CN103761719A - Self-adaptive wavelet threshold de-noising method based on neighborhood correlation - Google Patents

Abstract

The invention discloses a self-adaptive wavelet threshold de-noising method based on neighborhood correlation. The method includes the following steps that (1) wavelet transformation is performed on images with noise to obtain wavelet coefficients; (2) according to the wavelet coefficients, self-adaptive threshold functions of each layer of wavelet coefficients are constructed, and wavelet threshold values of an ith decomposition layer are selected; (3) attenuation coefficients are selected by the utilization of a mid-point method, and threshold processing is performed by the adoption of the threshold functions and the wavelet threshold values; (4) wavelet inverse transformation is performed on the wavelet coefficients, corresponding to threshold function processing, of the selected attenuation coefficients to obtain restored original signal estimation values; (5) PSNR values of the original signal estimation values are worked out to obtain an optimal value, an optimal attenuation coefficient under the PSNR optimal value is obtained according to the mid-point method, and the wavelet coefficients corresponding to the threshold function processing are reconstructed, and obtained estimation values are used as final de-noising images. According to the method, the defects of hard threshold and soft threshold de-noising methods are overcome, more accurate wavelet coefficient estimation values are obtained, and the edges of the images are protected.

Description

A kind of adaptive wavelet threshold denoising method based on neighborhood relevance

Technical field

The invention belongs to the Image Denoising Technology field in image pre-service, particularly a kind of adaptive wavelet threshold denoising method based on domain-specific.

Background technology

Noise is a key factor that affects picture quality, is gathering, is transmitting, obtains in the process of image, because picture noise can be inevitably introduced in the interference of imaging device or external environment condition.The membership that adds of noise brings very large trouble to the subsequent treatment of image, therefore, before image is used, is necessary to carry out denoising, improves signal to noise ratio (S/N ratio).Wherein the object of image denoising is when removing most noise, to protect as far as possible the marginal information of image to reduce the impact of noise on subsequent treatment.Image denoising is very helpful for the processing of Image Engineering, and therefore, image denoising has researching value and using value.

In order to meet the actual requirement of image denoising, image denoising has a great development at present, denoising method is also varied, it is separated that traditional method the most directly perceived is that the different qualities that shows at frequency domain with noise according to image carries out noise, image spectrum be generally distributed in limited frequency band and frequency lower, and noise generally concentrates on high-frequency region, therefore can adopt the method for filtering to carry out image denoising, as low-pass filtering, mean filter, medium filtering, Wiener filtering etc., these methods can reduce the impact that noise brings to a certain extent, but also make image border and detailed information fog simultaneously.Traditional filtering method requires the overlapping the smaller the better of image and noise, and more when spectrum overlapping part, denoising effect is not just very desirable.

For the deficiency of classic method, wavelet analysis, as a kind of new time-frequency instrument, has overcome traditional Fourier and has changed the defect with fixed resolution.Wavelet analysis has the feature of multiresolution analysis, can portray well the local characteristics of signal at time domain and frequency domain, is called as school microscop.Therefore wavelet analysis is very practical and welcome in image denoising field.For Wavelet domain image denoising, its basic thought is that the wavelet coefficient after wavelet field is to wavelet transformation carries out respective handling, and the wavelet coefficient of noise is removed, and the wavelet coefficient of stick signal, to reach the object of denoising.For Wavelet Denoising Method, mainly contain three kinds of methods at present; One, the denoising of film maximum value; Its two, utilize scale correlations to carry out to signal the effect that filtering reaches denoising; Its three, wavelet threshold denoising.Because the above two calculated amount are quite large, denoising effect is not very desirable, so practicality is not strong.

