CN101930598B - Natural image denoising method based on non-local mean value of shearlet region - Google Patents

Abstract

The invention discloses a natural image denoising method based on a non-local mean value of a shearlet region, which mainly solves the problem that the traditional non-local mean value method has poor denoising effect of a natural image corroded by high noise. The method comprises the following implementation steps of: inputting a test image, and adding gaussian white noise with the noise standard deviation of 50; decomposing the image into three layers by utilizing a Laplacian pyramid method, wherein denoising treatment is carried out on the first layer by using a non-local mean value method, the second layer and the third layer are respectively decomposed into four groups of shearlet coefficients by using a shearlet directional filter group firstly, then estimation of a beta value is carried out on each group of shearlet coefficients, and then the denoising treatment of the non-local mean value method under a general Gauss model is carried out on each group of shearlet coefficients; and reconstructing a denoising result to obtain a final denoising result. The invention has the advantages of favorable denoising effect for the natural image corroded by high noise, can restore the original characteristics of the image and be used for variation detection and pretreatment of the image when an object is identified.

Description

Natural image denoising method based on shearlet territory non-local mean

Technical field

The invention belongs to technical field of image processing; Relate to the denoising of natural image under the strong noise situation, can be used for carrying out forest inventory investigation, soil utilization, cover the preconditioning technique that often can use in the field Flame Image Process such as changing research, environmental hazard assessment, city planning, the monitoring of national defence military situation, medical image and uranology image.

Background technology

The fast development of computer science and technology has produced tremendous influence to digital image processing field, and image denoising is as an important branch of image processing field, and fundamental method is estimated noise image exactly during processing: v (i)=u (i)+n (i); V (i) representes noise image, and u (i) representes original image, and n (i) expression noise; Handle the purpose of image and remove n (i) exactly, estimate u (i) as far as possible accurately, image denoising; Nothing more than in spatial domain and two big directions of frequency domain, but no matter be, still carry out denoising at frequency domain in the spatial domain; In the whole bag of tricks, all be based on " local level and smooth " this thought, but no matter this thought is at frequency domain; Still in the spatial domain, all can make a lot of detailed information of missing image at last, in order to overcome the shortcoming of this thought; Someone has proposed the thought of non-local mean; The method of non-local mean can be utilized the analog information in the entire image as far as possible fully, thereby estimates the information of point to be estimated, but the non-local mean method just is applied to the spatial domain when proposing; And along with the increase of picture noise, the relevant information of entire image has been suffered the destruction of noise, makes the non-local mean method be difficult to effectively utilize the analog information in the image.

The Shearlet conversion, a kind of as in the third generation wavelet transformation has been widely used in image denoising; It has overcome wavelet transformation when image is handled; Because the disappearance of directivity, a lot of minutias that can not well approach image make that the denoising result of image is visually fuzzyyer; More serious cut phenomenon is arranged, cause image denoising effect poor.

Summary of the invention

The objective of the invention is to deficiency to above-mentioned prior art; A kind of natural image denoising method based on shearlet territory non-local mean is proposed; Visually fuzzyyer to natural image under the strong noise situation to overcome existing method; The problem that more serious cut phenomenon is arranged improves denoising effect.

For realizing above-mentioned purpose, the present invention includes following steps:

(1) choosing test pattern, is 50 white Gaussian noise to its adding standard deviation;

(2) be that the test pattern of 50 white Gaussian noise carries out laplacian pyramid and decomposes to adding standard deviation; Test pattern is decomposed into three layers; Wherein to the second layer and the 3rd layer of shearlet bank of filters travel direction filtering of using the generation of shearlet basis function more respectively; The number of filter that is about to the shearlet bank of filters is appointed as four, obtains four groups of shearlet coefficients respectively; To ground floor execution in step (5);

(3) four groups of shearlet coefficients and the 3rd layer of four groups of shearlet coefficients estimation of travel direction parameter beta as follows that obtains of the second layer being obtained:

