CN101477681A - Wavelet image denoising process based on adaptive sliding window adjacent region threshold - Google Patents

Abstract

The invention relates to a method for denoising wavelet images chosen on the basis of the neighbor data of a self-adapting sliding window. The method comprises the following steps: step 1, decomposing a noisy image into sub-bands by wavelet transformation processing; step 2, processing the wavelet coefficient of each sub-band separately according to the following steps: 1), carrying out threshold judgment of the center wavelet coefficient of each neighbor centering on each wavelet coefficient in each sub-band, comparing the correlativity coefficient Theta of each neighbor of the coefficient, and setting a sliding window, in which the maximal correlativity coefficient Theta is located, as the window for threshold processing; and 2), calculating the Bayes adaptive threshold value of the threshold processing window chosen in 1) so as to obtain a scaling factor; and scaling the wavelet coefficient in the center of the window according to the scaling factor; and step 3, reconstructing the wavelet coefficient so as to obtain the filtered image after processing each sub-band of the wavelet with adaptive sliding window neighbor wavelet process. The method achieves a higher peak value signal-to-noise ratio, thereby having a better protection effect for image edges.

Description

Wavelet image denoising process based on adaptive sliding window adjacent region threshold

Technical field

The invention belongs to technical field of image processing, be specifically related to a kind of method of Wavelet image denoising.

Background technology

Many methods have appearred in Wavelet image denoising at present, as soft-threshold and hard-threshold denoising method.Wherein NeighCoeff and NeighBlock method, the wavelet coefficient that will handle places by in the square window that coefficient is formed on every side, is determined the processing of this wavelet coefficient jointly by wavelet coefficients all in the window; The NeighShrink method then decides the processing of the wavelet coefficient that is in this window center according to the size of the quadratic sum of all wavelet coefficients in the neighborhood window.Though the NeighShrink method is being better than common soft or hard threshold method aspect the reservation image detail, when utilizing the NeighShrink method to carry out denoising, the size of moving window is by virtue of experience decision only.And the size of moving window has different influences for the different sub-band denoising effect: the excessive easily level and smooth detailed information of sliding window in high-frequency sub-band; The too small data message of sliding window is few in the low frequency sub-band, influences the effect of denoising.In order to address this problem, the improved NeighShrink method of adaptive threshold is suggested.Adaptive threshold can solve the uncertain problem of window area to a certain extent, but can not control data volume and effective information in the window well, and these two be the basic basis of denoising.

Summary of the invention

The present invention be directed to the above-mentioned deficiency of prior art, a kind of Wavelet image denoising process based on adaptive sliding window adjacent region threshold is provided.This method makes sliding window ara adjust window size automatically according to the coefficient of autocorrelation of data in the sliding window, selects the highest window of correlativity to handle, thereby reaches the purpose of interior data volume of control window and effective information, improves the denoising performance to image.

Wavelet image denoising process based on adaptive sliding window adjacent region threshold of the present invention comprises the following steps (flow process is as shown in Figure 1):

A kind of Wavelet image denoising process based on adaptive sliding window adjacent region threshold comprises the following steps:

Step 1: noisy image through wavelet transform process, is decomposed into each subband;

Step 2: to the wavelet coefficient individual processing in each subband, treatment step is as follows:

1) in each subband, be the center with each wavelet coefficient, the center wavelet coefficient of wavelet coefficient neighborhood in each moving window is done threshold decision, by $\mathrm{\Θ}=\frac{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\left|{\mathrm{\ρ}}_{\mathrm{ij}}\right|}{n}+\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|{\mathrm{\ρ}}_{\mathrm{is}}\right|}{n}$ The correlation coefficient Θ of this each neighborhood of coefficient place relatively, with the sliding window at maximal correlation degree coefficient Θ place window as threshold process, in the formula, wherein (i, the j) neighborhood at the sliding window of ∈ place, (t s) is the central point of sliding window,

