CN102637294A - Image enhancement method based on non-down-sampling Contourlet transform and improved total variation - Google Patents

Abstract

The invention relates to an image enhancement method based on non-down-sampling Contourlet transform and improved total variation. Through the method, the pseudo-Gibbs phenomenon existing in the enhanced image is effectively reduced by an improved total variation method based on the good expression feature of the non-down-sampling Contourlet transform on the edge/contour, and the noise is suppressed while enhancing the edge feature and contrast of the image so as to further improve the image quality. The experimental result indicates that: the method provided by the invention can obtain a better enhancement effect than the traditional method based on the wavelet and non-down-sampling Contourlet. The method can synchronously realize noise elimination and edge preservation, is very sensitive to noise, and suppresses noise while enhancing the edge feature and contrast of the image; and moreover, the method can effectively reduce the pseudo-Gibbs phenomenon to further improve the image quality.

Description

Image enchancing method based on non-downsampling Contourlet conversion and improved total variation

Technical field

The invention belongs to image processing field, relate generally to a kind of image enchancing method based on non-downsampling Contourlet conversion and improved total variation.

Background technology

Picture signal receives various interference of noise through regular meeting in generation, transmission and recording process, problems such as contrast is low, signal to noise ratio (S/N ratio) is low, weak edge is many, texture is fuzzy often occur.Image enhancement technique can be in keeping image in original strong edge or the clear texture, and edge a little less than it or fuzzy texture are strengthened, and improves the contrast of image.

Algorithm for image enhancement is divided spatial domain and transform domain 2 big classes.The spatial domain algorithm is directly in the enterprising row operation of former figure, and its common algorithm comprises linear stretch, histogram enhancing etc., but for soft image, such algorithm existence being prone to make noise increases, problems such as enhancing are crossed at the edge.In order to overcome above problem, people analyze the spatial domain conversion of signals in special domain, and obtain good result, form transform-domain algorithm thus.Transform-domain algorithm is mapped to transform domain with image by time domain, and through coefficient in transform domain is handled, to reach the purpose of enhancing, its representational conversion comprises Fourier transform, wavelet transformation etc. again.Fourier transform has solved insoluble problem in many time domains with the spectral characteristic of signal, but this conversion does not have the ability of time-frequency localization, and wavelet transformation has solved this problem well.But wavelet transformation is often relatively responsive to a singularity, and limited to the edge direction ability to express, can not be to the edge sparse expression.In order to overcome the limitation of wavelet transformation; M.N.Do in 2002 and Martin Vetterli have proposed the Contourlet conversion, and it has effectively remedied above-mentioned deficiency effectively, is a kind of " really " two dimensional image method for expressing; This method can be caught the geometry of image well; " fine " picture engraving edge is widely used in denoising, fields such as enhancing.Simultaneously; Because the Contourlet conversion does not have translation invariance; 2006; (Nonsubsampled Contourlet Transform NSCT) is proposed by people such as M.N.Do, shows himself advantage aspect denoising, enhancing gradually to have the Contourlet conversion-non-downsampling Contourlet conversion of translation invariant characteristic.

Present stage; The method of utilizing NSCT to carry out the figure image intensifying mainly is that first image to noisy carries out the NSCT conversion; Remove the coefficient of mainly forming at transform domain through an appropriate threshold, carry out the image after the NSCT inverse transformation is enhanced then less than threshold value by noise.Though this method has well been removed noise,, in the process of little coefficient zero setting, also removed the useful coefficient of part simultaneously, thereby caused the image after the denoising to have certain pseudo-Gibbs phenomenon.

Summary of the invention

The technical matters that solves

For fear of the weak point of prior art, the present invention proposes a kind of image enchancing method based on non-downsampling Contourlet conversion and improved total variation, overcomes the pseudo-Gibbs phenomenon that image contains after the enhancing that existing method caused.