3a) span with β is taken as 0 to 4; The amplitude a of increasing progressively is taken as 0.001; C is defined as

wherein s be the standard deviation of shearlet coefficient; is the expectation of the absolute value of shearlet coefficient; D is defined as

Γ () expression gamma function wherein is taken as 0.001 with the error parameter b of c and d;

3b) β is increased progressively the processing that increases progressively that amplitude is a since 0, when the difference of c and d during less than error parameter b, finishing iteration process, obtain increasing progressively the iterations n of amplitude a, the product of a and n is the parameter result of β;

(4) after direction parameter β confirms, adopt and the second layer and the 3rd layer of shearlet coefficient of respectively organizing that obtains are carried out denoising based on the non-local mean method of Generalized Gaussian model;

(5) picture content that ground floor is obtained adopts the non-local mean method to carry out denoising;

(6) denoising result that step (4) and step (5) is obtained carries out the shearlet inverse transformation, obtains the reconstruction result figure of test pattern.

The present invention has the following advantages compared with prior art:

A, the present invention be owing to carried out three layers of decomposition of shearlet with natural image, respectively organizes the denoising that coefficient has carried out the non-local mean method to what decomposition obtained, overcome the deficiency that existing non-local mean method can not be applied to transform domain.

B, the present invention be owing to confirm as 0 to 4 with the β span, carry out iterative search β value since 0 again, overcome prior art and found the solution the low excessively deficiency of efficient for β.

The simulation experiment result shows, it is the denoising of the natural image of 50 noise corrosion that the non-local mean method based on the shearlet territory that the present invention proposes can be effectively applied to by the noise criteria difference.

Description of drawings

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is experiment test figure of the present invention;

Fig. 3 is that the present invention and existing non-local mean natural image denoising method are 50 o'clock experiment comparing result in the noise criteria difference.

Embodiment

With reference to Fig. 1, performing step of the present invention is following:

Step 1 is chosen test pattern, is 50 white Gaussian noise to its adding standard deviation.

Step 2; To adding standard deviation is that the test pattern of 50 white Gaussian noise carries out laplacian pyramid and decomposes; Test pattern is decomposed into three layers; Wherein to the second layer and the 3rd layer of shearlet bank of filters travel direction filtering of using the generation of shearlet basis function more respectively, the number of filter that is about to the shearlet bank of filters is appointed as four, obtains four groups of shearlet coefficients respectively; To ground floor execution in step 5.

Shearlet basis function described in the step 2, concrete formula is following:

Wherein $f\left(\mathrm{\ω}\right)=(1/e^{28\×{((\mathrm{\ω}-1)/2)}^{14}})\×{(1-e^{1/(\mathrm{\ω}-1)})}^{\frac{1}{2}}---2)$

Wherein ω representes the independent variable of shearlet basis function

; ω ∈ R, R representes real number.

Step 3, four groups of shearlet coefficients and the 3rd layer of four groups of shearlet coefficients estimation of travel direction parameter beta as follows that obtains that the second layer is obtained:

3a) span with β is taken as 0 to 4; The amplitude a of increasing progressively is taken as 0.001; C is defined as wherein s be the standard deviation of shearlet coefficient;

is the expectation of the absolute value of shearlet coefficient; D is defined as

Γ () expression gamma function wherein is taken as 0.001 with the error parameter b of c and d.

3b) β is increased progressively the processing that increases progressively that amplitude is a since 0, when the difference of c and d during less than error parameter b, finishing iteration process, obtain increasing progressively the iterations n of amplitude a, the product of a and n is the parameter result of β.

Step 4 after parameter beta is confirmed, adopts and based on the non-local mean method of Generalized Gaussian model the second layer and the 3rd layer of shearlet coefficient of respectively organizing that obtains is carried out denoising.

