CN104217406A - SAR image noise reduction method based on shear wave coefficient processing - Google Patents

Abstract

The invention discloses a SAR image noise reduction method based on shear wave coefficient processing. It belongs to the technical field of digital image processing. It utilizes the sparse characteristic of the coefficients after the image shearlet transform, first establishes a sparse representation model based on the image shearlet coefficients, and then realizes the unbiased estimation of the sparse representation coefficients in the statistical mean sense through the piecewise orthogonal matching pursuit StOMP algorithm , and reconstruct the sparsely represented shearlet coefficients into a denoised image; in order to make up for the loss of image details caused by the loss of some coefficients in the sparse representation, and use the shearlet function corresponding to these coefficients to have the ability to extract image edge details Aiming at the result of projection and reconstruction of the image in the shear wave function space corresponding to the loss coefficient, combined with the total variational TV method based on energy functional to further iteratively denoise, and finally obtain a denoising image with rich details, which not only suppresses SAR Image speckle noise maintains the detailed texture of the image and can be used for SAR image noise reduction.

Description

A Noise Reduction Method for SAR Image Based on Shearlet Coefficient Processing

technical field

The invention belongs to the technical field of digital image processing, and in particular relates to a SAR image noise reduction method, which is used to perform noise reduction processing on the SAR image.

Background technique

Synthetic aperture radar has all-weather and all-weather detection and reconnaissance tracking capabilities in imaging, and can effectively identify camouflage and penetrate cover objects. Therefore, SAR images are widely used in aerial photogrammetry and remote sensing, satellite ocean observation, space reconnaissance, Image matching guidance, deep space exploration, etc. However, the speckle noise brought to the image by the SAR coherent imaging mechanism has an adverse effect on post-processing such as target recognition and image compression. Whether the speckle noise can be effectively filtered out has become an important prerequisite for subsequent image interpretation.

Since SAR images have rich textures and edges, it is the focus of SAR image denoising to fully preserve the textures and edges of images while effectively filtering out speckle noise. In recent years, due to the good performance of sparse representation in natural image denoising, it is gradually becoming one of the effective methods for image denoising. However, such methods inevitably suffer from the loss of image details while sparsely representing them. In order to improve the ability to preserve image details, most of the existing methods are limited to processing the image after sparse noise reduction, but because the information lost in the sparse representation cannot be recovered, the degree of improvement is limited, and the edge details lost in the noise-reduced image cannot be obviously restored. .

Contents of the invention

The present invention provides a SAR image noise reduction method based on shear wave coefficient processing in order to overcome the deficiency of image edge detail information loss in the existing SAR image noise reduction method and obtain a noise reduction SAR image with clear details. This method fully considers the characteristics of shear wave coefficients, first establishes the noise reduction model with sparse representation of shear wave coefficients, and then uses the TV method to further repair the image, which can not only suppress the speckle noise of SAR images well, but also solve the problem of speckle reduction The detail texture of the image remains a problem, so this method can effectively achieve SAR image noise reduction. Include the following steps:

Step 1. Image noise model conversion

Using a non-logarithmic additive noise model, the multiplicative noise with a mean value of 1 in the input SAR image is transformed into an additive noise with a mean value of 0.

Step 2. Sparse noise reduction in the shear wave domain

First, shearlet transform is performed on the noise image to obtain the shearlet coefficient w of the image. In order to realize the sparse representation of the coefficients, the coefficient w is transformed by the measurement matrix Φ, that is, y=Φw. Suppose further that the sparse approximation of y under the measurement matrix Φ is denoted as z. The following optimized sparse representation model is obtained:

$g\left(a\right)={\left|\right|\mathrm{the\; y}-\mathrm{\Φz}\left|\right|}_2^2+\mathrm{\γ}{\left|\right|z\left|\right|}_0$ Formula 1)

When formula (1) takes the minimum value, the corresponding optimal solution z is the sparse representation of the original coefficient w and sparse representation The means of are unbiased estimates of the mean of the clean image shearlet coefficients. Using the StOMP algorithm to solve formula (1), first project y onto each atom of the measurement matrix Φ, and then put the corresponding atom of the projection value greater than the threshold into the index set I ₁ , and approximate y by the atoms in the index set to obtain the residual Difference R ¹ y. In order to use more atoms to further approximate y, the residual R ¹ y can be further decomposed in the same way. If the residual of the mth iteration is R ^m y, then R ^m+1 y can be expressed as:

R ^m y＝<R ^m y,φ _rm >φ _rm +R ^m+1 y Formula (2)