Technical scheme

A kind of SAR image enchancing method that combines based on non-downsampling Contourlet conversion and improved total variation is characterized in that step is following:

Step 1: SAR gradation of image value matrix is carried out logarithm operation, obtain SAR gradation of image value matrix to matrix number;

Step 2: to SAR gradation of image value matrix matrix number is carried out the non-downsampling Contourlet direct transform under the given scale parameter, obtain the non-downsampling Contourlet conversion matrix of coefficients of all directions under the different decomposition yardstick; Said given scale parameter comprises decomposition scale number and direction number;

Step 3: utilize matrix of coefficients in the non-downsampling Contourlet conversion matrix of coefficients that gain function and step 2 obtain to multiply each other and realize the nonlinear transformation of matrix of coefficients, obtain after the nonlinear transformation non-downsampling Contourlet conversion matrix of coefficients of all directions under the different decomposition yardstick; Described gain function is:

$y=\left\{\begin{array}{cc}0& x<T_1\\ \frac{x-T_1}{T_1}{\left(\frac{T_3}{T_2}\right)}^p+\frac{T_2-x}{T_1}& T_1\&le;x<T_2\\ {\left(\frac{T_3}{x}\right)}^p& T_2\&le;x<T_3\\ {\left(\frac{T_3}{x}\right)}^s& x\&GreaterEqual;T_3\end{array}\right.$

Wherein, x is the coefficient in the non-downsampling Contourlet conversion matrix of coefficients that obtains of step 2; P ∈ (0,1], s ∈ (0,1]; T ₁, T ₂, T ₃Computing formula be respectively:

$T_1=\left\{\begin{array}{cc}{s}_1{\mathrm{\&sigma;\&sigma;}}_x& j=1\\ s_2{\mathrm{\&sigma;\&sigma;}}_x& j>1\end{array}\right.$

T ₂＝s ₃T ₁

T ₃＝s ₄T ₂

Wherein, j is a decomposition scale, σ for press σ=median (| S _HH|)/noise criteria to matrix number of the 0.6745 noise image gray-scale value matrix that calculates is poor, and intermediate value is got in median () expression, || expression delivery, S _HHBe that noise image gray-scale value matrix is carried out the diagonal high-frequency sub-band wavelet coefficient matrix that the one-level wavelet decomposition obtains; σ _xTwo norms for input x; s ₁∈ [1,5], s ₂∈ [1,5], s ₃∈ [2,3], s ₄∈ [1.5,2.5];

Step 4: the non-downsampling Contourlet conversion matrix of coefficients that step 3 is obtained carries out the non-downsampling Contourlet inverse transformation, obtains non-downsampling Contourlet inverse transformation matrix of consequence, and the scale parameter of inverse transformation is consistent with the scale parameter of direct transform;

Step 5: the non-downsampling Contourlet inverse transformation matrix of consequence that step 4 is obtained carries out exponent arithmetic, obtains the SAR gradation of image value matrix after first denoising and characteristic strengthen;

Step 6: utilize the SAR gradation of image value matrix after first denoising that improved total variation method obtains step 5 and characteristic strengthen to carry out second denoising, to remove because the pseudo-Gibbs' effect that step 3 causes obtains final enhancing gradation of image value matrix: I _Con-tv=TV (I _Con);

Said improved total variation model is:

$\arg \min \left\{\underset{\mathrm{\&Omega;}}{\&Integral;}\right|\&dtri;u|\mathrm{d\&Omega;}+\frac{\mathrm{\&lambda;}}{2}\underset{\mathrm{\&Omega;}}{\&Integral;}{(u-S\left(u_0\right))}^2\mathrm{d\&Omega;}\}$

Wherein: Ω ∈ R ², u ₀The expression initial pictures, u ecbatic image,

Be the gradient computing, || represent European norm, λ ∈ R ₊Be regularization parameter, S is ripple atom conversion hard-threshold denoising operation, the T in threshold value and the step 3 that gets ₁Identical.

Said scale parameter is got 3-4.

Said direction number is got 2-4.

