CN103903232A - Method for conducting image denoising and enhancing in wavelet domain through evolutionary programming - Google Patents

Abstract

The invention provides a method for conducting image denoising and enhancing in a wavelet domain through evolutionary programming. An algorithm aims at conducting denoising and enhancing on an unmanned aerial vehicle image in the wavelet domain through evolutionary programming. The method includes the steps of converting the image into the wavelet domain through double-tree discrete wavelets, estimating a denoising threshold value through evolutionary programming, conducting soft threshold value denoisting on a high-resolution coefficient in a high-frequency sub-band, estimating enhancing parameters in the wavelet domain through evolutionary programming, enhancing low-resolution coefficients in the high-frequency sub-band, and conducting wavelet inverse transformation to obtain a reconstructed image. According to the method, the image which is quite excellent in vision quality and processed through denoising can be obtained through the designed algorithm of conducting image denoising and enhancing in the wavelet domain through evolutionary programming, and edge and texture detail information can be well reserved.

Description

Utilize evolutional programming to carry out the method for image noise reduction and enhancement in wavelet field

Technical field

The present invention relates to technical field of image processing and intelligent computation field, particularly a kind of adaptive denoising and Enhancement Method combining based on two tree discrete wavelet packets and evolutional programming.

Background technology

In unmanned plane image denoising, Analysis On Multi-scale Features analysis is very important, and small echo is processed and is also very important simultaneously.The basic scheme of the image noise reduction and enhancement based on small echo is as follows: 1) wavelet decomposition; 2) at different scale to wavelet coefficient correction; 3) according to the wavelet coefficient restored image of revising.Some image enchancing methods only consider that details strengthens now, and ignore noise-cut or inhibition.Some image enchancing methods only consider to reduce noise and ignore details strengthen.Some image enchancing methods had both been considered the noise-cut enhancing of also paying attention to detail.But they estimate noise-removed threshold value with the static attribute of noise at major part.In fact, this is very difficult, because accurate noise static attribute can not be known in advance or accurately estimate.In addition, their major part strengthens details by user intervention to can obtain a good result.This will limit their widespread use in real image strengthens.

Summary of the invention

Object of the present invention is intended to solve above-mentioned technological deficiency, improves the effect of two tree discrete wavelet denoise algorithm and protects better edge and the detailed information of image.

In order to achieve the above object, the present invention proposes the image noise reduction and enhancement methods of the two tree of a kind of self-adaptation combining based on two tree discrete wavelets and evolutional programming discrete wavelet packet, comprises following step:

S1: adopt two tree discrete wavelets to carrying out the decomposition of L layer containing noisy image g, the high-frequency sub-band (being detail coefficients matrix) that obtains low frequency sub-band (being approximation coefficient matrix) and 1st～L decomposition layer of L decomposition layer, wherein detail coefficients matrix is divided into again high resolving power matrix of coefficients and low resolution matrix of coefficients;

S2: adopt wavelet threshold denoising method to process for high resolving power matrix of coefficients, obtain the high resolving power matrix of coefficients after denoising, specific as follows:

S2.1: utilize evolutional programming to estimate the optimum noise-removed threshold value that each high resolving power matrix of coefficients is corresponding.

S2.1.1: the individuality using initial noise-removed threshold value corresponding each high resolving power matrix of coefficients as initial population, random initializtion colony also carries out fitness calculating to all individualities, obtain the fitness of each individuality, wherein, s decomposition layer, a l individual fitness computing formula are as follows:

$\mathrm{function}\left({\mathrm{\λ}}_s^l\right)=\frac{N{\left|\right|W_s^l-{\mathrm{\λ}}_s^l\left|\right|}^2}{{\left(N_0\right)}^2}$

Wherein,

be the wavelet coefficient of s decomposition layer, a l high resolving power matrix of coefficients, N is the number of wavelet coefficient,

s decomposition layer, initial noise-removed threshold value that a l high resolving power matrix of coefficients is corresponding, N ₀to be less than

the number of wavelet coefficient, || || being a norm at function space, is generally L ²norm, i.e. Euclidean distance.