Where φ _rm represents the atoms selected from the measurement matrix Φ at the mth iteration, and these selected atoms are incorporated into Im _-1 to obtain an updated _Im . If the termination condition ||R ^m y|| ² ≤ ε or |I _m |>L is satisfied, the iteration ends, otherwise the iteration continues. When the iteration ends, the optimal solution z can be obtained by formula (3)

${\left(z_m\right)}_{I_m}={\left({\mathrm{\&Phi;}}_{I_m}^T{\mathrm{\&Phi;}}_{I_m}\right)}^{-1}{\mathrm{\&Phi;}}_{I_m}^T\mathrm{the\; y}$ Formula (3)

The optimal solution z is the sparse representation of the original coefficient w Will and the small coefficients discarded in the sparse representation of w are subjected to inverse shearlet transformation to obtain the denoised image u _s and the residual image u _d , and the shearlet space corresponding to the discarded small coefficients in the sparse representation is denoted as M.

Step 3: TV noise reduction and detail restoration

According to the characteristics of the shear wave coefficient, combined with the processing results of step 2, the TV model based on the energy functional is established:

$f\left(u\right)=\underset{\mathrm{\&Omega;}}{\&Integral;}\mathrm{\&phi;}\left(\right||\&dtri;P_S\left(u\right)|\left|\right)\mathrm{dxdy}+\frac{\mathrm{\&lambda;}}{2}\underset{\mathrm{\&Omega;}}{\&Integral;}{(u-u_0)}^2\mathrm{dxdy}$ Formula (4)

Where P _S (u) is shown in formula (5):

$P_S\left(u\right)=\underset{j,l,k\&Element;m}{\mathrm{\&Sigma;}}<u,{\mathrm{\&psi;}}_{j,l,k}>{\mathrm{\&psi;}}_{j,l,k}$ Formula (5)

Among them, M is the set to which j, k, and l belong, and the set is determined by the shear wave function corresponding to the missing coefficient in the sparse representation in step 2. P _S (u) represents the projection and reconstruction of image u on this part of the shear wave function space result. when When the energy functional function of formula (3) takes a minimum value, u at this time is the denoised image after TV processing. From formula (3) can get As follows:

$\frac{\&PartialD;u}{\&PartialD;t}=\&dtri;(\frac{{\mathrm{\&phi;}}^{\&prime;}\left(\right||\&dtri;\mathrm{PS}\left(u\right)|\left|\right)}{\left|\right|\&dtri;\mathrm{PS}\left(u\right)\left|\right|}\&dtri;\mathrm{PS}\left(u\right)-\mathrm{\&lambda;}(u-u_0)$ Formula (6)

The first term of formula (6) is the diffusion term, let ρ(x)=φ'(x)/x, where Then ρ(x) can control the smoothness of the diffusion process.

Use the steepest descent method to solve equation (6) through equation (7)

u ^k+1 ＝u ^k +Δt[η(Ps(u ^k ))-λ(u ^k -u ₀ )] Formula (7)

in Δt is the iteration step size, k is the kth iteration, u ₀ is the original noisy image, the initial value of the iteration is u _s +Δt[η(u _d )], when the MAD between the current and subsequent two iterations is less than a certain threshold End the iteration and get the final denoised image.

The innovation of the present invention is to use the sparsity of image shear wave coefficients and the ability to extract image edges, use the advantages of unbiased estimation of clean image shear wave coefficients in sparse representation to reduce noise, and aim at the process of sparse representation The edge texture information of the image loss, using the small shearlet coefficient to distinguish the image noise and the edge details, adopts TV processing for the projection result of the image in this space, and further realizes the noise reduction and detail restoration of the image.

Beneficial effects of the present invention: use the noise reduction model based on statistical optimization to sparsely represent the shear wave coefficient instead of the traditional soft and hard threshold processing method, and at the same time, when solving the model optimization problem, the StOMP algorithm is used to ensure the solution accuracy The calculation efficiency is also improved, so the overall noise reduction effect can reach a higher level; and the TV processing based on energy functional is established, and the information lost in the sparse representation process is further repaired on the basis of noise reduction, so this method is both It can maintain image texture details while reducing noise, and has high computing efficiency.

The present invention mainly adopts the method of simulation experiment to verify, and all steps and conclusions are verified correctly on MATLAB8.0.