Beneficial effect

A kind of image enchancing method that the present invention proposes based on non-downsampling Contourlet conversion and improved total variation; Based on the good characterization of non-downsampling Contourlet conversion to edge/profile; Utilize improved total variation method effectively to subdue and strengthen the pseudo-Gibbs phenomenon that exists in the image; When edge of image characteristic and contrast are strengthened, wherein noise is suppressed, further improve picture quality.Experimental result shows, the present invention and traditional method based on wavelet and non-downsampling Contourlet specific energy mutually obtain reinforced effects preferably.This method can realize synchronously that noise removing and edge keep, but very responsive to noise, in edge of image characteristic and the contrast enhancing, wherein noise is suppressed, and can effectively subdue pseudo-Gibbs phenomenon, further improves picture quality.

The invention has the beneficial effects as follows: based on the good characterization of non-downsampling Contourlet conversion edge/profile; Utilize improved total variation method effectively to subdue and strengthen the pseudo-Gibbs phenomenon that exists in the image; In to edge of image characteristic and contrast enhancing; Noise to wherein suppresses, and further improves picture quality.

Description of drawings

Fig. 1: be the process flow diagram that the present invention is based on the noise image Enhancement Method that non-downsampling Contourlet conversion and improved total variation combine.

Embodiment

Combine embodiment, accompanying drawing that the present invention is further described at present:

Used image is for being defined in R in the embodiment of the invention ²On contain noise SAR image I ₀, all corresponding matrix of every width of cloth image, a corresponding element in the corresponding matrix of each pixel in the image.

Step 1: to the SAR gradation of image value matrix I of input ₀Carry out logarithm operation, obtain SAR gradation of image value matrix to matrix number I ₁

Step 2: to SAR gradation of image value matrix matrix number is carried out the non-downsampling Contourlet direct transform under the given scale parameter, obtain the non-downsampling Contourlet conversion matrix of coefficients C of different directions l under the different decomposition yardstick j ₀(j, l), j=1 wherein, 2, Λ, J, J separates yardstick, l=1, L, L for segmentation _j, L _jIt is the direction number under j the yardstick;

Step 3: to input log-transformation image array I ₁Press σ=median (| S _HH|)/0.6745 carry out the noise criteria difference and estimate, median () the expression intermediate value of getting all coefficients in the matrix wherein, || expression delivery, S _HHBe to logarithmic image matrix I ₁Carry out diagonal high-frequency sub-band (HH subband) the wavelet coefficient matrix that the one-level wavelet decomposition obtains;

The calculated gains function $y=\left\{\begin{array}{cc}0& x<T_1\\ \frac{x-T_1}{T_1}{\left(\frac{T_3}{T_2}\right)}^p+\frac{T_2-x}{T_1}& T_1\&le;x<T_2\\ {\left(\frac{T_3}{x}\right)}^p& T_2\&le;x<T_3\\ {\left(\frac{T_3}{x}\right)}^s& x\&GreaterEqual;T_3\end{array}\right.$ In each threshold value, $T_1=\left\{\begin{array}{cc}{s}_1{\mathrm{\&sigma;\; \&sigma;}}_x& j=1\\ s_2{\mathrm{\&sigma;\; \&sigma;}}_x& j>1\end{array}\right.,$ T ₂=s ₃T ₁, T ₃=s ₄T ₂, s wherein ₁∈ [1,5], s ₂∈ [1,5], s ₃∈ [2,3], s ₄∈ [1.5,2.5], σ _xTwo norms for input x;

Utilize gain function to the C in the step 3 ₀(j; L) the non-downsampling Contourlet conversion matrix of coefficients under the different decomposition yardstick all directions except that the thickest yardstick stretches respectively/shrinks, and obtains the non-downsampling Contourlet conversion matrix of coefficients of different decomposition yardstick all directions after the nonlinear transformation;

Step 4: the non-downsampling Contourlet conversion matrix of coefficients that step 6 is obtained carries out the non-downsampling Contourlet inverse transformation, obtains non-downsampling Contourlet inverse transformation matrix of consequence; The scale parameter of inverse transformation is consistent with the scale parameter of direct transform;

Step 5: the non-downsampling Contourlet inverse transformation matrix of consequence to obtaining carries out exponent arithmetic, obtains the SAR gradation of image value matrix I after first denoising and characteristic strengthen _Con

Step 6: the initial enhancing image I that step 8 is obtained _ConUtilize improved total variation model to carry out second denoising and obtain final enhancing image I _Con-tv=TV (I _Con).

