=\underset{i=0}{\overset{7}{\mathrm{\&Sigma;}}}{w}_{i}S(M_i,p)$

W wherein _iThe weight of expression predictive coefficient, the size of embodiment predicting function, S (M _i, p) be the significance state function.Function f is reduced to one-dimensional problem to the higher-dimension problem, has embodied the integrated forecasting effect that a plurality of neighbours occupy coefficient.

For weight w _iSetting, mainly be the experimental result of join probability statistics, and distribute according to the size of predicting function, as shown in table 1.For the HL frequency band, according to correlation by to weak order being by force: Vertical factor＞horizontal coefficients＞diagonal coefficient, according to further The result of statistics, consider the accumulative effect of different directions prediction, make similar probability distribution to merge, the design weight is followed successively by 4,2,1.In like manner can get the predictive coefficient weight of LH frequency band, just the weight of horizontal dimension coefficients is greater than vertical direction.For the HH frequency band, because directivity is not obvious, only weight is divided into 2 classes, namely the weight of level and vertical 4 coefficients is 2, the weight of 4 coefficients in diagonal angle is 1.Utilize the weighted value of table 1 pair significance state weighted direction function to arrange, both distinguished the different predicting function of different directions predictive coefficient, can embody the cumulative effects of different directions again preferably, realized the effective differentiation to probability distribution.In addition, according to statistical experiment, when anterior layer importance far away from upper strata importance, the importance of current vertical direction is near the importance of upper strata to the angular direction, so the K in the important character state function should be made as 4: 1, is classified as a class with these two.

Table 1 neighbour occupies the predictive coefficient weighted value

Predictive coefficient

The HL direction

The LH direction

The HH direction

N 1，N 6	4	2	2
				N 3，N 4	2	4	2
N 0，N 2，N 5，N 7	1	1	1

Utilize significance state weighted direction expression formula, by the structure forecast functional inequality, can realize the preliminary classification to current coefficient to be encoded.The essence of prediction is to distinguish different probability distribution, therefore with f ₁(M) value for the inequality of base configuration the right is very natural and direct, i.e. important character state function classical prescription each discrete point value after the weighting: 32,16,8,4,2,1.So far, the present invention utilizes 8 neighbours to occupy predictive coefficient preliminary classification has for the first time been realized in current position to be encoded, is shown below, and obtains 7 pred1 predicted values, can be 7 classes with current position to be encoded Preliminary division.

$\mathrm{pred}1=\left\{\begin{array}{cc}6& f_1\left(M\right)\&GreaterEqual;32\\ 5& f_1\left(M\right)\&GreaterEqual;16\\ 4& f_1\left(M\right)\&GreaterEqual;8\\ 3& f_1\left(M\right)\&GreaterEqual;4\\ 2& f_1\left(M\right)\&GreaterEqual;2\\ 1& f_1\left(M\right)\&GreaterEqual;1\\ 0& f_1\left(M\right)\&GreaterEqual;0\end{array}\right.$

(3) significance state and function

Significance state and function embody the effect of area coherence between coefficient emphatically, and the expression neighbour occupies the important number of predictive coefficient to the influence of current coefficient to be encoded.Because the significance state of different layers having arrived expression preferably to the influence of current coefficient probability distribution to be encoded in the weighted direction function, therefore, no longer distinguish this layer importance and upper strata importance here.For this reason, at first construct importance discriminant function σ (M _i) this layer importance and the upper strata importance of predictive coefficient is merged, expression formula is specially

${\mathrm{\&sigma;}}_3\left(M_i\right)=\left\{\begin{array}{cc}1& S(M_i,p)\&NotEqual;0\\ 0& S(M_i,p)=0\end{array}\right.$

S (M wherein _i, p) be the significance state function, importance discriminant function σ (M _i) represented predictive coefficient when anterior layer bit plane p whether important.

In order to express the area coherence between coefficient, also be that important coefficient is more many around the current position to be encoded, its important probability is just more big, and directly the mode of significant coefficient number designs significance state and function f around it by counting ₂(M), expression formula is

$f_2\left(M\right)=\underset{i=0}{\overset{7}{\mathrm{\&Sigma;}}}\mathrm{\&sigma;}\left(M_i\right)$

σ (M wherein _i) be the importance discriminant function.