Be (X ₁, X ₂..., X _n) correlation matrix,

${\mathrm{\ρ}}_{X_1{X}_2}=\frac{\mathrm{Cov}(X_1,X_2)}{\sqrt{\mathrm{Var}\left(X_1\right)\mathrm{Var}\left(X_2\right)}}$ Be related coefficient,

Cov (X ₁, X ₂)=E{[X ₁-E (X ₁)] [X ₂-E (X ₂)] be X ₁, X ₂Covariance definition;

2) establish { d _{M, n}Be the set of the coefficient behind the noisy image wavelet, to each wavelet coefficient d _{M, n}, establishing with it is that the neighborhood window at center is W _{M, n}, definition neighborhood N _{M, n}(d) comprising all, to drop on current thresholding wavelet coefficient be the center, radius is interior all wavelet coefficients of the square formation of d, d is the interval of adjacent wavelet coefficient on level or the vertical direction, calculates 1) in the Bayes's adaptive threshold based on the Generalized Gaussian model of the threshold process window chosen

Wherein, the noise criteria difference adopts the robustness intermediate value to estimate

One deck diagonal angle high-frequency sub-band, signal variance is then pressed

Estimate, obtain zoom factor ${\mathrm{\α}}_{m,n}=1-{\left(\frac{\mathrm{n\λ}}{S_{m,n}}\right)}^2,$ Wherein $S_{m,n}^2=\underset{(m,n)\∈W_{m,n}}{\mathrm{\Σ}}{d}_{m,n}^2;$

3) wavelet coefficient with window center shrinks by zoom factor;

Step 3: successively each subband of small echo is carried out after self-adaptation slip window neighborhood small echo handles,, obtain the image after the filtering again with wavelet coefficient reconstruct.

The Wavelet image denoising process of adaptive sliding window adjacent region threshold provided by the invention, taken into full account the correlative factor of interior data volume of window and effective information, and providing a kind of as certificate is the adaptive sliding window threshold denoising method of basis for estimation based on small echo neighborhood related coefficient, reach higher Y-PSNR, have better image denoising effect.

Description of drawings

The overview flow chart of the wavelet de-noising method of Fig. 1 adaptive sliding window adjacent region threshold of the present invention.

Fig. 2 wavelet coefficient 3 * 3 moving window neighborhood examples.Small circle is represented wavelet coefficient, and black circles is the center wavelet coefficient, and coefficient is its neighborhood in the square frame.

Fig. 3 noise reduction process master drawing of the present invention.Fig. 3 (a) is the former figure of noise reduction process master drawing; Fig. 3 (b) adds the image of making an uproar for the former figure of master drawing; Fig. 3 (c) is an image after the use noise-reduction method noise reduction process of the present invention.

Embodiment

Below by drawings and Examples the present invention is further described.

1. image transformation

To add the image of making an uproar and carry out wavelet transformation, and obtain the wavelet coefficient matrix, and decompose 4 layers, wavelet basis is the sym8 small echo.

Wavelet transformation is derived as follows:

If one dimension multiresolution analysis { V _jTwo yardstick equations and little wave equation be

$\left\{\begin{array}{c}\mathrm{\φ}\left(t\right)=\sqrt{2}\underset{k}{\mathrm{\Σ}}{h}_k\mathrm{\φ}(2t-k)\\ \mathrm{\ψ}\left(t\right)=\sqrt{2}\underset{k}{\mathrm{\Σ}}{g}_k\mathrm{\φ}(2t-k)\end{array}\right.$

{ h wherein _kBe real wave filter, g _k=(1) ^kh _1-kThe derivation of a then similar orthogonal dimension multiresolution analysis, by It is as follows to calculate two-dimentional Mallat algorithm:

Decomposition algorithm:

$\left\{\begin{array}{c}{c}_{k,m}^j=\underset{l,n}{\mathrm{\Σ}}{h}_{l-2k}{h}_{n-2m}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,1}=\underset{l,n}{\mathrm{\Σ}}{h}_{l-2k}{g}_{n-2m}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,2}=\underset{l,n}{\mathrm{\Σ}}{g}_{l-2k}{h}_{n-2m}{c}_{l,n}^{j+1}\\ c_{k,m}^{j,3}=\underset{l,n}{\mathrm{\Σ}}{g}_{l-2k}{g}_{n-2m}{c}_{l,n}^{j+1}\end{array}\right.$

Reconstruct is calculated $c_{l,n}^{j+1}=\underset{l,n}{\mathrm{\Σ}}{h}_{k-2l}{h}_{m-2n}{c}_{l,n}^j+\underset{l,n}{\mathrm{\Σ}}{h}_{k-2l}{g}_{m-2n}{d}_{l,n}^{j,1}+\underset{l,n}{\mathrm{\Σ}}{g}_{k-2l}{h}_{m-2n}{d}_{l,n}^{j,2}+\underset{l,n}{\mathrm{\Σ}}{g}_{k-2l}{g}_{m-2n}{d}_{l,n}^{j,3}$ Method:

For low frequency part c ^jRepeat two-dimensional wavelet transformation, can obtain c at last ^J+1Multipole wavelet transformation.Accordingly, also can obtain f _J+1(x, many resolutions y) are represented.

2. divide the subband threshold process

Wavelet transformation can recursively use low pass and Hi-pass filter to realize by the low frequency coefficient of same subband, means that wavelet coefficient is correlated with in a small neighbourhood, is called the interior correlativity of layer of wavelet coefficient.In the neighborhood of the bigger wavelet coefficient of value, may have one group of bigger wavelet coefficient.

To the wavelet coefficient individual processing in each subband, treatment step is as follows:

1) in each subband, be the center with each wavelet coefficient, the center wavelet coefficient in each neighborhood is done threshold decision, pass through correlation coefficient $\mathrm{\Θ}=\frac{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\left|{\mathrm{\ρ}}_{\mathrm{ij}}\right|}{n}+\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|{\mathrm{\ρ}}_{\mathrm{is}}\right|}{n}$ The correlation coefficient Θ of this each neighborhood of coefficient place relatively, ((t s) is the central point of sliding window for i, the j) neighborhood at the sliding window of ∈ place.With the sliding window at maximal correlation degree coefficient Θ place window as threshold process.X ₁, X ₂Covariance be defined as Cov (X ₁, X ₂)=E{[X ₁-E (X ₁)] [X ₂-E (X ₂)].Can understand two relations between the stochastic variable by covariance: positive covariance represents that two stochastic variables tend to obtain simultaneously higher value or smaller value; Negative covariance represents that two stochastic variables have rightabout variation tendency.The variation tendency of two stochastic variables is on average meaning.

Related coefficient is designated as ${\mathrm{\ρ}}_{X_1{X}_2}=\frac{\mathrm{Cov}(X_1,X_2)}{\sqrt{\mathrm{Var}\left(X_1\right)\mathrm{Var}\left(X_2\right)}},$ Related coefficient

With covariance Cov (X ₁, X ₂) between have quantitative relation,

It is the covariance under the standard scale.Covariance unit depends on X ₁, X ₂Linear module,

Can better reflect X ₁, X ₂Between relation, and be not subjected to the influence of used linear module.

Less explanation X ₁, X ₂Linear relationship contact relatively poor, vice versa.N dimension random vector (X ₁, X ₂..., X _n), note Cov (X _i, X _j)=E{[X _i-E (X _i)] [X _j-E (X _j)], i, j=1,2 ..., n can be obtained by the relation of covariance and related coefficient:

Matrix

Be (X ₁, X ₂..., X _n) correlation matrix.