4a) calculate the yardstick function alpha:

$\mathrm{\α}={\left(\frac{\mathrm{\β}}{L}\underset{i=1}{\mathrm{\Σ}}L{\left|x_i\right|}^{\mathrm{\β}}\right)}^{\frac{1}{\mathrm{\β}}}---4)$

Wherein L representes one group of coefficient number in the shearlet coefficient, x _iThe value of representing each shearlet coefficient;

4b) with α, β value substitution following formula:

${\mathrm{\ω}}_1(i_1,j_1)=\frac{1}{Z_1\left(i_1\right)}{e}^{\frac{{\left|\right|\mathrm{\υ}\left(N_{i_1}\right)-\mathrm{\υ}\left(N_{j_1}\right)\left|\right|}_{2,\mathrm{\σ}}^{\mathrm{\β}}}{{\left(\mathrm{h\α}\right)}^{\mathrm{\β}}}}---5)$

$Z_1\left(i_1\right)={\underset{j_1}{\mathrm{\Σ}}e}^{\frac{{\left|\right|\mathrm{\υ}\left(N_{i_1}\right)-\mathrm{\υ}\left(N_{j_1}\right)\left|\right|}_{2,\mathrm{\σ}}^{\mathrm{\β}}}{\mathrm{h\α}}}---6)$

At formula 5), 6) in, ω ₁(i ₁, j ₁) similarity between two shearlet coefficients of expression,

Be that the normalization of similarity is handled, h representes to control the parameter of power function decay, and when second layer shearlet coefficient was carried out denoising, h got 1.5, and when the 3rd layer of shearlet carried out denoising, h got 1/10th of noise criteria difference value, i ₁, j ₁Expression shearlet coefficient point,

Expression is with i ₁Be 7 * 7 the sliding window at center, Expression is with j ₁7 * 7 sliding window for the center;

4c) with ω ₁(i ₁, j ₁) be updated to following formula:

$\mathrm{NL}{\left(v\right)}_1\left(i_1\right)=\underset{j_1\∈I_1}{\mathrm{\Σ}}{\mathrm{\ω}}_1(i_1,j_1)v_1\left(j_1\right)---7)$

At formula 7) in, NL is (v) ₁(i ₁) expression adopts the value of the shearlet coefficient that Generalized Gaussian model non-local mean method estimates, v ₁(j ₁) expression treats the value of shearlet coefficient of denoising, I ₁The search window of expression shearlet coefficient, size is 21 * 21.

Step 5, the picture content that ground floor is obtained adopts the non-local mean method to carry out denoising.

5a) the similarity ω between the calculating ground floor picture content ₂(i ₂, j ₂):

${\mathrm{\ω}}_2(i_2,j_2)=\frac{1}{Z_2\left(i_2\right)}{e}^{-\frac{\left|\right|v\left(N_{i_2}\right)-v\left(N_{j2}\right)\left|\right|}{h^2}}---8)$

Wherein $Z_2\left(i_2\right)={\underset{j_2}{\mathrm{\Σ}}e}^{-\frac{\left|\right|v\left(N_{i_2}\right)-v\left(N_{j2}\right)\left|\right|}{h^2}}---9)$

At formula 8), 9) in, Z ₂(i ₂) be that the normalization of similarity is handled, h representes to control the parameter of power function decay, and when the ground floor picture content was carried out denoising, h got the value size of noise criteria difference, i ₂, j ₂The pixel of expression ground floor picture content,

Expression is with i ₂Be 7 * 7 the sliding window at center,

Expression is with j ₂7 * 7 sliding window for the center;

5b) with ω ₂(i ₂, j ₂) be updated to following formula:

$\mathrm{NL}{\left(v\right)}_2\left(i_2\right)=\underset{j_2\∈I_2}{\mathrm{\Σ}}{\mathrm{\ω}}_2(i_2,j_2){\mathrm{\υ}}_2\left(j_2\right)---10)$

At formula 10) in, NL is (v) ₂(i ₂) pixel value of the picture content that estimates of expression non-local mean method, υ ₂(j ₂) expression treats the pixel value of picture content of denoising, I ₂Search window in the expression ground floor picture content, size is 21 * 21.

