CN106023103A - Adaptive orthogonal wavelet image denoising method based on accurate local variance priori modeling - Google Patents

Abstract

The invention provides an adaptive orthogonal wavelet image denoising method based on accurate local variance priori modeling. The method is characterized by carrying out accurate modeling on orthogonal wavelet transform detail coefficient local variance prior distribution through maximum likelihood estimation, thereby realizing a better denoising performance, improving peak signal-to-noise ratio of a de-noised image, and improving visual effect of the de-noised image. The beneficial effects are that the method overcomes the defect that an existing method is not high in local variance estimation, can better express statistical property of the image orthogonal wavelet decomposition detail coefficient, can give a denoising result adaptively, can remove additive white Gaussian noise in a natural image more effectively, and meanwhile, can better protect regions having rich edge and texture detail information and the like in an original image, and improves visual effect and peak signal-to-noise ratio of the de-noised image. The method is low in computation complexity, and is suitable for immense image denoising application in the age of big data.

Description

A kind of adaptive orthogonal wavelet image denoising based on the modeling of accurate local variance priori Method

Technical field

The present invention relates to a kind of adaptive orthogonal wavelet image de-noising method based on the modeling of accurate local variance priori.

Background technology

Noise is unavoidable in the collection and transmitting procedure of image at present, and image denoising is the weight in image processing field Want research topic.Wavelet transformation is a kind of efficient multi-resolution time-frequency analysis method, and wherein orthogonal wavelet transformation has calculating The advantages such as efficiency is high, coefficient redundancy is little, are widely used in image denoising field.Denoising framework at additive white Gaussian noise Under, the wavelet conversion coefficient y=x+n of the given noise image obtained, while the purpose of denoising is to suppress noise n, to the greatest extent may be used The clean image x that the undistorted recovery of energy is original.

The ultimate principle of Wavelet Denoising Method is to utilize image information and noise at the different qualities of wavelet transformation domain coefficient to making an uproar Sound is filtered, and therefore the Accurate Model of coefficient of wavelet decomposition has important decision meaning to the performance of Denoising Algorithm. Mihcak et al. propose based on the adaptive denoising algorithm of wavelet coefficient statistical modeling in local window, use double random mistake Journey to wavelet coefficient model: the wavelet coefficient in local window be average be 0, variance is the independent identically distributed gaussian variable of θ, and The priori statistics of local variance θ is portrayed by the exponential that parameter is λ, achieves preferable denoising effect.

But, the modeling effect due to the best to the estimation effect of index Study first λ in its method, to local variance θ Unsatisfactory, directly affects the performance of Denoising Algorithm.The Y-PSNR of denoising image is the highest, and corresponds in denoising image The details such as edge, texture enriches that region artifact is serious, poor visual effect.Efficient local variance priori modeling method is to based on certainly The performance boost of the orthogonal wavelet Denoising Algorithm adapting to local window is most important.

Summary of the invention

For solving above technical deficiency, the invention provides a kind of based on the modeling of accurate local variance priori adaptive Answering orthogonal wavelet image de-noising method, the method denoising effect is good, and computation complexity is low, is suitable for the large nuber of images of big data age Denoising is applied.

The present invention is achieved by the following measures:

A kind of based on the modeling of accurate local variance priori the adaptive orthogonal wavelet image de-noising method of the present invention, including Following steps:

Step 1, selects mother wavelet, determines wavelet decomposition number of plies L, noisy image carries out the orthogonal wavelet transformation of L layer, point Do not obtain different sub-band coefficients: top low frequency sub-band coefficient A, level detail sub-band coefficients H_l, vertical detail subband system Number V_lWith diagonal detail sub-band coefficients D_l, wherein l=1,2 ..., L；

Step 2, the detail subbands coefficient H to each layer_l、V_l、D_lIt is handled as follows, is calculated wavelet coefficient office successively The maximal possibility estimation of portion's varianceThe parameter lambda of Part portions deviation index priori, wavelet coefficient local variance in subband MAP estimationEstimated value with denoising image wavelet coefficient

Step 3, keeps low frequency coefficient A constant, wavelet coefficient carries out the reconstruct of orthogonal inverse transformation and obtains denoising image.

In step 2, carry out calculated below:

All wavelet coefficients y (k) in a subband that () is indexed by k, centered by it, the length of side square neighborhood as NIn, calculate the maximal possibility estimation of its variance θ

Wherein, M=N²Represent neighborhoodThe number of interior wavelet coefficient, σ_nFor image comprises the standard deviation of noise；

B (), to current sub-band b, estimates the index Study first λ of its local variance,

Wherein, b=1,2 ..., 3L is to high-frequency sub-band H_l、V_l、D_lIndex, N (b) is non-zero in current sub-band Number；

C (), to all wavelet coefficients y (k) in current sub-band, calculates the MAP estimation of its variance θ

Wherein, M=N²Represent neighborhoodThe number of interior wavelet coefficient, σ_nFor image comprises the standard deviation of noise, λ Index Study first for local variance；

D (), according to minimum mean square error criterion, calculates the estimated value of denoising image wavelet coefficient

Wherein,Represent the MAP estimation in variance θ of all wavelet coefficients y (k) in current sub-band, σ_nFor Image comprises the standard deviation of noise.