Image after wavelet transformation, the energy correspondence of itself wavelet coefficient that amplitude is larger, mainly concentrates on low frequency; Noise energy is corresponding the less wavelet coefficient of amplitude, and is dispersed in the whole wavelet field after wavelet transformation.Wavelet threshold denoising method, according to this feature, arranges a threshold value, thinks that the wavelet coefficient Main Ingredients and Appearance that is greater than this threshold value is useful signal, shrink rear reservation, the wavelet coefficient Main Ingredients and Appearance that is less than this threshold value is noise, is rejected, and so just can reach the object of denoising.The most frequently used wavelet threshold denoising method is hard-threshold denoising and soft-threshold denoising at present.Wherein hard-threshold function is:

$\widehat{w_{j,k}}=\left\{\begin{array}{c}{w}_{j,k},\left|w_{j,k}\right|\&GreaterEqual;\mathrm{\&lambda;}\\ 0,\left|w_{j,k}\right|<\mathrm{\&lambda;}\end{array}\right.;$

Soft-threshold function is:

$\widehat{w_{j,k}}=\left\{\begin{array}{c}\mathrm{sign}\left(w_{j,k}\right)\&times;\left(\right|w_{j,k}|-\mathrm{\&lambda;}),\left|w_{j,k}\right|\&GreaterEqual;\mathrm{\&lambda;}\\ 0,\left|w_{j,k}\right|<\mathrm{\&lambda;}\end{array}\right.;$

Wherein in above formula

for Donoho wavelet threshold, N is signal length; W _j,kfor wavelet coefficient;

estimated value for purified signal wavelet coefficient.

Although these two kinds conventional wavelet threshold denoising methods are widely used, effect is also better, has obvious shortcoming.Uncontinuity in hard-threshold denoising method makes reconstruction signal can produce some vibrations; Although but soft-threshold method is continuous estimated signal and actual signal, there is constant deviation, can produce that some are fuzzy.

Summary of the invention

The shortcoming that the object of the invention is to overcome prior art is with not enough; a kind of adaptive wavelet threshold denoising method based on neighborhood relevance is provided; the method has overcome the uncontinuity of hard-threshold denoising method; the constant deviation defect of Soft-threshold Denoising Method; the estimated value of wavelet coefficient can be obtained more exactly, and edge can be better protected.

Object of the present invention is achieved through the following technical solutions: a kind of adaptive wavelet threshold denoising method based on neighborhood relevance, comprises the following steps:

(1) Noise image is carried out to the wavelet transform process of multilayer, obtain the wavelet coefficient of each layer;

(2), according to resulting each layer of wavelet coefficient of step (1), be constructed as follows the adaptive thresholding value function of wavelet coefficient in each layer of all directions:

$\widehat{w_{i,j,k}}=\left\{\begin{array}{c}{w}_{i,j,k}\&CenterDot;(1-\mathrm{\&alpha;}{\left(\frac{{\mathrm{\&lambda;}}_i}{s_{i,j,k}}\right)}^2),\left|s_{i,j,k}\right|\&GreaterEqual;{\mathrm{\&lambda;}}_i\\ 0,\left|s_{i,j,k}\right|<{\mathrm{\&lambda;}}_i\end{array}\right.,\mathrm{\&alpha;}\&Element;\left(\mathrm{0,1}\right);$

Wherein α is attenuation coefficient; I is the wavelet decomposition number of plies, λ _iit is the threshold value of i decomposition layer; w _{i, j, k}that i layer decomposes the original wavelet coefficients obtaining,

the estimated value that represents purified signal wavelet coefficient, the position of pixel in j, k presentation video;

S wherein _{i, j, k}for:

$s_{i,j,k}=\sqrt{\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000453561390000011.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}\&CenterDot;\underset{(i,j,k)\&Element;B}{\mathrm{\&Sigma;}}{W_{i,j,\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000453561390000011.png"\; state="\{\{state\}\}">k</figure-callout>}}}^2};$

B be take the neighborhood window that some size is N * N centered by pixel (j, k) in the image that decomposes of i layer;

Choose i decomposition layer wavelet threshold λ _i:

${\mathrm{\&lambda;}}_i=\mathrm{\&beta;\&sigma;}\sqrt{2\lg \left(N\right)/\lg (i+1)},0<\mathrm{\&beta;}\&le;1;$