S2.1.2: utilize the variation rule redesigning to make a variation to colony, obtain filial generation of future generation, wherein variation rule is as follows:

(1) if | d ^j-d ^j-1|>=a,

x ^j+1(k)＝x ^j(k)+(d ^j-d ^j-1)*|N(0,1)|,age ^j+1(k)＝1

(2) if X ^{max, j}-X ^{min, j}>=b,

x ^j+1(k)＝x ^j(k)+(X ^max,j-X ^min,j)*N(0,1),age ^j+1(k)＝1

(3) if do not meet (1) (2),

x ^j+1(k)＝x ^j(k)+age ^j(k)*c*N(0,1),age ^j+1(k)＝age ^j(k)+1

Wherein, N (0,1) represents the one-dimensional random normal distribution that average is 0, variance is 1, X ^{max, j}be j for the maximal value in population, X ^{min, j}be j for the minimum value in population, x ^j(k) represent that j is for k individual value in colony, d ^jrepresent the center of j for population, age ^j(k) be used for being recorded to j for time k individual variation stagnate number of times, a, b and c are adjustable parameter, choose according to experiment.

S2.1.3: the fitness that calculates each filial generation, and the fitness of parent and offspring individual is compared between two, utilize random q competition system of selection, i.e. algorithm of tournament selection pattern, q >=1st, the parameter of selection algorithm, selects the most successful individual one-tenth as follow-on parent.

S2.1.4: repeating step S2.1.2 and step S2.1.3, until meet end condition, obtain the optimum noise-removed threshold value of each high resolving power matrix of coefficients

S2.2: utilize soft-threshold function to carry out denoising to high resolving power matrix of coefficients, obtain the high resolving power matrix of coefficients after denoising, wherein soft-threshold function is as follows:

$w_{{\mathrm{\&lambda;}}_s^{\&prime;l}}=\left\{\begin{array}{c}\left[\mathrm{sign}\left(w_s^l\right)\right]\left(\right|w_s^l|-{\mathrm{\&lambda;}}_s^{\&prime;l}),\left|w_s^l\right|\&GreaterEqual;{\mathrm{\&lambda;}}_s^{\&prime;l}\\ 0,\left|w_s^{\&prime;l}\right|<{\mathrm{\&lambda;}}_s^{\&prime;l}\end{array}\right.$

Wherein,

the wavelet coefficient after s decomposition layer, a l high resolving power matrix of coefficients threshold value quantizing,

the wavelet coefficient of s decomposition layer, a l high resolving power matrix of coefficients, s decomposition layer, optimum noise-removed threshold value that a l high resolving power matrix of coefficients is corresponding.

S3: carry out small echo enhancing for low resolution matrix of coefficients, the low resolution matrix of coefficients after being enhanced, specific as follows:

S3.1: referring to the step in S2.1, the optimum that utilizes evolutional programming to estimate each decomposition layer strengthens threshold value;

S3.2: utilize the optimum of each decomposition layer that S3.1 obtains to strengthen threshold value, strengthen low resolution matrix of coefficients, the low resolution matrix of coefficients after being enhanced, wherein, the wavelet coefficient enhancing formula that in s decomposition layer, a r subband, i is capable, j is listed as is as follows:

$g_s^r[i,j]=\left\{\begin{array}{c}{f}_s^r[i,j],\left|f_s^r\right[i,j\left]\right|<T_s^{\&prime;r}\\ \mathrm{aa}*\max f_s^r[i,j]\left\{\mathrm{sign}\right[\mathrm{cc}\left(y_s^r\right[i,j]-\mathrm{bb})]-\mathrm{sign}[-\mathrm{cc}\left(y_s^r\right[i,j]+\mathrm{bb})\left]\right\},\left|f_s^r\right[i,j\left]\right|\&GreaterEqual;T_s^{\&prime;r}\end{array}\right.$

Wherein,

the wavelet coefficient that in s the decomposition layer, a r subband after strengthening, i is capable, j is listed as, the wavelet coefficient that i is capable in s decomposition layer, a r subband, j is listed as,

the optimum that is s decomposition layer, a r subband strengthens threshold value, max

be

in the maximal value of all wavelet coefficients,

will

value after normalization,

its span is [1,1], and s=1,2 ..., L, r=1,2,3,4.Aa, bb, cc is adjustable parameter, can choose according to experiment.