The invention has the beneficial effects as follows: instant invention overcomes the shortcoming that existing method local variance estimation is inefficient, energy Enough statistical properties to image orthogonal wavelet decomposition detail coefficients preferably represent, can provide denoising knot adaptively Really, and can preferably protect original image while the additive white Gaussian noise in significantly more efficient removal natural image The region that the detailed information such as middle edge, texture are abundant, improves visual effect and the Y-PSNR of denoising image.Meanwhile, originally Inventive method computation complexity is low, is suitable for the large nuber of images denoising application of big data age.

Accompanying drawing explanation

Fig. 1 is the flow chart of the present invention.

Fig. 2 is the local neighborhood schematic diagram of orthogonal wavelet transformation domain coefficient, wherein neighborhood size N=5.

Fig. 3 is denoising visual effect comparison diagram of the present invention.Fig. 3 (a) is the original image of not Noise；Fig. 3 (b) is Add the noise image that standard deviation is 25；Fig. 3 (c) is the denoising image of maximum likelihood method；Fig. 3 (d) uses based in local window The denoising image of the adaptive denoising algorithm of wavelet coefficient statistical modeling；Fig. 3 (e) is the denoising image of the inventive method.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is done further detailed description:

The invention provides a kind of adaptive orthogonal wavelet image de-noising method based on the modeling of accurate local variance priori, The method uses maximal possibility estimation that the prior distribution of orthogonal wavelet transformation detail coefficients local variance is carried out Accurate Model, from And obtain more preferable denoising performance, promote the Y-PSNR of denoising image, improve the visual effect of denoising image.

1. orthogonal wavelet decomposition

Select mother wavelet, determine wavelet decomposition number of plies L, noisy image is carried out the orthogonal wavelet transformation of L layer, it is thus achieved that general picture Sub-band coefficients A, and the detail subbands coefficient H of each layer_l、V_l、D_l, l=1,2 ..., L.

2. detail subbands coefficient modeling

For each detail subbands, carry out denoising one by one.Concrete, use local square neighborhood as shown in Figure 2 Window, uses doubly stochastic process that the wavelet coefficient in local window carries out statistical modeling: the wavelet coefficient in local window is that average is 0, variance is the independent identically distributed gaussian variable of θ, and local variance θ obedience parameter is the exponential of λ.

3. the maximal possibility estimation of local variance

In view of dot density function and the independent identically distributed characteristic of wavelet coefficient normal distribution, use maximum likelihood method And combine the restriction of variance non-negative, calculate the estimated value of local variance:

Wherein, M=N²Represent neighborhoodThe number of interior wavelet coefficient, σ_nFor image comprises the standard deviation of noise；

4. the Accurate Model of local variance Study first λ

Above-mentioned steps obtainsThe local variance of wavelet coefficient can be provided and well add up description, permissible Use the Study first λ of method of maximum likelihood estimation index distribution based on this.But, the break-in operation taking maximum will cause The existence of zero valued coefficients in the local variance obtained, this is owing to the interference of noise causes, and should get rid of estimating in priori parameter lambda Outside meter:

Wherein, b=1,2 ..., 3L is to high-frequency sub-band H_l、V_l、D_lIndex, N (b) is non-zero in current sub-bandNumber；

5. local variance MAP estimation and Wavelet filtering

The information of summary Study first under Bayesian frame, calculates each wavelet coefficient local side in current sub-band The MAP estimation of difference θ

Wherein, M=N²Represent neighborhoodThe number of interior wavelet coefficient, σ_nFor image comprises the standard deviation of noise, λ Index Study first for local variance；

And calculate the estimated value of denoising image wavelet coefficient according to this

Wherein,Represent the MAP estimation in variance θ of all wavelet coefficients y (k) in current sub-band, σ_nFor Image comprises the standard deviation of noise.

6. wavelet reconstruction and denoising performance evaluation

Keep the low frequency coefficient A of noisy image constant, carry out orthogonal inverse transformation reconstruct with the detail subbands coefficient after denoising Obtain denoising image.Use Y-PSNR (Peak Signal to Noise Ratio, PSNR) as image denoising performance Evaluation index:

Wherein f is original image, and g is image to be evaluated, and W, H are the size of image.

Below, the present invention will be further described in conjunction with specific embodiments.