Description of drawings

Fig. 1 is a workflow block diagram of the present invention;

Fig. 2 is the real noisy hilly SAR image used by the simulation of the present invention;

The white rectangular area is the selected homogeneous area;

Fig. 3 is the noise reduction result diagram of Fig. 2 by the KSVD method;

Figure 4 is the noise reduction result of Figure 2 by the KSVD_TV method;

Fig. 5 is a graph of the denoising result of Fig. 2 by the method of the present invention.

Detailed ways

With reference to Fig. 1, the present invention is based on the SAR image denoising method of shearlet coefficient processing, and concrete steps comprise as follows:

Step 1. Image noise model conversion

The non-logarithmic noise transformation model of formula (8) is used to transform the multiplicative noise model of SAR image into an additive noise model

I＝RX＝X+(R-1)X＝X+N formula (8)

Among them, I is the image intensity polluted by noise, R stands for coherent speckle noise, X stands for the real backscattering intensity of ground objects, and N=(R-1)X is zero-mean additive noise.

Step 2. Sparse noise reduction in the shear wave domain

The noise image is subjected to shearlet transform to obtain the shearlet coefficients at 5 scales of the horizontal cone and the vertical cone, and the coefficients at each scale are sparsed column by column. First construct a random measurement matrix Φ={φ _r } _r∈Γ , and then normalize it. Assuming that w represents the column of coefficients, transform w with the measurement matrix Φ, that is, y=Φw, and then establish the optimal sparse representation model And use the StOMP algorithm to solve the sparse model. Initially, the StOMP algorithm sparsely approximates the value z ₀ =0, the residual R ⁰ y=y, and the subscript index set I ₀ of the selected atom is empty. When the number of iterations m=1, first calculate the inner product of R ⁰ y and each atom of Φ, that is, the projection of R ⁰ y on each atom, and then introduce a hard threshold t ₁ and select the best value with R ⁰ y through formula (9). Atoms that match

I ₁ ＝{i:|<φ _r ,R ⁰ y>|≥t ₁ ,r∈Γ} Formula (9)

Orthogonalize the selected atoms, re-project R ⁰ y onto the orthogonalized atoms, obtain the residual R ¹ y after the first sparse approximation, and judge whether the number of atomic subscripts in the index set is less than the set sparsity L, if less than continue to iterate. When the cycle ends, the final z _m is calculated by formula (3). The size of L is the number of elements in w that are greater than the threshold, and the threshold is between 0.3 and 0.8 according to the size of the noise. The denoised image u _d is reconstructed by inverse shearlet transform. According to the sparse coefficients, find out the small coefficients discarded in the process of sparse representation and the set M to which their corresponding shear waves belong, and reconstruct these small coefficients to obtain the residual image u _s .

Step 3: TV noise reduction and detail restoration

Firstly, a TV model based on energy functional is established. When the derivative of F(u) is equal to 0, this energy functional obtains the minimum value. The discretized form of formula (6) is as formula (7), where The iteration step size Δt=0.1, λ=0.15. Obtain the iterative initial value u ⁰ by u ⁰ =u _s +Δt[η(u _d )], bring u ⁰ into the iterative cycle of formula (7), and calculate Ps(u ^k ) in the loop process through formula (5) have to. Calculate the mean absolute deviation of the image by formula (10) before each cycle

$\mathrm{MAD}=\frac{1}{N}{\left|\right|u^k-u^{k-1}\left|\right|}_1$ Formula (10)

Where N is the image pixel value; when MAD is smaller than the set threshold ε, stop the iteration and get the final repaired image u ^k , otherwise continue to repair u ^k , where the threshold ε is set to 2.5e-04.

Effect of the present invention can be further illustrated by following simulation experiments:

1. Experimental conditions and content

Experimental conditions: The input image used in the experiment is Figure 2, with a pixel size of 512×512. All noise reduction algorithms in the experiment are implemented by programming in MATLAB language.

Experimental content: under the above-mentioned experimental conditions, a comparative experiment was carried out using the KSVD method, the KSVD_TV method combining KSVD and ordinary TV, and the method of the present invention. The objective evaluation results of the denoising effect are measured by the homogeneous area mean μ, variance σ ² , and equivalent visual number ENL.

Experiment 1: use the method of the present invention and existing KSVD and KSVD_TV method to carry out denoising to Fig. 2 respectively, wherein KSVD method overlapping image block size is 8 * 8, and dictionary size is 64 * 256; KSVD_TV method TV iteration times is 10, The step size is 0.2, and the weight λ between the diffusion item and the fidelity item is 0.15, and the noise reduction effects obtained are shown in Fig. 3 and Fig. 4 respectively; in the present invention β=5, λ=0.15, the iteration step size Δt=0.1, and the number of iterations is 20. The noise reduction results are shown in Figure 5. Comparing Fig. 3 and Fig. 4, it can be seen that the noise reduction effect of the present invention is stronger, and at the same time, it has richer edge detail information.