Significance state and function only have 8 discrete values, further, according to statistical experiment, based on significance state and function, the structure forecast functional inequality.Following two kinds of situations are done special processing: the significant coefficient number is 8 and 7 o'clock, because corresponding number of coefficients is less, they is merged into a class; The significant coefficient number is that the probability distribution of 6,5,4 o'clock correspondences is similar substantially, and they are divided into a class.So far, can obtain occupying predictive coefficient to second kind of preliminary classification of current position to be encoded based on the neighbour the corresponding a kind of classification situation of each value of following formula predicted value pred2.

$\mathrm{pred}2=\left\{\begin{array}{cc}5& f_2\left(M\right)\&GreaterEqual;7\\ 4& f_2\left(M\right)\&GreaterEqual;4\\ 3& f_2\left(M\right)\&GreaterEqual;3\\ 2& f_2\left(M\right)\&GreaterEqual;2\\ 1& f_2\left(M\right)\&GreaterEqual;1\\ 0& f_2\left(M\right)\&GreaterEqual;0\end{array}\right.$

Step 3: for other and position to be encoded correlation more weak father, father neighbours, neighbours' predictive coefficient far away, according to its dependency relation with to be encoded, choose above-mentioned a kind of function expression form respectively and construct its anticipation function;

The situation of paternal number P is fairly simple, owing to have only a coefficient, utilizes the important character state function just can show preferably, and the formula of embodying is

g(M _p)＝S(M _p，p)

Wherein, M _pBe the amplitude of paternal number P, obviously, this anticipation function correspondence 0,1,4 three function value.

Father neighbours' FACTOR P N selects significance state weighted direction function for use, and the reference neighbour occupies the anticipation function of coefficient and constructs, and the formula of embodying is

g(M _PN)＝f ₁(M _PN)

Wherein, M _PNFor the amplitude of father neighbours' FACTOR P N, according to experiment, choose 16,8,4,2,1 as corresponding 6 the prediction classification of division points (last class correspondence 0).

The number of neighbours' coefficient FN far away occupies much larger than the neighbour, can the analogy neighbour occupies the coefficient significance state and the function mode is constructed, and expression formula is

$g\left(M_{\mathrm{FN}}\right)=f_2\left(M_{\mathrm{FN}}\right)=\underset{i=0}{\overset{15}{\mathrm{\&Sigma;}}}\mathrm{\&sigma;}\left(M_{\mathrm{FNi}}\right)$

Wherein, M _FNBe the amplitude of neighbours' coefficient correspondence far away, 0≤i≤15 according to experiment, choose 16,8,4,2,1 as corresponding 6 the prediction classification of division points.

So far, on the basis that takes full advantage of three kinds of correlations between the wavelet coefficient, according to selected described predictive coefficient, the present invention has constructed a series of probability distribution anticipation functions, corresponding a plurality of anticipation function expression formulas, as shown in table 2, position to be encoded tentatively can be divided into a plurality of classes.

Table 2 anticipation function table

Anticipation function

The classification number

f 1(M)	7
		f 2(M)	6
g(M P)	3
		g(M PN)	6
g(M FN)	6

Step 4: according to the reduction amplitude of entropy, the multiple dependency prediction function of having constructed is screened, set up a kind of forecast model based on local minimum entropy, according to the actual value of predictive coefficient the wavelet coefficient bit data is predicted as some classification.

Problem for fear of the context dilution, namely since specimen types too much and the problem of the study cost prohibitive that lazy weight causes, effectively distinguish different probability distribution simultaneously, assurance approaches the high-order entropy, the multiple dependency prediction function that utilization of the present invention has been constructed, size according to its predicting function, adopt greedy algorithm that anticipation function is progressively screened, its basic thought is as follows: according to the size of predictive coefficient predicting function, the variation of entropy when considering each prediction inequality of introducing its correspondence successively, if reducing entropy, the introducing of this prediction inequality surpasses threshold value, to predict that then inequality is retained in the last forecast model, a corresponding class predicted value.

In addition, the difference of prediction inequality has put in order different codomain dividing mode corresponding in the forecast model, also just corresponding different entropy.A kind of simple mode is that new prediction inequality is inserted in each codomain division of former forecast model successively, select that division that entropy wherein reduces at most (corresponding minimum conditional entropy), whether the reduction degree of investigating its entropy reaches threshold value, if reach the threshold value requirement, then it is retained in the last forecast model, and entropy is reduced maximum that divide new division as forecast model, otherwise, then it is abandoned.