σ is noise variance;

(3) utilize mid-point method to choose the value of attenuation coefficient α, adopt the selected corresponding threshold function table of attenuation coefficient α value and wavelet threshold in mid-point method respectively every layer of wavelet coefficient decomposing to be carried out to threshold process;

(4) wavelet coefficient of threshold function table corresponding to each attenuation coefficient α value of choosing through step (3) being processed carries out respectively inverse wavelet transform reconstruct, the original signal estimated value being restored;

(5) calculate the corresponding PSNR(Peak Signalto of each original signal estimated value Noise Ratio in step (4), Y-PSNR) value, then according to mid-point method, select PSNR optimal value, obtain corresponding optimized attenuation coefficient and the corresponding threshold function table of optimized attenuation function under this PSNR optimal value; The wavelet coefficient that threshold function table corresponding to this optimized attenuation function processed carries out original signal estimated value that inverse wavelet transform reconstruct is restored as final denoising image.

Preferably, wavelet threshold λ in described step (2) _iin β value be

Preferably, describedly utilize mid-point method to choose the value of attenuation coefficient α and to obtain the concrete steps of PSNR optimal value as follows:

(1.1) by attenuation coefficient α, obtaining PSNR value about the derivative PSNR ' of attenuation coefficient α is (a):

${\mathrm{PSNR}}^{\&prime;}\left(a\right)=\underset{d->0}{\lim }\frac{\mathrm{PSNR}(a+d)-\mathrm{PSNR}\left(a\right)}{d};$

(1.2) first choose attenuation coefficient α initial searches interval;

(1.3) choose current search interval (a, b) mid point (a+b)/2 of a and b in, according to the PSNR ' in step (1.1) (a) the derivative PSNR ' when formula calculates attenuation coefficient and is c (c), then judge PSNR ' (c) whether be greater than zero;

If not, by a in current search interval (a, b), give c value, be about to the region of search and reduce by half, then execution step (1.4);

If so, by the b in current search interval (a, b), give c value, be about to the region of search and reduce by half, then execution step (1.4)

(1.4), using the search volume (a, b) after above-mentioned reducing by half as current search space, then judge in this current search volume (a, b) and whether meet | a-b|<F;

If not, perform step (1.3);

If so, export PSNR (c) for optimal value, using mid point c as optimized attenuation coefficient.

Further, in described step (3-2), initial searches interval is (0,1); F value in described step (3-4) is 0.001.

Further, described derivative PSNR ' (a) in d be chosen for 0.000001.

Preferably, the low frequency wavelet coefficient decomposing for last one deck in described step (3) is not made threshold process.

Preferably, in described step (1), Noise image is carried out the wavelet transform process of 3 layers, described i is 1,2 or 3.

Preferably, in described step (5), the corresponding PSNR value of each original signal estimated value is:

$\mathrm{PSNR}=10\log 10\frac{{255}^2}{\frac{1}{M\&times;Y}\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{Y-1}{\mathrm{\&Sigma;}}}{(u(m-n)-v(m.n))}^2};$

Wherein u (m, y) is original noise-free picture, the original signal estimated value that v (m.n) is the recovery that obtains in step (4), i.e. image after denoising; M * Y is the size of image.

Preferably, described noise variance σ is:

${\mathrm{\&sigma;}}^2=\frac{\mathrm{Median}\left(\right|\mathrm{wi},j,k\left|\right)}{0.6475}.$

Preferably, the size of described neighborhood window B is 5 * 5 or 3 * 3.

The present invention has following advantage and effect with respect to prior art:

(1) the inventive method for signal and noise on the distribution of wavelet field and the basis of mutation analysis; the information of neighborhood wavelet coefficient is applied to the structure of threshold function table and choosing of wavelet threshold; the wavelet coefficient obtaining for every layer of decomposition selects respectively adaptive threshold function table and wavelet threshold to carry out threshold process; wherein the neighborhood information that utilizes is equivalent to utilize the prior imformation of image, has protected well the local messages such as edge of image.