For standard testing image Lena (512 × 512) as shown in Fig. 3 (a), it is separately added into standard deviation sigma_n=10, The white Gaussian noise of 15,20,25,30,40,50}.For eliminating the randomness disturbance of different noise, at above-mentioned each noise etc. All be repeated 10 times experiment under Ji, and remove make an uproar after the average peak signal to noise ratio of image as the denoising result of this algorithm.Use " Sym8 " small echo carries out L=5 layer orthogonal wavelet decomposition, has selected N={3, the square local window of 5,7} respectively.Table 1 gives Build under framework based on wavelet coefficient statistics in local window, the inventive method and employing maximum likelihood method and maximum a posteriori method The Y-PSNR of denoising image, wherein optimum under the same terms experimental result is given by black matrix.

The Y-PSNR of table 1 different orthogonal Wavelet noise-eliminating method compares (dB)

From the point of view of the experimental result that table 1 provides, having benefited from the Accurate Model of local variance, denoising method of the present invention is being selected The highest Y-PSNR is all given in the case of different size local neighborhood, different noise grade.Compare and maximum likelihood method And employing is promoted to based on the average signal-to-noise ratio of the adaptive denoising algorithm of wavelet coefficient statistical modeling in local window 1.43dB and 0.41dB.

Fig. 3 gives the visual effect contrast of distinct methods denoising image.For the standard testing image of Fig. 3 (a), σ_n= Shown in noise image when 25 such as Fig. 3 (b).Different orthogonal small echo when the local window of the employing 5 × 5 be given of Fig. 3 (c)-(e) From the point of view of the contrast of the denoising image that denoising method obtains, the artifact that the denoising image of the inventive method introduces is minimum, to brim part It is best that the edge divided and texture are protected, and has best visual effect.

The above is only the preferred implementation of this patent, it is noted that for the ordinary skill people of the art For Yuan, on the premise of without departing from the art of this patent principle, it is also possible to make some improvement and replacement, these improve and replace Also should be regarded as the protection domain of this patent.

Claims (2)

1. an adaptive orthogonal wavelet image de-noising method based on the modeling of accurate local variance priori, it is characterised in that bag Include following steps:

Step 1, selects mother wavelet, determines wavelet decomposition number of plies L, noisy image carries out the orthogonal wavelet transformation of L layer, obtains respectively Different sub-band coefficients: top low frequency sub-band coefficient A, level detail sub-band coefficients H_l, vertical detail sub-band coefficients V_lWith Diagonal detail sub-band coefficients D_l, wherein l=1,2 ..., L；

Step 2, the detail subbands coefficient H to each layer_l、V_l、D_lIt is handled as follows, is calculated wavelet coefficient local side successively The maximal possibility estimation of differenceThe parameter lambda of Part portions deviation index priori in subband, wavelet coefficient local variance are Big Posterior estimatorEstimated value with denoising image wavelet coefficient

Step 3, keeps low frequency coefficient A constant, wavelet coefficient carries out the reconstruct of orthogonal inverse transformation and obtains denoising image.

Adaptive orthogonal wavelet image de-noising method based on the modeling of accurate local variance priori the most according to claim 1, It is characterized in that: in step 2, carry out calculated below:

(a) for all wavelet coefficients y (k) in the subband that indexed by k, centered by it, the length of side square neighborhood as NIn, calculate the maximal possibility estimation of its variance θ

Wherein, M=N²Represent neighborhoodThe number of interior wavelet coefficient, σ_nFor image comprises the standard deviation of noise；

B (), to current sub-band b, estimates the index Study first λ of its local variance,

$\mathrm{\λ}=\frac{N\left(b\right)}{\underset{k=1}{\overset{N\left(b\right)}{\Σ}}{\widehat{\mathrm{\θ}}}_{ML}\left(k\right)}$

Wherein, b=1,2 ..., 3L is to high-frequency sub-band H_l、V_l、D_lIndex, N (b) is non-zero in current sub-band? Number；

C (), to all wavelet coefficients y (k) in current sub-band, calculates the MAP estimation of its variance θ

Wherein, M=N²Represent neighborhoodThe number of interior wavelet coefficient, σ_nFor comprising the standard deviation of noise in image, λ is office The index Study first of portion's variance；

D (), according to minimum mean square error criterion, calculates the estimated value of denoising image wavelet coefficient

$\hat{x}\left(k\right)=\frac{{\widehat{\mathrm{\θ}}}_{MAP}\left(k\right)}{{\widehat{\mathrm{\θ}}}_{MAP}\left(k\right)+{\mathrm{\σ}}_n^2}y\left(k\right)$

Wherein,Represent the MAP estimation in variance θ of all wavelet coefficients y (k) in current sub-band, σ_nFor in image Comprise the standard deviation of noise.