S4: utilize the low resolution matrix of coefficients after high resolving power matrix of coefficients and the enhancing after approximation coefficient matrix and denoising, image is carried out to wavelet reconstruction, obtain the image after denoising and enhancing.

Parameter d used in step S2.1 ^jrepresent the center of j for population, its computing formula is as follows:

$d^j=\frac{\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{X}^j\left(k\right)}{m}$

Wherein, X ^j(k) represent that j is for value individual in population, m represents quantity individual in population.

Beneficial effect

The present invention is by utilizing two tree discrete wavelets and evolutional programming for unmanned plane image minimizing noise and strengthening details, the image noise reduction and enhancement method of designing not only can be removed noise effectively, and can be by coming preserving edge and grain details at wavelet field Enhanced feature.

Brief description of the drawings

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the sub band structure schematic diagram that two-layer two tree discrete wavelets of one embodiment of the invention decompose.

Embodiment

Describe embodiments of the invention below in detail, the example of described embodiment is shown in the drawings, and wherein same or similar label represents same or similar element or has the element of identical or similar functions from start to finish.Be exemplary below by the embodiment being described with reference to the drawings, only for explaining the present invention, and can not be interpreted as limitation of the present invention.

As shown in Figure 1, embodiments of the invention utilize the image noise reduction and enhancement algorithm of evolutional programming in wavelet field, comprise following step:

Step S1, the two tree of utilization discrete wavelets arrive wavelet field the picture breakdown gathering.

In one embodiment of the invention, first, read in containing noisy picture signal, i.e. noisy image g.Wherein, the pixel value that noisy image g locates at pixel (i, j) can be expressed as g (i, j)=f (i, j)+n (i, j), i, and j=1,2 ..., m.Wherein, g (i, j) be that noisy image g is at pixel (i, j) pixel value of locating, f (i, j) is that the original image f of not Noise is at pixel (i, j) pixel value of locating, n (i, j) is the noise figure that noise matrix n locates at pixel (i, j).Then, adopt two tree discrete wavelets to decomposing containing noisy image g, obtain high-frequency sub-band and low frequency sub-band, namely obtained its detail coefficients matrix and approximation coefficient matrix, wherein detail coefficients matrix is divided into again high resolving power matrix of coefficients and low resolution matrix of coefficients.Be illustrated in figure 2 the two-layer pair of sub band structure schematic diagram that tree wavelet decomposition obtain of an example.

Wavelet threshold denoising algorithm utilizes a kind of threshold function table exactly, processes each wavelet coefficient Y of all high-frequency sub-band of noisy image _ij, obtain threshold value quantizing wavelet coefficient after treatment, then pass through wavelet inverse transformation, obtain the estimator f'=W of reconstructed image ^-1x', wherein W ^-1for wavelet inverse transformation operator, X' is the low frequency sub-band LL of noisy image g _jwavelet coefficient and the matrix of the wavelet coefficient composition of threshold value quantizing high-frequency sub-band after treatment.

Step S2, adopts wavelet threshold denoising method to process for high resolving power matrix of coefficients, obtains the high resolving power matrix of coefficients after denoising.

Image carries out after wavelet decomposition, in high frequency sub-image, has a large amount of image detail informations.But, in these sub-images, also have much noise.The smoothing function of wavelet transformation can help us to reduce picture noise, but it may not meet our demand.Wavelet transformation also can help us to reduce some noises, but still has much noise in high frequency sub-image.If we now strengthen high frequency coefficient, image detail information and noise all can be enhanced.We reduce the noise of high frequency sub-image by nonlinear method.Because noise is different in the characteristic of different high frequency sub-images, different soft-thresholds is used in different high frequency sub-images and reduces noise.