For narrate convenient for the purpose of, the present invention is defined as follows several concepts: anticipation function inequality formation F, deposit selected prediction inequality, it has divided forecast model finally corresponding; Candidate's anticipation function inequality formation R initially comprises whole anticipation function inequality to be selected, and the order of formation is arranged according to the predicting function size of a last joint definition; The corresponding entropy of a partition value defined of formation F is H _F, the threshold value that entropy reduces is defined as T _H

Progressively the basic process of screening method is as follows:

(1) initialization setting: formation F is initialized as and comprises two nodes, f ₁(M) 〉=72 as a node, f ₁(M) 〉=0 as the caudal knot point, this class between two nodes is divided and has been comprised all bit data; R is initialized as all prediction inequality and sorts from big to small by predicting function.

(2) from candidate's anticipation function inequality formation R, take out the prediction inequality successively and join among the prediction inequality formation F, calculate new entropy of a partition value H; Select entropy to reduce maximum divisions, if its entropy reduces greater than threshold value T _H, should predict then that inequality inserted formation F, the insertion point is exactly that entropy reduces that maximum points; If should be worth less than threshold value T _H, should predict then that inequality abandoned.

Wherein, threshold value T _HSetting should satisfy following requirement: can guarantee that on the one hand prediction classification corresponding sample amount is abundant, avoid the problem of context dilution; The degree of its entropy reduction is enough big on the other hand, makes and can obtain income in code efficiency, is unlikely to increase complexity again meaninglessly.Based on a large amount of statistical experiments, the present invention is with threshold value T _HBe set at 200bit, can satisfy the requirement of above two aspects preferably.In the practical application, according to concrete needs, can adjust this value.

Screening method progressively more than the utilization, all prediction inequality are added forecast model successively according to its predicting function order from big to small, with the foundation of sorted minimal condition entropy as its value of differentiation, determine whether it is selected into model, the process of inserting successively and traveling through has guaranteed that the foundation of model can be at the local implementation optimum, so far, set up the forecast model based on local minimum entropy, as follows:

$\mathrm{pred}=\left\{\begin{array}{cc}15& f_1\left(M\right)\&GreaterEqual;32\\ 14& f_2\left(M\right)\&GreaterEqual;4\\ 13& f_1\left(M\right)\&GreaterEqual;16\\ 12& f_1\left(M\right)\&GreaterEqual;8\\ 11& f_2\left(M\right)\&GreaterEqual;2\\ 10& f_1\left(M\right)\&GreaterEqual;4\\ 9& f_1\left(M\right)\&GreaterEqual;2\\ 8& f_1\left(M\right)\&GreaterEqual;1\\ 7& f\left(M\right)=0,g\left(M_P\right)=4\\ 6& f\left(M\right)=0,g\left(M_{\mathrm{FN}}\right)\&GreaterEqual;2\\ 5& f\left(M\right)=0,g\left(M_{\mathrm{FN}}\right)\&GreaterEqual;1\\ 4& f\left(M\right)=0,g\left(M_{\mathrm{PN}}\right)\&GreaterEqual;8\\ 3& f\left(M\right)=0,g\left(M_P\right)=1\\ 2& f\left(M\right)=0,g\left(M_{\mathrm{PN}}\right)\&GreaterEqual;4\\ 1& f\left(M\right)=0,g\left(M_{\mathrm{PN}}\right)\&GreaterEqual;1\\ 0& f\left(M\right)0,g(\&CenterDot;)=0\end{array}\right.$

This forecast model is divided into 16 bit data stream with whole bit data stream, has approached the high-order entropy of original source.For model is clear directly perceived, the present invention has simplified the form of expression formula, and in fact, the process of division is top-down, when a last prediction inequality is ungratified, just differentiate with next prediction inequality.For example, the complete prediction expression formula of predicted value 6 correspondences is f ₁(M)=0, f ₂(M)=0, g (M _p) ≠ 4, g (M _FN) 〉=2, but other situation analogies obtain.

For the validity of Forecasting Methodology of the present invention is described, following table has provided the JPEG2000 Forecasting Methodology probability distribution situation corresponding with Forecasting Methodology of the present invention.Table 3 has provided the probability distribution of correspondence when the JPEG2000 Forecasting Methodology is got each predicted value, in table 3, predicted value is that the probable value of 2 class correspondence is 3 class greater than predicted value, the probability distribution of the different predicted value correspondences of each direction is little when big when also being, the foundation of JPEG2000 Forecasting Methodology fails to reflect well the difference of bit data probability distribution.And as can be seen from Table 4, the all directions probability distribution is along with successively decreasing of predicted value has monotonicity preferably in the Forecasting Methodology of the present invention, difference between the probability distribution is also more even, we can say that Forecasting Methodology of the present invention distinguished different probability distribution better.