Improved non-downsampling Contourlet conversion model is: $\mathrm{Arg}\mathrm{Min}\left\{\underset{\mathrm{\&Omega;}}{\&Integral;}\right|\&dtri;u|\mathrm{D\&Omega;}+\frac{\mathrm{\&lambda;}}{2}\underset{\mathrm{\&Omega;}}{\&Integral;}{(u-S\left(u_0\right))}^2\mathrm{D\&Omega;}\},$

Wherein: Ω ∈ R ², u ₀The expression initial pictures, u ecbatic image,

Be the gradient computing, || represent European norm, λ ∈ R ₊Be regularization parameter, S is ripple atom conversion hard-threshold denoising operation, the T in threshold value and the step 3 that gets ₁Identical.

Improved non-downsampling Contourlet conversion model specific descriptions be:

The total variation denoising model (ROF model) that people such as Rudin propose can be expressed as and minimize following energy functional

$\arg \min \left\{\underset{\mathrm{\&Omega;}}{\&Integral;}\right|\&dtri;u|\mathrm{d\&Omega;}+\frac{\mathrm{\&lambda;}}{2}\underset{\mathrm{\&Omega;}}{\&Integral;}{(u-S\left(u_0\right))}^2\mathrm{d\&Omega;}\}$

First in the formula is regular terms, guarantees to separate to have certain slickness; Second is the fidelity item, guarantees to separate and initial value u ₀Between deviation not too large; λ ∈ R ₊Be regularization parameter, in regular terms and fidelity Xiang Zhongqi equilibrium activity.The total variation model can keep edge and the integral oscillation property that suppresses image preferably when removing noise.But this model only has good denoising effect to simple image, then can produce staircase effect for the image of complex texture.

Fidelity item λ (u in the total variation model ₀-u) be for make the denoising image in diffusion process with original image u ₀Be consistent, but u ₀Be the image that has noise, cause final denoising result that deviation is arranged.This paper introduces nonlinear operation operator S to the fidelity item and makes it to become λ (S (u ₀)-u), wherein S should be able to keep and strengthen the material particular characteristic of image, then S (u ₀) can be expressed as:

S(u ₀)＝T ^-1θ _hT(u ₀)

Wherein T and T ^-1Represent atom direct transform of mirror image continuation ripple and the inverse transformation of mirror image continuation ripple atom respectively. ${\mathrm{\&theta;}}_h\left(x\right)=\left\{\begin{array}{c}x,\left|x\right|>T_1\\ 0,\left|x\right|\&le;T_1\end{array}\right.$ Expression hard-threshold contracting function, T ₁Computing formula and step 2 in T ₁Computing formula identical.

Finally, improved total variation model can be expressed as:

$\arg \min \left\{\underset{\mathrm{\&Omega;}}{\&Integral;}\right|\&dtri;u|\mathrm{d\&Omega;}+\frac{\mathrm{\&lambda;}}{2}\underset{\mathrm{\&Omega;}}{\&Integral;}{(u-S\left(u_0\right))}^2\mathrm{d\&Omega;}\}.$

Claims (3)

1. SAR image enchancing method that combines based on non-downsampling Contourlet conversion and improved total variation is characterized in that step is following:

Step 1: SAR gradation of image value matrix is carried out logarithm operation, obtain SAR gradation of image value matrix to matrix number;