But the noise-removed threshold value obtaining by classic method is difficult.In fact, SGVA(d) curve is just as nonlinear multimodal function.Use EP is solved this problem by we.EP can find fast Approximate Global Optimal Solution in a large solution space.We will obtain noise-removed threshold value in wavelet field with EP.Particularly, can be divided into following 2 little steps:

Step S2.1, utilizes evolutional programming to estimate the optimum noise-removed threshold value that each high resolving power matrix of coefficients is corresponding.

Step S2.1.1, the individuality using initial noise-removed threshold value corresponding each high resolving power matrix of coefficients as initial population, random initializtion colony also carries out fitness calculating to all individualities, obtains the fitness of each individuality.

Evolutionary Programming Algorithm is a kind of random search algorithm based on population.Therefore, each Evolutionary Programming Algorithm can safeguard that one by the alternative population being deconstructed into.The first step that application Evolutionary Programming Algorithm solves optimization problem is to produce an initial population.The standard method that produces initial population is in feasible zone, to produce random value, and distributes to each chromosomal each gene.The random target of selecting is to guarantee that initial population is the even expression of whole search volume.If initial population does not cover search volume, likely make the searched process of uncovered area ignore.At this, our individuality using initial noise-removed threshold value corresponding high frequency coefficient matrix as initial population, and its colony is carried out to random initializtion.

The fitness of each individuality successfully predicts that with it the ability of next output symbol measures.Use a symbol sebolic addressing for this reason.First symbol of sequence is passed to each individuality, and the symbol doping is compared with next symbol.Afterwards using next symbol as input, this process of iteration in whole sequence.The individuality the most repeatedly with correct Prediction is considered to optimal individuality.At this, by GCV(Generalized Cross Validation) definition fitness function as follows:

$\mathrm{function}\left({\mathrm{\&lambda;}}_s^l\right)=\frac{N{\left|\right|W_s^l-{\mathrm{\&lambda;}}_s^l\left|\right|}^2}{{\left(N_0\right)}^2}$

Wherein, be the wavelet coefficient of s decomposition layer, a l high resolving power matrix of coefficients, N is the number of wavelet coefficient,

s decomposition layer, initial noise-removed threshold value that a l high resolving power matrix of coefficients is corresponding, N ₀to be less than

the number of wavelet coefficient, || || being a norm at function space, is generally L ²norm, i.e. Euclidean distance.

Step S2.1.2, utilizes the variation rule redesigning to make a variation to colony, obtains filial generation of future generation.

Because variation is the only resource from variant to evolutional programming colony that introduce, therefore in the design of mutation operator, consider that the balance of explore-exploitation is very important.The process of variation should promote the exploration at the initial stage of searching for, the ensuring coverage large search volume of trying one's best.After the initial exploratory stage, the information about search volume that should allow individual exploitation to obtain, to improve and to adjust solution.Some mutation operators of having developed, are reflecting this balance in varying degrees.For this reason, the new variation rule designing in the present invention is as follows:

(1) if | d ^j-d ^j-1|>=a,

x ^j+1(k)＝x ^j(k)+(d ^j-d ^j-1)*|N(0,1)|,age ^j+1(k)＝1

(2) if X ^{max, j}-X ^{min, j}>=b,

x ^j+1(k)＝x ^j(k)+(X ^max,j-X ^min,j)*N(0,1),age ^j+1(k)＝1

(3) if do not meet (1) (2),

x ^j+1(k)＝x ^j(k)+age ^j(k)*c*N(0,1),age ^j+1(k)＝age ^j(k)+1

Wherein, N (0,1) represents the one-dimensional random normal distribution that average is 0, variance is 1, X ^{max, j}be j for the maximal value in population, X ^{min, j}be j for the minimum value in population, x ^j(k) represent that j is for k individual value in colony, d ^jrepresent the center of j for population, age ^j(k) be used for being recorded to j for time k individual variation stagnate number of times, a, b and c are adjustable parameter, choose according to experiment.