Step 6, the denoising result that step (4) and step (5) are obtained carries out the shearlet inverse transformation, obtains the reconstruction result figure of test pattern.

6a) four groups of shearlet coefficient denoising results of the 3rd layer are superposeed, obtain the denoising result of the 3rd tomographic image component;

6b) four groups of shearlet coefficient denoising results with the second layer superpose, and obtain the denoising result of second layer picture content;

The reconstructing method that 6c) utilizes laplacian pyramid carries out reconstruct to the denoising result of ground floor, the second layer, the 3rd tomographic image component, obtains reconstruction result figure.

Effect of the present invention can further specify through the test result of following two test patterns:

1, experiment condition

The present invention adopts like the described original noise-free picture of Fig. 2, as experimental result with reference to image, the size of image is 512 * 512.Test used input picture shown in Fig. 3 (a), it is that adding noise criteria difference is 50 noise image.

Experiment of the present invention is at windows XP, and SPI, CPU Pentium (R) 4, basic frequency 2.9GHZ, software platform are Matlab7.0.4 operation down.

2, experimental result

Fig. 3 (a) is carried out the denoising experiment with existing non-local mean natural image denoising method and the non-local mean natural image denoising method that the present invention is based on the shearlet territory respectively; The denoising result of wherein existing non-local mean natural image denoising method shown in Fig. 3 (b), the present invention to the result of natural image denoising shown in Fig. 3 (c).Can find out that from the result of Fig. 3 (c) the present invention has well kept the detailed information of image, visual effect more approaches original image Fig. 2, and Y-PSNR PSNR also is higher than existing non-local mean natural image denoising method simultaneously.

Table 1 is that the present invention is the experimental result contrast under 50 situation to Fig. 2 in the noise criteria difference:

The contrast experiment of table 1 couple Fig. 2

Visible from table 1, the non-local mean natural image denoising method in shearlet territory is under 50 the situation in the noise criteria difference, the natural image denoising method of the non-local mean that its denoising effect is better than.

Claims (1)

1. the natural image denoising method based on shearlet territory non-local mean comprises the steps:

(1) choosing test pattern, is 50 white Gaussian noise to its adding standard deviation;

(2) be that the test pattern of 50 white Gaussian noise carries out laplacian pyramid and decomposes to adding standard deviation; Test pattern is decomposed into three layers; Wherein to the second layer and the 3rd layer of shearlet bank of filters travel direction filtering of using the generation of shearlet basis function more respectively; The number of filter that is about to the shearlet bank of filters is appointed as four, obtains four groups of shearlet coefficients respectively; To ground floor execution in step (5),

Described shearlet basis function, concrete formula is following:

Wherein

$f\left(\mathrm{\ω}\right)=(1/e^{28\×{((\mathrm{\ω}-1)/2)}^{14}})\×{(1-e^{1/(\mathrm{\ω}-1)})}^{\frac{1}{2}}---2)$

Wherein ω representes the independent variable of shearlet basis function

; ω ∈ R, R representes real number;

(3) four groups of shearlet coefficients and the 3rd layer of four groups of shearlet coefficients estimation of travel direction parameter beta as follows that obtains of the second layer being obtained:

3a) span with β is taken as 0 to 4; The amplitude a of increasing progressively is taken as 0.001; C is defined as

wherein σ be the standard deviation of shearlet coefficient; E [| x|] be the expectation of the absolute value of shearlet coefficient; D is defined as

Γ () expression gamma function wherein is taken as 0.001 with the error parameter b of c and d;

3b) β is increased progressively the processing that increases progressively that amplitude is a since 0, when the difference of c and d during less than error parameter b, finishing iteration process, obtain increasing progressively the iterations n of amplitude a, the product of a and n is the parameter result of β;

(4) after parameter beta is confirmed, as follows the second layer and the 3rd layer of shearlet coefficient of respectively organizing that obtains are carried out denoising:

4a) calculate the yardstick function alpha:

$\mathrm{\α}={\left(\frac{\mathrm{\β}}{L}\underset{i=1}{\mathrm{\Σ}}L{\left|x_i\right|}^{\mathrm{\β}}\right)}^{\frac{1}{\mathrm{\β}}}---4)$

Wherein L representes one group of coefficient number in the shearlet coefficient, x _iThe value of representing each shearlet coefficient;

4b) with α, β value substitution following formula:

${\mathrm{\ω}}_1(i_1,j_1)=\frac{1}{Z_1\left(i_1\right)}{e}^{-\frac{{\left|\right|\mathrm{\υ}\left(N_{i_1}\right)-\mathrm{\υ}\left(N_{j_1}\right)\left|\right|}_{2,\mathrm{\σ}}^{\mathrm{\β}}}{{\left(\mathrm{h\α}\right)}^{\mathrm{\β}}}---5)}$

Wherein $Z_1\left(i_1\right)=\underset{j_1}{\mathrm{\Σ}}{e}^{-\frac{{\left|\right|\mathrm{\υ}\left(N_{i_1}\right)-\mathrm{\υ}\left(N_{j_1}\right)\left|\right|}_{2,\mathrm{\σ}}^{\mathrm{\β}}}{\mathrm{H\α}}---6)}$

At formula 5), 6) in, ω ₁(i ₁, j ₁) similarity between two shearlet coefficients of expression, Z ₁(i ₁) be that the normalization of similarity is handled, h representes to control the parameter of power function decay, i ₁, j ₁Expression shearlet coefficient point,

I is thought in expression ₁7 * 7 the sliding window at center,

Expression is with j ₁7 * 7 sliding window for the center;

4c) with ω ₁(i ₁, j ₁) be updated to following formula:

$\mathrm{NL}{\left(v\right)}_1\left(i_1\right)=\underset{j_1\∈I_1}{\mathrm{\Σ}}{\mathrm{\ω}}_1(i_1,j_1){\mathrm{\υ}}_1\left(j_1\right)---7)$

At formula 7) in, NL is (v) ₁(i ₁) expression adopts the value of the shearlet coefficient that Generalized Gaussian model non-local mean method estimates, v ₁(j ₁) expression treats the value of shearlet coefficient of denoising, I ₁The search window of expression shearlet coefficient, size is 21 * 21;

(5) picture content that ground floor is obtained carries out denoising as follows:

5a) the similarity ω between the calculating ground floor picture content ₂(i ₂, j ₂):

${\mathrm{\ω}}_2(i_2,j_2)=\frac{1}{Z_2\left(i_2\right)}{e}^{-\frac{\left|\right|v\left(N_{i_2}\right)-v\left(N_{j_2}\right)\left|\right|}{h^2}}---8)$

Wherein $Z_2\left(i_2\right)=\underset{j_2}{\mathrm{\Σ}}{e}^{\frac{\left|\right|v\left(N_{i_2}\right)-v\left(N_{j_2}\right)\left|\right|}{h^2}}---9)$

At formula 8), 9) in, Z ₂(i ₂) be that the normalization of similarity is handled, h representes to control the parameter of power function decay, i ₂, j ₂The pixel of expression ground floor picture content, Expression is with i ₂Be 7 * 7 the sliding window at center, Expression is with j ₂7 * 7 sliding window for the center;

5b) with ω ₂(i ₂, j ₂) be updated to following formula:

$\mathrm{NL}{\left(v\right)}_2\left(i_2\right)=\underset{j_2\∈I_2}{\mathrm{\Σ}}{\mathrm{\ω}}_2(i_2,j_2){\mathrm{\υ}}_2\left(j_2\right)---10)$

At formula 10) in, NL is (v) ₂(i ₂) pixel value of the picture content that estimates of expression non-local mean method, υ ₂(j ₂) expression treats the pixel value of picture content of denoising, I ₂Search window in the expression ground floor picture content, size is 21 * 21;

(6) denoising result that step (4) and step (5) is obtained carries out the shearlet inverse transformation, obtains the reconstruction result figure of test pattern.

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