Step 2: to SAR gradation of image value matrix matrix number is carried out the non-downsampling Contourlet direct transform under the given scale parameter, obtain the non-downsampling Contourlet conversion matrix of coefficients of all directions under the different decomposition yardstick; Said given scale parameter comprises decomposition scale number and direction number;

Step 3: utilize matrix of coefficients in the non-downsampling Contourlet conversion matrix of coefficients that gain function and step 2 obtain to multiply each other and realize the nonlinear transformation of matrix of coefficients, obtain after the nonlinear transformation non-downsampling Contourlet conversion matrix of coefficients of all directions under the different decomposition yardstick; Described gain function is:

$y=\left\{\begin{array}{cc}0& x<T_1\\ \frac{x-T_1}{T_1}{\left(\frac{T_3}{T_2}\right)}^p+\frac{T_2-x}{T_1}& T_1\&le;x<T_2\\ {\left(\frac{T_3}{x}\right)}^p& T_2\&le;x<T_3\\ {\left(\frac{T_3}{x}\right)}^s& x\&GreaterEqual;T_3\end{array}\right.$

Wherein, x is the coefficient in the non-downsampling Contourlet conversion matrix of coefficients that obtains of step 2; P ∈ (0,1], s ∈ (0,1]; T ₁, T ₂, T ₃Computing formula be respectively:

$T_1=\left\{\begin{array}{cc}{s}_1{\mathrm{\&sigma;\&sigma;}}_x& j=1\\ s_2{\mathrm{\&sigma;\&sigma;}}_x& j>1\end{array}\right.$

T ₂＝s ₃T ₁

T ₃＝s ₄T ₂

Wherein, j is a decomposition scale, σ for press σ=median (| S _HH|)/noise criteria to matrix number of the 0.6745 noise image gray-scale value matrix that calculates is poor, and intermediate value is got in median () expression, || expression delivery, S _HHBe that noise image gray-scale value matrix is carried out the diagonal high-frequency sub-band wavelet coefficient matrix that the one-level wavelet decomposition obtains; σ _xTwo norms for input x; s ₁∈ [1,5], s ₂∈ [1,5], s ₃∈ [2,3], s ₄∈ [1.5,2.5];

Step 4: the non-downsampling Contourlet conversion matrix of coefficients that step 3 is obtained carries out the non-downsampling Contourlet inverse transformation, obtains non-downsampling Contourlet inverse transformation matrix of consequence, and the scale parameter of inverse transformation is consistent with the scale parameter of direct transform;

Step 5: the non-downsampling Contourlet inverse transformation matrix of consequence that step 4 is obtained carries out exponent arithmetic, obtains the SAR gradation of image value matrix after first denoising and characteristic strengthen;

Step 6: utilize the SAR gradation of image value matrix after first denoising that improved total variation method obtains step 5 and characteristic strengthen to carry out second denoising, to remove because the pseudo-Gibbs' effect that step 3 causes obtains final enhancing gradation of image value matrix: I _Con-tv=TV (I _Con);

Said improved total variation model is:

$\arg \min \left\{\underset{\mathrm{\&Omega;}}{\&Integral;}\right|\&dtri;u|\mathrm{d\&Omega;}+\frac{\mathrm{\&lambda;}}{2}\underset{\mathrm{\&Omega;}}{\&Integral;}{(u-S\left(u_0\right))}^2\mathrm{d\&Omega;}\}$

Wherein: Ω ∈ R ², u ₀The expression initial pictures, u ecbatic image,

Be the gradient computing, || represent European norm, λ ∈ R ₊Be regularization parameter, S is ripple atom conversion hard-threshold denoising operation, the T in threshold value and the step 3 that gets ₁Identical.

2. the SAR image enchancing method that combines based on non-downsampling Contourlet conversion and improved total variation according to claim 1, it is characterized in that: said scale parameter is got 3-4.

3. the SAR image enchancing method that combines based on non-downsampling Contourlet conversion and improved total variation according to claim 1, it is characterized in that: said direction number is got 2-4.