Experiment 2: Select two rectangular homogeneous regions in Fig. 2, and use the present invention and KSVD and KSVD_TV methods to denoise them respectively. The mean value μ, the variance σ ² , and the equivalent visual number ENL are used as the evaluation indexes of the denoising effect, and they are listed in Table 1.

Table 1 Performance parameters of different noise reduction algorithms in homogeneous area 1 and 2

The result of table 1 shows, the average amount of change of the image before and after the noise reduction of the method of the present invention is the smallest in several other methods, and it is stronger to keep the radar radiation characteristic ability when illustrating noise reduction; The reduction of variance and the significant improvement of NEL have shown that the present invention The method has strong noise reduction ability.

The above experiments show that the noise reduction method of the present invention is better in terms of the visual effect and objective evaluation index of the image after noise reduction, so it can be seen that the present invention is effective for SAR image noise reduction.

Claims (1)

1. the SAR image denoising method based on shearing wave coefficient processing, is characterized in that concrete steps are as follows:

Step 1, the conversion of SAR image noise model

Under the coherent spot hypothesis of development completely, the coherent spot in SAR image is all to adopt Multiplicative random noise to carry out modeling, for the noise reduction model that adapts to set up on additive noise basis, multiplicative noise is converted into additive noise;

Step 2, the sparse noise reduction of shearing wave zone

First noisy SAR image is carried out to shearing wave conversion, obtain shearing wave coefficient w; The Sparse Problems of w is converted into and is asked the optimization problem of minimum value, wherein Φ is the stochastic matrix that meets consistent uncertainty principle, and y equals Φ and w multiplies each other, and z is that sparse under dictionary Φ of y approaches expression; Equation right-hand member Section 1 is carried out fidelity to z, guarantees that z and w differ not too large, and Section 2 is the sparse property that regularization term ensures z, and regularization parameter γ carries out equilibrium between data fidelity item and regular terms; Then use segmentation orthogonal matching pursuit algorithm to solve optimization problem, it is from Φ, to select in the mode of greedy iteration the sparse y of approaching of atom mating most with y, can make like this that z is sparse has ensured that again the value of fidelity item is less; When g (z) gets minimum value, corresponding z is the rarefaction representation of former coefficient w and average be clean image cut ripple Coefficient Mean without inclined to one side estimation; Will and the little coefficient abandoning after rarefaction representation carries out shearing wave inverse transformation and can obtain image u after noise reduction _sand residual image u _d, and shearing wave the space corresponding little coefficient abandoning in rarefaction representation is designated as to M;

Step 3, TV noise reduction and details reparation

From the principle of rarefaction representation, the shearing wave coefficient of lost part is the coefficient going to zero, and the edge details information that has comprised much noise and image in the image of this part coefficient reconstruct; According to shearing wave characteristic, can be used for edge and the noise in differentiate between images when shearing wave yardstick a levels off to the rate of decay of shearing wave coefficient 0 time, when adopting TV to be further implemented in noise reduction in conjunction with the Variation Model based on energy functional, repair image texture details: $F\left(u\right)=\underset{\mathrm{\&Omega;}}{\&Integral;}\mathrm{\&phi;}\left(\right||\&dtri;P_S\left(u\right)|\left|\right)\mathrm{dxdy}+(\mathrm{\&lambda;}/2)\underset{\mathrm{\&Omega;}}{\&Integral;}{(u-u_0)}^2\mathrm{dxdy},$ Wherein u ₀for original noisy image, || || be standard European norm, φ ∈ C ²(R) be a kind of Regularization function, λ is regular parameter; Equation right-hand member Section 1 is regular terms, ensures to separate u and has the noncontinuity in certain regularity and specific region, and Section 2 is fidelity item, to retain original image characteristic; P _s(u) result of presentation video u reconstruction from projection in the shearing wave substrate that belongs to M space; When time F (u) get minimal value, corresponding u is the image after noise reduction is repaired, and can be obtained by F (u) discrete form be u ^k+1=u ^k+ Δ t[η (Ps (u ^k))-λ (u ^k-u ₀)], wherein Δ t is iteration step length, and by u _s+ Δ t[η (u _d)] as iteration initial value, finishing iteration in the time that the mean absolute deviation MAD between the iteration of twice of front and back is less than a certain thresholding ε, obtains final noise reduction image.