The inventive method considers that noise weakens along with the increase of decomposition level and signal strengthens along with decomposing the increase of the number of plies adaptive wavelet threshold λ choosing _ialong with the increase of decomposition level, reduce, so the inventive method can carry out threshold process to each layer of wavelet coefficient more exactly, obtain more exactly the estimated value of wavelet coefficient, have advantages of that self-adaptation is strong; Overcome in prior art as the wavelet threshold of global threshold and do not considered the threshold process not accurate enough defect that noise and signal bring at the different qualities of wavelet field.

Threshold function table in the present invention in addition, because signal strengthens along with decomposing the increase of the number of plies, therefore along with decomposing the increase of the number of plies, original wavelet coefficients w _{i, j, k}increase s _{i, j, k}value also increase, and wavelet threshold λ _ireduce the estimated value of the purified signal wavelet coefficient obtaining

also just more approach w _{i, j, k}, so the threshold function table using in the inventive method has overcome the constant deviation that exists in soft-threshold function and the shortcoming of hard-threshold denoising method uncontinuity.

(2) the inventive method is chosen the optimal value of PSNR by mid-point method, thereby obtain optimized attenuation coefficient in threshold function table, the wavelet coefficient that the corresponding threshold function table of this optimized attenuation function was processed carries out original signal estimated value that inverse wavelet transform reconstruct is restored as final denoising image, therefore by the inventive method, can access optimum denoising image.

(3) threshold function table of the inventive method is simple, and the region of search of the mid-point method adopting is less, can obtain fast the optimal result of PSNR by mid-point method, thereby can faster obtain optimum denoising image.

Accompanying drawing explanation

Fig. 1 is the denoising schematic diagram of the inventive method.

Fig. 2 is three layers of exploded view of small echo in the inventive method.

Fig. 3 is the process flow diagram that utilizes mid-point method to choose the value of attenuation coefficient α and obtain PSNR optimal value in the inventive method.

Fig. 4 a to 4f is the inventive method and denoising effect comparison diagram with other gate method.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited to this.

Embodiment

As shown in Figure 1, the present embodiment discloses a kind of adaptive wavelet threshold denoising method based on neighborhood relevance, comprises the following steps:

(1) as shown in Figure 2, Noise image 1 is carried out to the wavelet transform process of 3 layers, the details component HHi (i=1 that includes the level and smooth component LL of low frequency, high frequency diagonal line direction after decomposition, 2,3), details component LHi (i=1,2 of high frequency vertical direction, 3) and the details component HLi (i=1 of high frequency horizontal direction, 2,3), then obtain the wavelet coefficient of every layer of all directions.

(2), according to the wavelet coefficient of resulting each layer of step (1), be constructed as follows the adaptive thresholding value function of wavelet coefficient in each layer of all directions:

$\widehat{w_{i,j,k}}=\left\{\begin{array}{c}{w}_{i,j,k}\&CenterDot;(1-\mathrm{\&alpha;}{\left(\frac{{\mathrm{\&lambda;}}_i}{s_{i,j,k}}\right)}^2),\left|s_{i,j,k}\right|\&GreaterEqual;{\mathrm{\&lambda;}}_i\\ 0,\left|s_{i,j,k}\right|<{\mathrm{\&lambda;}}_i\end{array}\right.,\mathrm{\&alpha;}\&Element;\left(\mathrm{0,1}\right);$

Wherein α is attenuation coefficient; I is the wavelet decomposition number of plies, λ _iit is the wavelet threshold of i decomposition layer; w _{i, j, k}that i layer decomposes the original wavelet coefficients obtaining,

the estimated value that represents purified signal wavelet coefficient, the position of pixel in j, k presentation video;

S wherein _{i, j, k}for:

$s_{i,j,k}=\sqrt{\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000453561390000011.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}\&CenterDot;\underset{(i,j,k)\&Element;B}{\mathrm{\&Sigma;}}{W_{i,j,\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000453561390000011.png"\; state="\{\{state\}\}">k</figure-callout>}}}^2};$