Forecasting Methodology of the present invention has been carried out meticulousr division to whole bit data stream, and probability distribution has better uniformity and consistency.These 2 all is very important: on the one hand, the quantity of wavelet coefficient bit-plane data is very huge, as long as avoid the problem of context dilution, meticulousr division helps to approach littler high-order conditional entropy; Uniform probability distribution helps to improve the efficient of arithmetic coding on the other hand, reduces the study cost of arithmetic encoder, and this also is the obviously place of deficiency of JPEG2000 model.

The corresponding frequency band probability distribution (%) of each predicted value of table 3JPEG2000

The corresponding frequency band probability distribution (%) of each predicted value of table 4 the present invention

Forecasting Methodology precision height of the present invention, thus make it possible to approach the high-order entropy of information source, realized the high efficient coding of wavelet coefficient.Compare with the predictive coding method of still image compression international standard JPEG2000, experimental result is as shown in table 5, under identical compression multiple, recovers the image objective quality and all is significantly improved.

Bit-Plane Encoding Forecasting Methodology based on local minimum entropy of the present invention is particularly suitable for the coding to significant bits in the wavelet coefficient bit plane, and different images is had universality preferably.In addition, described method is not limited to wavelet transformation, is equally applicable to the coding of other multi-scale transform coefficient.

Table 5 the present invention and JPEG2000 predictive coding compression performance be (dB) relatively

For one of ordinary skill in the art, any apparent change of under the prerequisite that does not deviate from connotation of the present invention it being done all will constitute to infringement of patent right of the present invention, with corresponding legal responsibilities.

Claims (2)

1. the image coded prediction method based on local minimum entropy is characterized in that, may further comprise the steps:

Step 1: image is carried out wavelet transformation and wavelet coefficient quantification, with each wavelet coefficient binary number representation, scanning wavelet coefficient bit plane; Choose with the stronger coefficient of position to be encoded correlation as predictive coefficient, comprise that the neighbour occupies coefficient, neighbours' coefficient far away, paternal number and father neighbours' coefficient;

Step 2: for occupying predictive coefficient with the strongest neighbour of position to be encoded correlation, the function of three kinds of predictive coefficients of structure, embody the multiple correlation of itself and coefficient to be encoded, the function of described predictive coefficient comprises important character state function, significance state weighted direction function, significance state and function;

Step 3: for the more weak predictive coefficient of other and position to be encoded correlation, comprise neighbours far away, father, father neighbours' predictive coefficient, according to its dependency relation with to be encoded, choose above-mentioned a kind of function expression form respectively and construct its anticipation function;

Step 4: according to the reduction amplitude of entropy, the multiple dependency prediction function of having constructed is screened, set up a kind of forecast model based on local minimum entropy, according to the actual value of predictive coefficient the wavelet coefficient bit data is predicted as some classification;

Wherein neighbour described in the step 1 to occupy coefficient be 8 coefficient N around the current position to be encoded ₀～N ₇, neighbours' coefficient far away occupies peripheral 16 the coefficient FN of coefficient for the neighbour ₀～FN ₁₅Described paternal number is the FACTOR P of the low one-level frequency band correspondence position in current position to be encoded, and 8 neighbours that father neighbours' coefficient enclosed for paternal several weeks occupy FACTOR P N ₀～PN ₇

In the described step 2, the significance state anticipation function be used for distinguishing described predictive coefficient important at the upper strata bit plane, when the anterior layer bit plane important or unimportant these three kinds of states also, its expression formula is defined as follows:

$S(M_i,p)=\left\{\begin{array}{cc}K& 2^p\&le;M_i\\ 1& 2^{p-1}\&le;M_i<2^p\\ 0& M_i<2^{p-1}\end{array}\right.$

Wherein, M _iRepresent described predictive coefficient N _iAmplitude, 0≤i≤7 wherein, p represents the current bit plane number of plies of encoding, S (M _i, p) functional value is represented described predictive coefficient in the significance state value when the anterior layer bit plane, K is ratio parameter, is the positive integer greater than 1;

In the described step 2, significance state weighted direction anticipation function is the important character state function weighted sum to described predictive coefficient, and assigns weight for each predictive coefficient according to the size of predictive coefficient and current position to be encoded correlation:

$f_1\left(M\right)=\underset{i=0}{\overset{7}{\mathrm{\&Sigma;}}}{w}_{i}S(M_i,p)$

F wherein ₁(M) the weighted direction anticipation function value of the described predictive coefficient of expression, w _iThe weight of representing described predictive coefficient, S (M _i, p) be the significance state anticipation function;

In the described step 2, significance state and function are used for distinguishing the important number of described predictive coefficient not simultaneously to the influence of probability distribution, and its expression formula is defined as follows:

$f_2\left(M\right)=\underset{i=0}{\overset{7}{\mathrm{\&Sigma;}}}\mathrm{\&sigma;}\left(M_i\right)$

F wherein ₂(M) the anticipation function value of the described predictive coefficient of expression, σ (M _i) represent described predictive coefficient at the importance discriminant value of bit plane p, whether important on the present bit plane in order to distinguish this predictive coefficient, be defined as follows:

${\mathrm{\&sigma;}}_3\left(M_i\right)=\left\{\begin{array}{cc}1& S(M_i,p)\&NotEqual;0\\ 0& S(M_i,p)=0\end{array}\right.$

S (M wherein _i, p) be the significance state anticipation function;

In the described step 4, size according to the predictive coefficient predicting function, the variation of entropy when considering each prediction inequality of introducing its correspondence successively, if reducing entropy, the introducing of this prediction inequality surpasses threshold value, to predict that then inequality is retained in the last forecast model, a corresponding class predicted value; Set up the forecast model based on local minimum entropy, as follows:

$\mathrm{pred}=\left\{\begin{array}{cc}15& f_1\left(M\right)\&GreaterEqual;32\\ 14& f_2\left(M\right)\&GreaterEqual;4\\ 13& f_1\left(M\right)\&GreaterEqual;16\\ 12& f_1\left(M\right)\&GreaterEqual;8\\ 11& f_2\left(M\right)\&GreaterEqual;2\\ 10& f_1\left(M\right)\&GreaterEqual;4\\ 9& f_1\left(M\right)\&GreaterEqual;2\\ 8& f_1\left(M\right)\&GreaterEqual;1\\ 7& f\left(M\right)=0,g\left(M_P\right)=4\\ 6& f\left(M\right)=0,g\left(M_{\mathrm{FN}}\right)\&GreaterEqual;2\\ 5& f\left(M\right)=0,g\left(M_{\mathrm{FN}}\right)\&GreaterEqual;1\\ 4& f\left(M\right)=0,g\left(M_{\mathrm{PN}}\right)\&GreaterEqual;8\\ 3& f\left(M\right)=0,g\left(M_P\right)=1\\ 2& f\left(M\right)=0,g\left(M_{\mathrm{PN}}\right)\&GreaterEqual;4\\ 1& f\left(M\right)=0,g\left(M_{\mathrm{PN}}\right)\&GreaterEqual;1\\ 0& f\left(M\right)=0,g(\&CenterDot;)=0\end{array}\right.$

This forecast model is divided into 16 bit data stream with whole bit data stream, has approached the high-order entropy of original source;

g(M _p)＝S(M _p,p)

Wherein, M _pBe the amplitude of paternal number P, father neighbours' FACTOR P N selects significance state weighted direction function for use, and the reference neighbour occupies the anticipation function of coefficient and constructs, and the formula of embodying is

g(M _PN)＝f ₁(M _PN)

Wherein, M _PNAmplitude for father neighbours' FACTOR P N; The number of neighbours' coefficient FN far away occupies much larger than the neighbour, and the analogy neighbour occupies the coefficient significance state and the function mode is constructed, and expression formula is

$g\left(M_{\mathrm{FN}}\right)=f_2\left(M_{\mathrm{FN}}\right)=\underset{i=0}{\overset{15}{\mathrm{\&Sigma;}}}\mathrm{\&sigma;}\left(M_{\mathrm{FNi}}\right)$

Wherein, M _FNBe the amplitude of neighbours' coefficient correspondence far away, 0≤i≤15.

2. a kind of image coded prediction method based on local minimum entropy as claimed in claim 1 is characterized in that:

In the described step 4, adopt greedy algorithm to screen anticipation function, its distinguishing rule is that choosing of certain anticipation function can make the entropy of its corresponding prediction classification reduce amplitude greater than pre-set threshold.

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