Step S2.1.3, calculates the fitness of each filial generation, and the fitness of parent and offspring individual is compared between two, utilize random q competition system of selection, be algorithm of tournament selection pattern, q >=1st, the parameter of selection algorithm, selecting the most successful individuality becomes follow-on parent.Wherein, the step of algorithm of tournament selection pattern is as follows:

(1) the population P'(t that μ the filial generation group of individuals population P (t) of the individual composition of μ parent being produced after the computing that once makes a variation with P (t) becomes) combine, form one and contain altogether 2 μ the P of group of individuals (t) ∪ P'(t), be designated as I;

(2) to each individual x _i∈ I, q individuality of random selection from I, and by q individual fitness function value F _j(j ∈ (1,2 ..., q)) and x _ifitness function value compare, calculate fitness function value in this q individuality and compare x _ithe number of individuals w of fitness function value difference _i, and w _ias x _iscore, wherein w _i∈ (0,1 ..., q).

(3) at all 2 μ individualities all through after this comparison procedure, by the score w of each individuality _isort, select μ the individuality with top score as population of future generation.

Step S2.1.4, repeating step S2.1.2 and step S2.1.3, until meet end condition, obtain the optimum noise-removed threshold value of each high resolving power matrix of coefficients

.

In evolutional programming, the continuous iteration of mutation operator is carried out, until meet end condition.The simplest end condition is the algebraically of restriction evolutional programming or the number of times that calls fitness function.This restriction can not be too little, goes to explore unknown space otherwise evolutional programming does not have the sufficient time.

Except the restriction execution time, another standard whether restraining for definite population is also through conventional.When convergence can undemandingly be defined as population and becomes stable, in other words, while not having exactly gene or performance characteristic to change in population.Below some convergence criterions of commonly using.

● in the time all not improving in constant generations, stop.As monitor the fitness of optimum individual, if give in the time window of sizing and significantly do not upgrade at one, evolutional programming can stop.On the contrary, if this condition does not meet, obtain larger exploration space by other mechanism to increase diversity, as increased variation probability and variation number of times.

● in the time not changing in population, stop.In constant generations, the average change amount of gene information is too little, and evolutional programming can stop.

● in the time obtaining an acceptable solution, stop.If x ^*(t) optimal value of expression objective function, as optimum individual x _i, meet f (x _i)≤| f (x)-ε |, an acceptable solution is found.ε is error thresholds, if excessive, it is poor that accepting of finding separated; If too small, evolutional programming is difficult to stop.

● in the time that approaching 0, objective function slope stops.

Step S2.2, selects soft-threshold function to carry out denoising to high resolving power matrix of coefficients, and wherein soft-threshold function is as follows:

$w_{{\mathrm{\&lambda;}}_s^{\&prime;l}}=\left\{\begin{array}{c}\left[\mathrm{sign}\left(w_s^l\right)\right]\left(\right|w_s^l|-{\mathrm{\&lambda;}}_s^{\&prime;l}),\left|w_s^l\right|\&GreaterEqual;{\mathrm{\&lambda;}}_s^{\&prime;l}\\ 0,\left|w_s^{\&prime;l}\right|<{\mathrm{\&lambda;}}_s^{\&prime;l}\end{array}\right.$

Wherein,

the wavelet coefficient after s decomposition layer, a l high resolving power matrix of coefficients threshold value quantizing,

the wavelet coefficient of s decomposition layer, a l high resolving power matrix of coefficients,

s decomposition layer, optimum noise-removed threshold value that a l high resolving power matrix of coefficients is corresponding.

Step S3, carries out small echo enhancing for low resolution matrix of coefficients, and the low resolution matrix of coefficients after being enhanced is specific as follows:

Step S3.1, the optimum that utilizes evolutional programming to estimate each decomposition layer strengthens threshold value;

Step S3.1.1, individuality using initial enhancing threshold value corresponding each low resolution matrix of coefficients as initial population, random initializtion colony also carries out fitness calculating to all individualities, obtain the fitness of each individuality, wherein, s decomposition layer, a r individual fitness computing formula are as follows:

$\mathrm{function}\left(T_s^r\right)=\frac{N{\left|\right|W_s^r-T_s^r\left|\right|}^2}{{\left(N_0\right)}^2}$

Wherein, be the wavelet coefficient of s decomposition layer, a r low resolution matrix of coefficients, N is the number of wavelet coefficient,

s decomposition layer, initial enhancing threshold value that a r low resolution matrix of coefficients is corresponding, N ₀to be less than the number of wavelet coefficient, || || being a norm at function space, is generally L ²norm, i.e. Euclidean distance.