B be take the neighborhood window that some size is N * N centered by pixel (j, k) in the image that decomposes of i layer; The size of choosing neighborhood window B in the present embodiment is 5 * 5; Can certainly select other big or small neighborhood window B, as 3 * 3;

Choose the wavelet threshold λ of i decomposition layer _i:

${\mathrm{\&lambda;}}_i=\mathrm{\&beta;\&sigma;}\sqrt{2\lg \left(N\right)/\lg (i+1)},0<\mathrm{\&beta;}\&le;1;$

In the present embodiment σ is noise variance; Wherein noise variance σ is:

${\mathrm{\&sigma;}}^2=\frac{\mathrm{Median}\left(\right|\mathrm{wi},j,k\left|\right)}{0.6475}.$

(3) utilize mid-point method to choose the value of attenuation coefficient α, adopt the selected corresponding threshold function table of attenuation coefficient α value and wavelet threshold in mid-point method respectively every layer of wavelet coefficient decomposing to be carried out to threshold process; After wavelet decomposition, signal energy mainly concentrates on low frequency component LL part, so the low frequency component LL part that decomposes of the 3rd layer of the present embodiment is main, and what concentrate is the image information of Noise not substantially, is carrying out when wavelet threshold is processed it not being carried out to threshold process; The detailed information that high fdrequency component after each layer of decomposition had not only contained image but also contain noise signal, so the high fdrequency component of the threshold process of the present embodiment after for each layer of decomposition.

(4) wavelet coefficient of threshold function table corresponding to each attenuation coefficient α value of choosing through step (3) being processed carries out respectively inverse wavelet transform reconstruct, the original signal estimated value being restored;

(5) calculate the corresponding PSNR(Peak Signalto of each original signal estimated value Noise Ratio in step (4), Y-PSNR) value, then according to mid-point method, select PSNR optimal value, obtain corresponding optimized attenuation coefficient and the corresponding threshold function table of optimized attenuation function under this PSNR optimal value; The wavelet coefficient that the corresponding threshold function table of this optimized attenuation function was processed carries out original signal estimated value that inverse wavelet transform reconstruct is restored as final denoising image 2.

In the present embodiment, the corresponding PSNR value of each original signal estimated value is:

$\mathrm{PSNR}=10\log 10\frac{{255}^2}{\frac{1}{M\&times;Y}\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{Y-1}{\mathrm{\&Sigma;}}}{(u(m-n)-v(m.n))}^2};$

Wherein u (m, y) is original noise-free picture, the original signal estimated value that v (m.n) is the recovery that obtains in step (4), i.e. image after denoising; M * Y is the size of image.

As shown in Figure 3, in the present embodiment, utilize mid-point method to choose the value of attenuation coefficient α and to obtain the concrete steps of PSNR optimal value as follows:

(1.1) by attenuation coefficient α, obtaining PSNR value about the derivative PSNR ' of attenuation coefficient α is (a):

${\mathrm{PSNR}}^{\&prime;}\left(a\right)=\underset{d->0}{\lim }\frac{\mathrm{PSNR}(a+d)-\mathrm{PSNR}\left(a\right)}{d};$

(1.2) first choose the initial region of search of attenuation coefficient α for (0,1);

(1.3) choose current search interval (a, b) mid point (a+b)/2 of a and b in, according to the PSNR ' in step (1.1) (a) the derivative PSNR ' when formula calculates attenuation coefficient and is c (c), then judge PSNR ' (c) whether be greater than zero;

If not, by a in current search interval (a, b), give c value, be about to current search interval and reduce by half, then execution step (1.4);

If so, by the b in current search interval (a, b), give c value, be about to current search interval and reduce by half, then execution step (1.4)

(1.4), using the search volume (a, b) after above-mentioned reducing by half as current search space, then judge in this current search volume (a, b) and whether meet | a-b|<0.001;

If not, perform step (1.3);

If so, export PSNR (c) for optimal value, using above-mentioned attenuation coefficient c as optimized attenuation coefficient.