By calculating the correlation matrix of view data in the sliding window ara, can obtain the relation of data in current thresholding wavelet coefficient and its neighborhood.

By comparing the size of correlation coefficient Θ, come the correlation degree of the interior current thresholding wavelet coefficient of judgment matrix and all the other coefficients, the window of selecting the correlation degree maximum is for sliding the size of window.By the differentiation of related coefficient, can well play the purpose at denoising and protection edge, prevent that threshold value is excessive or too small.

2) calculate Bayes's adaptive threshold, obtain zoom factor.

Suppose { d _{M, n}Be the set of the coefficient behind the noisy image wavelet, on each subband, wavelet coefficient is obeyed generalized Gaussian distribution GGD.To each wavelet coefficient d _{M, n}, establishing with it is that the neighborhood window at center is W _{M, n}Definition neighborhood N _{M, n}(d) comprising all, to drop on current thresholding wavelet coefficient be the center, and radius is all wavelet coefficients in the square formation of d.D is the interval of adjacent wavelet coefficient on level or the vertical direction.

To the wavelet coefficient of thresholding, use d _{M, n}=d _{M, n}α _{M, n}Shrink, wherein contraction factor is defined as

${\mathrm{\α}}_{m,n}=1-{\left(\frac{\mathrm{n\λ}}{S_{m,n}}\right)}^2,$ $S_{m,n}^2=\underset{(m,n)\∈W_{m,n}}{\mathrm{\Σ}}{d}_{m,n}^2$

When this contraction factor when negative, be changed to zero; Otherwise, remain unchanged.

The adaptive threshold of the threshold value λ here based on the Bayes estimation of Generalized Gaussian model

Wherein the noise criteria difference adopts the robustness intermediate value to estimate:

Y (i, j) ∈ HH ₁, i.e. one deck diagonal angle high-frequency sub-band, signal variance is then pressed

Estimate.

Wherein, generalized Gaussian distribution is also referred to as the broad sense laplacian distribution, is defined as:

${\mathrm{GG}}_{{\mathrm{\σ}}_x,\mathrm{\β}}\left(x\right)=C({\mathrm{\σ}}_x,\mathrm{\β})\exp \{-{\left[\mathrm{\α}({\mathrm{\σ}}_x,\mathrm{\β})\right|x\left|\right]}^{\mathrm{\β}}\}$ This is distributed with two parameter: σ _xBe the variance of signal, the rate of propagation of control of density function; β is a form parameter, has determined the rate of decay of GGD density function.

If g _{I, j}=f _{I, j}+ ε _{I, j}, i, j=1,2 ..., N.G wherein _{I, j}, f _{I, j}, ε _{I, j}Represent noisy image respectively, true picture and noise.ε wherein _{I, j}Independent same distribution iid and obedience N (0, σ ²), f _{I, j}, ε _{I, j}Independent.

The purpose of denoising is to obtain f _{I, j}Estimated value Make square error MSE minimum.

If Y _{I, j}=X _{I, j}+ V _{I, j}Be corresponding wavelet coefficient, above-mentioned two formulas are written as g=f+ ε and Y=X+V.T is a threshold value, $X~N(0,{\mathrm{\σ}}_X^2),$

Y|X～N (x, σ ²), under the Bayes framework, the Bayes risk, promptly estimated mean-square is:

Make that the optimal threshold of r (T) risk minimum is T ^*: $T^{*}({\mathrm{\σ}}_x,\mathrm{\β})=\arg \underset{T}{\min }r\left(T\right)$

Through experimental study, the near-optimization formula of of obtaining on minimum Bayes risk meaning, i.e. BayesShrink threshold value: $T_B=\frac{{\mathrm{\σ}}^2}{{\mathrm{\σ}}_X}.$ T _BBe T ^*Approximate, maximum deviation is no more than 5%.

3) image coefficient of window center is shunk according to the zoom factor that obtains.