Step S3.1.2, utilizes the variation rule redesigning to make a variation to colony, obtains filial generation of future generation, and wherein variation rule is as follows:

(1) if | d ^j-d ^j-1|>=a,

x ^j+1(k)＝x ^j(k)+(d ^j-d ^j-1)*|N(0,1)|,age ^j+1(k)＝1

(2) if X ^{max, j}-X ^{min, j}>=b,

x ^j+1(k)＝x ^j(k)+(X ^max,j-X ^min,j)*N(0,1),age ^j+1(k)＝1

(3) if do not meet (1) (2),

x ^j+1(k)＝x ^j(k)+age ^j(k)*c*N(0,1),age ^j+1(k)＝age ^j(k)+1

Wherein, N (0,1) represents the one-dimensional random normal distribution that average is 0, variance is 1, X ^{max, j}be j for the maximal value in population, X ^{min, j}be j for the minimum value in population, x ^j(k) represent that j is for k individual value in colony, d ^jrepresent the center of j for population, age ^j(k) be used for being recorded to j for time k individual variation stagnate number of times, a, b and c are adjustable parameter, choose according to experiment.

Step S3.1.3, calculates the fitness of each filial generation, and the fitness of parent and offspring individual is compared between two, utilize random q competition system of selection, be algorithm of tournament selection pattern, q >=1st, the parameter of selection algorithm, selects the most successful individual one-tenth as follow-on parent.Wherein, the step of algorithm of tournament selection pattern is as follows:

(1) the population P'(t that μ the filial generation group of individuals population P (t) of the individual composition of μ parent being produced after the computing that once makes a variation with P (t) becomes) combine, form one and contain altogether 2 μ the P of group of individuals (t) ∪ P'(t), be designated as I;

(2) to each individual x _i∈ I, q individuality of random selection from I, and by q individual fitness function value F _j(j ∈ (1,2 ..., q)) and x _ifitness function value compare, calculate fitness function value in this q individuality and compare x _ithe number of individuals w of fitness function value difference _i, and w _ias x _iscore, wherein w _i∈ (0,1 ..., q).

(3) at all 2 μ individualities all through after this comparison procedure, by the score w of each individuality _isort, select μ the individuality with top score as population of future generation.

Step S3.1.4, repeating step S3.1.2 and step S3.1.3, until meet end condition, the optimum that obtains each low resolution matrix of coefficients strengthens threshold value

.

Step 3.2, utilize the optimum of each decomposition layer that S3.1 obtains to strengthen threshold value, strengthen low resolution matrix of coefficients, the low resolution matrix of coefficients after being enhanced, wherein, in s decomposition layer, a r subband i wavelet coefficient capable, j row to strengthen formula as follows:

$g_s^r[i,j]=\left\{\begin{array}{c}{f}_s^r[i,j],\left|f_s^r\right[i,j\left]\right|<T_s^{\&prime;r}\\ \mathrm{aa}*\max f_s^r[i,j]\left\{\mathrm{sign}\right[\mathrm{cc}\left(y_s^r\right[i,j]-\mathrm{bb})]-\mathrm{sign}[-\mathrm{cc}\left(y_s^r\right[i,j]+\mathrm{bb})\left]\right\},\left|f_s^r\right[i,j\left]\right|\&GreaterEqual;T_s^{\&prime;r}\end{array}\right.$

Wherein,

the wavelet coefficient that in s the decomposition layer, a r subband after strengthening, i is capable, j is listed as, the wavelet coefficient that i is capable in s decomposition layer, a r subband, j is listed as, the optimum that is s decomposition layer, a r subband strengthens threshold value, max

be

in the maximal value of all wavelet coefficients,

will value after normalization,

its span be [1,1, and s=1,2 ..., L, r=1,2,3,4.Aa, bb, cc is adjustable parameter, can choose according to experiment.