Described in above-mentioned steps (1.3), derivative PSNR ' is (c):

${\mathrm{PSNR}}^{\&prime;}\left(c\right)=\underset{d->0}{\lim }\frac{\mathrm{PSNR}(c+d)-\mathrm{PSNR}\left(c\right)}{d};$

Choosing respectively in the present embodiment attenuation coefficient α in adaptive thresholding value function is c+d and c; In above-mentioned steps (3), by attenuation coefficient c+d and threshold function table corresponding to c, each layer of wavelet coefficient done respectively to threshold process, the wavelet coefficient that attenuation coefficient c+d and threshold function table corresponding to c were processed carries out respectively inverse wavelet transform reconstruct, obtain the original signal estimated value of recovery corresponding under attenuation coefficient c+d and c, then according to the original signal estimated value of recovering, calculate respectively PSNR (c+d) and PSNR (c) value, finally by above formula, draw derivative PSNR ' (c).The value of wherein choosing in the present embodiment d is 0.000001.

The threshold function table of constructing in the present embodiment is based on neighborhood relevance, and this threshold function table not only relies on the wavelet coefficient values of each layer, also by the wavelet coefficient values in neighborhood, wavelet threshold function is constructed; According to the feature of correlativity in layer, in the larger neighborhood of wavelet coefficient values, may have one group of larger wavelet coefficient, vice versa; Therefore, if around the wavelet coefficient of neighborhood is relatively low, the wavelet coefficient of pending point is high, shows probably to contain noise, and in the present embodiment, utilizes neighborhood information to be equivalent to utilize the prior imformation of image can protect well the edge of image.Investigate the threshold function table of the present embodiment:

$\widehat{w_{i,j,k}}=\left\{\begin{array}{c}{w}_{i,j,k}\&CenterDot;(1-\mathrm{\&alpha;}{\left(\frac{{\mathrm{\&lambda;}}_i}{s_{i,j,k}}\right)}^2),\left|s_{i,j,k}\right|\&GreaterEqual;{\mathrm{\&lambda;}}_i\\ 0,\left|s_{i,j,k}\right|<{\mathrm{\&lambda;}}_i\end{array}\right.;$

From above-mentioned formula, when α=0, be hard-threshold denoising; When α=1 is soft-threshold denoising, and the present embodiment α ∈ (0,1); Wherein by above-mentioned threshold function table, can draw:

$\widehat{\underset{s_{i,j,k->\&infin;}}{\lim }{w}_{i,j,k}=\underset{s_{i,j,k->\&infin;}}{\lim }}{w}_{i,j,k}\&CenterDot;(1-\mathrm{\&alpha;}{\left(\frac{{\mathrm{\&lambda;}}_i}{s_{i,j,k}}\right)}^2)=w_{i,j,k};$

Along with decomposing the increase of the number of plies, wavelet coefficient w in threshold function table _{i, j, k}amplitude increases, s _{i, j, k}value also increase, and wavelet threshold λ _ireduce, now

more close to w _{i, j, k}; Therefore the method for the present embodiment has overcome the shortcoming of the constant deviation existing in soft-threshold function, has effectively kept the local messages such as edge of image.

Because noise weakens along with decomposing the increase of the number of plies, but signal strengthens along with decomposing the increase of the number of plies, and the wavelet threshold λ choosing in the present embodiment _ialong with the increase of decomposition level, reduce; Therefore the wavelet threshold of the present embodiment can make the threshold process of each layer of wavelet coefficient more accurate.Overcome in prior art as the wavelet threshold of global threshold and do not considered the threshold process not accurate enough defect that noise and signal bring at the different qualities of wavelet field.

In the present embodiment because PNSR value corresponding to differential declines factor-alpha only has a local optimum and for end points, therefore in the present embodiment, adopt mid-point method to choose best denoising image, by mid-point method, select PNSR optimal value and the corresponding optimized attenuation coefficient of this optimal value.The original signal estimated value that wavelet coefficient after the corresponding threshold function table of this optimized attenuation coefficient is processed is carried out to inverse wavelet transform reconstruct recovery is as final denoising image.Because the mid-point method region of search adopting in the present embodiment is little, therefore can obtain very soon optimum.