3. image reconstruction

Successively each subband of small echo is carried out after self-adaptation slip window neighborhood small echo handles,, obtain the image after the filtering again with wavelet coefficient reconstruct.

4. experimental result

In order to verify the validity of denoising method of the present invention, (shown in Fig. 3 (a)) tests to concrete picture.Adopt the sym8 small echo to carry out Flame Image Process in the experiment, image added the noise of varying strength, with image with 4 layers of wavelet decomposition.As the criterion of anti-acoustic capability quality, experimental result is as shown in table 1 with PSNR (Peak Signal to Noise Ratio).

PSNR/db under table 1 all size window and the noise variance relatively

Become sliding window	10	15	20	25
					PSNR (dB)	32.2378	29.6772	28.0438	26.6221

The data that provide from table 1 use the adaptive sliding window adjacent region bayes method that provides among the present invention can obtain higher Y-PSNR as can be seen.

On the visual effect of image (shown in Fig. 3 (c)) simultaneously, method provided by the invention also obviously is better than classic method.It has suppressed most noise in the image, has suppressed " level and smooth excessively " preferably, has kept the detailed information of image as much as possible, makes the image table behind the noise reduction reveal edge more clearly.And when noise pollution was heavy more, denoising effect was good more.

Claims (1)

1. the Wavelet image denoising process based on adaptive sliding window adjacent region threshold comprises the following steps:

Step 1: noisy image through wavelet transform process, is decomposed into each subband;

Step 2: to the wavelet coefficient individual processing in each subband, treatment step is as follows:

1) in each subband, be the center with each wavelet coefficient, the center wavelet coefficient of wavelet coefficient neighborhood in each moving window is done threshold decision, by $\mathrm{\Θ}=\frac{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\left|{\mathrm{\ρ}}_{\mathrm{tj}}\right|}{n}+\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|{\mathrm{\ρ}}_{\mathrm{iS}}\right|}{n}$ The correlation coefficient Θ of this each neighborhood of coefficient place relatively, with the sliding window at maximal correlation degree coefficient Θ place window as threshold process, in the formula, wherein (i, the j) neighborhood at the sliding window of ∈ place, (t s) is the central point of sliding window,

Be (X ₁, X ₂..., X _n) correlation matrix,

$\mathrm{\ρ}{x}_1{x}_2=\frac{\mathrm{Cov}(X_1,X_2)}{\sqrt{\mathrm{Var}\left(X_1\right)\mathrm{Var}\left(X_2\right)}}$ Be related coefficient,

Cov (X ₁, X ₂)=E{[X ₁-E (X ₁)] [X ₂-E (X ₂)] be X ₁, X ₂Covariance definition;

2) establish { d _{M, n}Be the set of the coefficient behind the noisy image wavelet, to each wavelet coefficient d _{M, n}, establishing with it is that the neighborhood window at center is W _{M, n}, definition neighborhood N _{M, n}(d) comprising all, to drop on current thresholding wavelet coefficient be the center, radius is interior all wavelet coefficients of the square formation of d, d is the interval of adjacent wavelet coefficient on level or the vertical direction, calculates 1) in the Bayes's adaptive threshold based on the Generalized Gaussian model of the threshold process window chosen

Wherein, the noise criteria difference adopts the robustness intermediate value to estimate

One deck diagonal angle high-frequency sub-band, signal variance is then pressed

Estimate, obtain zoom factor ${\mathrm{\α}}_{m,n}=1-{\left(\frac{\mathrm{n\λ}}{S_{m,n}}\right)}^2,$ Wherein $S_{m,n}^2=\underset{(m,n)\∈W_{m,n}}{\mathrm{\Σ}}{d}_{m,n}^2;$

3) wavelet coefficient with window center shrinks by zoom factor;

Step 3: successively each subband of small echo is carried out after self-adaptation slip window neighborhood small echo handles,, obtain the image after the filtering again with wavelet coefficient reconstruct.

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