S4: image is carried out to wavelet reconstruction, obtain the image after denoising and enhancing.

Utilize the low resolution matrix of coefficients after high resolving power matrix of coefficients and the enhancing after approximation coefficient matrix and denoising, image is carried out to wavelet reconstruction, obtain the image after denoising and enhancing.

The present invention utilizes the low resolution matrix of coefficients after high resolving power matrix of coefficients and the enhancing after approximation coefficient matrix and denoising, and image is carried out to wavelet reconstruction, obtains the image after denoising and enhancing.

According to the adaptive denoising and the Enhancement Method that combine based on two tree discrete wavelet packets and evolutional programming of the embodiment of the present invention, carry out image noise reduction and enhancement by utilizing evolutional programming estimation noise-removed threshold value and strengthening parameter, not only picture noise effectively of the denoise algorithm of designing, and can retain well edge and the detailed information of image.

Although illustrated and described embodiments of the invention, for the ordinary skill in the art, be appreciated that without departing from the principles and spirit of the present invention and can carry out multiple variation, amendment, replacement and modification to these embodiment, scope of the present invention is by claims and be equal to and limit.

Claims (2)

1. utilize evolutional programming to carry out the method for image noise reduction and enhancement in wavelet field, it is characterized in that comprising the following steps:

S1: adopt two tree discrete wavelets to carrying out the decomposition of L layer containing noisy image g, obtain the low frequency sub-band of L decomposition layer, it is the high-frequency sub-band of approximation coefficient matrix and 1st～L decomposition layer, be detail coefficients matrix, wherein detail coefficients matrix is divided into again high resolving power matrix of coefficients and low resolution matrix of coefficients;

S2: adopt wavelet threshold denoising method to process for high resolving power matrix of coefficients, obtain the high resolving power matrix of coefficients after denoising, specific as follows:

S2.1: utilize evolutional programming to estimate the optimum noise-removed threshold value that each high resolving power matrix of coefficients is corresponding;

S2.1.1: the individuality using initial noise-removed threshold value corresponding each high resolving power matrix of coefficients as initial population, random initializtion colony also carries out fitness calculating to all individualities, obtain the fitness of each individuality, wherein, s decomposition layer, a l individual fitness computing formula are as follows:

$\mathrm{function}\left({\mathrm{\&lambda;}}_s^l\right)=\frac{N{\left|\right|W_s^l-{\mathrm{\&lambda;}}_s^l\left|\right|}^2}{{\left(N_0\right)}^2}$

Wherein,

be the wavelet coefficient of s decomposition layer, a l high resolving power matrix of coefficients, N is the number of wavelet coefficient,

s decomposition layer, initial noise-removed threshold value that a l high resolving power matrix of coefficients is corresponding, N ₀to be less than

the number of wavelet coefficient, || || be a norm at function space;

S2.1.2: utilize the variation rule redesigning to make a variation to colony, obtain filial generation of future generation, wherein variation rule is as follows:

(1) if | d ^j-d ^j-1|>=a,

x ^j+1(k)=x ^j(k)+(d ^j-d ^j-1)*|N(0,1)|,age ^j+1(k)=1

(2) if X ^{max, j}-X ^{min, j}>=b,

x ^j+1(k)=x ^j(k)+(X ^max,j-X ^min,j)*N(0,1),age ^j+1(k)=1

(3) if do not meet (1) (2),

x ^j+1(k)=x ^j(k)+age ^j(k)*c*N(0,1),age ^j+1(k)=age ^j(k)+1

Wherein, N (0,1) represents the one-dimensional random normal distribution that average is 0, variance is 1, X ^{max, j}be j for the maximal value in population, X ^{min, j}be j for the minimum value in population, x ^j(k) represent that j is for k individual value in colony, d ^jrepresent the center of j for population, age ^j(k) be used for being recorded to j for time k individual variation stagnate number of times, a, b and c are adjustable parameter, choose according to experiment;