Table 1 is 0 for adopting the denoising method of the present embodiment to being superimposed with respectively average, noise criteria is poor is that 10,20,30,40 and 50 white Gaussian noise lena test pattern (this test pattern comprises smooth again abundant details) carries out the PSNR value obtaining after denoising, and the result of the PSNR value that the inventive method denoising is obtained and soft-threshold method, hard threshold method, soft or hard compromise method compares.

Table 1

By table 1, can find out, the image PSNR value obtaining after the inventive method denoising is compared additive method and is all wanted high, and denoising effect is all better than additive method.

The Barbara of the edge details of take in this enforcement Mandrill how, texture-rich and level and smooth Pepper tri-width images are as being test pattern, adding respectively average is 0, standard deviation is 30 white Gaussian noise, then adopt the present embodiment denoising method, soft-threshold method, hard threshold method and soft or hard folding method respectively three width images to be carried out to denoising, the PSNR value wherein obtaining after the denoising of four kinds of methods is as shown in table 2.

Table 2

By the comparing result of table 1 and table 2, can find out, the adaptive wavelet threshold denoising method of the present embodiment based on neighborhood relevance in each under noise level denoising effect be all obviously better than additive method, and be applicable to dissimilar image.

As shown in Fig. 4 c to 4f, for adopting the present embodiment denoising method, soft-threshold method, hard threshold method and soft or hard folding method, carry out the image obtaining respectively after denoising, wherein Fig. 4 a is the original image that does not have noise, Fig. 5 b is the image of Noise, and Fig. 4 c, 4d, 4e and 4f are for to adopt the image that soft-threshold method, hard threshold method, soft or hard folding method and the present embodiment denoising method are Noise to Fig. 4 b to carry out the final image that denoising obtains respectively.Comparison diagram 4c, 4d, 4e and 4f can find out, the denoising effect of the present embodiment method is best, the most approaching and edge is more clear with the original image that does not have a noise.

Above-described embodiment is preferably embodiment of the present invention; but embodiments of the present invention are not restricted to the described embodiments; other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplify; all should be equivalent substitute mode, within being included in protection scope of the present invention.

Claims (10)

1. the adaptive wavelet threshold denoising method based on neighborhood relevance, is characterized in that, comprises the following steps:

(1) Noise image is carried out to the wavelet transform process of multilayer, obtain the wavelet coefficient of each layer;

(2), according to resulting each layer of wavelet coefficient of step (1), be constructed as follows the adaptive thresholding value function of wavelet coefficient in each layer of all directions:

$\widehat{w_{i,j,k}}=\left\{\begin{array}{c}{w}_{i,j,k}\&CenterDot;(1-\mathrm{\&alpha;}{\left(\frac{{\mathrm{\&lambda;}}_i}{s_{i,j,k}}\right)}^2),\left|s_{i,j,k}\right|\&GreaterEqual;{\mathrm{\&lambda;}}_i\\ 0,\left|s_{i,j,k}\right|<{\mathrm{\&lambda;}}_i\end{array}\right.,\mathrm{\&alpha;}\&Element;\left(\mathrm{0,1}\right);$

Wherein α is attenuation coefficient; I is the wavelet decomposition number of plies, λ _iit is the threshold value of i decomposition layer; w _{i, j, k}that i layer decomposes the original wavelet coefficients obtaining, the estimated value that represents purified signal wavelet coefficient, the position of pixel in j, k presentation video;

S wherein _{i, j, k}for:

$s_{i,j,k}=\sqrt{\frac{1}{N^2}\&CenterDot;\underset{(i,j,k)\&Element;B}{\mathrm{\&Sigma;}}{W_{i,j,k}}^2};$

B be take the neighborhood window that some size is N * N centered by pixel (j, k) in the image that decomposes of i layer;

Choose i decomposition layer wavelet threshold λ _i:

${\mathrm{\&lambda;}}_i=\mathrm{\&beta;\&sigma;}\sqrt{2\lg \left(N\right)/\lg (i+1)},0<\mathrm{\&beta;}\&le;1;$

σ is noise variance;

(3) utilize mid-point method to choose the value of attenuation coefficient α, adopt the selected corresponding threshold function table of attenuation coefficient α value and wavelet threshold in mid-point method respectively every layer of wavelet coefficient decomposing to be carried out to threshold process;

(4) wavelet coefficient of threshold function table corresponding to each attenuation coefficient α value of choosing through step (3) being processed carries out respectively inverse wavelet transform reconstruct, the original signal estimated value being restored;

(5) calculate the corresponding PSNR value of each original signal estimated value in step (4), then according to mid-point method, select PSNR optimal value, obtain corresponding optimized attenuation coefficient and the corresponding threshold function table of optimized attenuation function under this PSNR optimal value; The wavelet coefficient that threshold function table corresponding to this optimized attenuation function processed carries out original signal estimated value that inverse wavelet transform reconstruct is restored as final denoising image.

2. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 1, is characterized in that, wavelet threshold λ in described step (2) _iin β value be

3. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 1, is characterized in that, describedly utilizes mid-point method to choose the value of attenuation coefficient α and to obtain the concrete steps of PSNR optimal value as follows:

(1.1) by attenuation coefficient α, obtaining PSNR value about the derivative PSNR ' of attenuation coefficient α is (a):

${\mathrm{PSNR}}^{\&prime;}\left(a\right)=\underset{d->0}{\lim }\frac{\mathrm{PSNR}(a+d)-\mathrm{PSNR}\left(a\right)}{d};$

(1.2) first choose attenuation coefficient α initial searches interval;

(1.3) choose current search interval (a, b) mid point (a+b)/2 of a and b in, according to the PSNR ' in step (1.1) (a) the derivative PSNR ' when formula calculates attenuation coefficient and is c (c), then judge PSNR ' (c) whether be greater than zero;

If not, by a in current search interval (a, b), give c value, be about to the region of search and reduce by half, then execution step (1.4);

If so, by the b in current search interval (a, b), give c value, be about to the region of search and reduce by half, then execution step (1.4)

(1.4), using the search volume (a, b) after above-mentioned reducing by half as current search space, then judge in this current search volume (a, b) and whether meet | a-b|<F;

If not, perform step (1.3);

If so, export PSNR (c) for optimal value, using mid point c as optimized attenuation coefficient.

4. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 3, is characterized in that, in described step (3-2), initial searches interval is (0,1); F value in described step (3-4) is 0.001.

5. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 3, is characterized in that, described derivative PSNR ' (a) middle d is chosen for 0.000001.

6. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 1, is characterized in that, the low frequency wavelet coefficient decomposing for last one deck in described step (3) is not made threshold process.

7. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 1, is characterized in that, in described step (1), Noise image is carried out the wavelet transform process of 3 layers, and described i is 1,2 or 3.

8. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 1, is characterized in that, in described step (5), the corresponding PSNR value of each original signal estimated value is:

$\mathrm{PSNR}=10\log 10\frac{{255}^2}{\frac{1}{M\&times;Y}\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{Y-1}{\mathrm{\&Sigma;}}}{(u(m-n)-v(m.n))}^2};$

Wherein u (m, y) is original noise-free picture, the original signal estimated value that v (m.n) is the recovery that obtains in step (4), i.e. image after denoising; M * Y is the size of image.

9. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 1, is characterized in that, described noise variance σ is:

${\mathrm{\&sigma;}}^2=\frac{\mathrm{Median}\left(\right|\mathrm{wi},j,k\left|\right)}{0.6475}.$

10. the adaptive wavelet threshold denoising method based on neighborhood relevance according to claim 1, is characterized in that, the size of described neighborhood window B is 5 * 5 or 3 * 3.

Images