S2.1.3: the fitness that calculates each filial generation, and the fitness of parent and offspring individual is compared between two, utilize random q competition system of selection, i.e. algorithm of tournament selection pattern, q >=1st, the parameter of selection algorithm, selects the most successful individual one-tenth as follow-on parent;

S2.1.4: repeating step S2.1.2 and step S2.1.3, until meet end condition, obtain the optimum noise-removed threshold value of each high resolving power matrix of coefficients

;

S2.2: utilize soft-threshold function to carry out denoising to high resolving power matrix of coefficients, obtain the high resolving power matrix of coefficients after denoising, wherein soft-threshold function is as follows:

$w_{{\mathrm{\&lambda;}}_s^{\&prime;l}}=\left\{\begin{array}{c}\left[\mathrm{sign}\left(w_s^l\right)\right]\left(\right|w_s^l|-{\mathrm{\&lambda;}}_s^{\&prime;l}),\left|w_s^l\right|\&GreaterEqual;{\mathrm{\&lambda;}}_s^{\&prime;l}\\ 0,\left|w_s^{\&prime;l}\right|<{\mathrm{\&lambda;}}_s^{\&prime;l}\end{array}\right.$

Wherein,

the wavelet coefficient after s decomposition layer, a l high resolving power matrix of coefficients threshold value quantizing,

the wavelet coefficient of s decomposition layer, a l high resolving power matrix of coefficients,

s decomposition layer, optimum noise-removed threshold value that a l high resolving power matrix of coefficients is corresponding;

S3: carry out small echo enhancing for low resolution matrix of coefficients, the low resolution matrix of coefficients after being enhanced, specific as follows:

S3.1: referring to the step in S2.1, the optimum that utilizes evolutional programming to estimate each decomposition layer strengthens threshold value;

S3.2: utilize the optimum of each decomposition layer that S3.1 obtains to strengthen threshold value, strengthen low resolution matrix of coefficients, the low resolution matrix of coefficients after being enhanced, wherein, the wavelet coefficient enhancing formula that in s decomposition layer, a r subband, i is capable, j is listed as is as follows:

$g_s^r[i,j]=\left\{\begin{array}{c}{f}_s^r[i,j],\left|f_s^r\right[i,j\left]\right|<T_s^{\&prime;r}\\ \mathrm{aa}*\max f_s^r[i,j]\left\{\mathrm{sign}\right[\mathrm{cc}\left(y_s^r\right[i,j]-\mathrm{bb})]-\mathrm{sign}[-\mathrm{cc}\left(y_s^r\right[i,j]+\mathrm{bb})\left]\right\},\left|f_s^r\right[i,j\left]\right|\&GreaterEqual;T_s^{\&prime;r}\end{array}\right.$

Wherein,

the wavelet coefficient that in s the decomposition layer, a r subband after strengthening, i is capable, j is listed as,

the wavelet coefficient that i is capable in s decomposition layer, a r subband, j is listed as,

the optimum that is s decomposition layer, a r subband strengthens threshold value, max

be

in the maximal value of all wavelet coefficients, will value after normalization, its span is [1,1], and s=1,2 ..., L, r=1,2,3,4, aa, bb, cc is adjustable parameter, can choose according to experiment;

S4: utilize the low resolution matrix of coefficients after high resolving power matrix of coefficients and the enhancing after approximation coefficient matrix and denoising, image is carried out to wavelet reconstruction, obtain the image after denoising and enhancing.

2. according to claim 1ly utilize evolutional programming to carry out the method for image noise reduction and enhancement in wavelet field, it is characterized in that parameter d used in step S2.1 ^jrepresent the center of j for population, its computing formula is as follows:

$d^j=\frac{\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{X}^j\left(k\right)}{m}$

Wherein, X ^j(k) represent that j is for value individual in population, m represents quantity individual in population.

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