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

Abstract

The invention discloses an SAR image noise reduction method based on shear wave coefficient processing and belongs to the technical field of digital image processing. The SAR image noise reduction method based on shear wave coefficient processing comprises the steps of based on the sparsity of converted image shear wave coefficients, firstly establishing a sparse representation model based on the image shear wave coefficients, and then realizing unbiased estimation on sparse representation coefficients in statistical mean sense by use of a Stagewise Orthogonal Matching Pursuit (StOMP) algorithm and reconstructing the sparse-represented shear wave coefficients into a noise-reduced image, making up for the loss of image details due to the partial lost coefficients in sparse representation, performing further iterative denoising on the result of the projection reconstruction of the image in the shear wave function space corresponding to the lost coefficients by use of the capacity of a shear wave function corresponding to the part of coefficients in extracting image edge details in combination with an energy functional-based Total Variation (TV) method, and finally, obtaining a denoised image rich in details; as a result, the speckle noise of the SAR image is suppressed and the detail texture of the image is also maintained; the SAR image noise reduction method based on shear wave coefficient processing can be applied to SAR image noise reduction.

Description

A kind of SAR image denoising method based on shearing wave coefficient processing

Technical field

The invention belongs to digital image processing techniques field, it is particularly related to SAR image denoising method, for SAR image is carried out to noise reduction process.

Background technology

Synthetic-aperture radar has round-the-clock in imaging, round-the-clock detection and scouting tracking power, can effectively identify camouflage and penetrate cloak, therefore SAR image is widely used in the aspects such as photogrammetric measurement and remote sensing, satellite oceanographic observation, space reconnaissance, pattern matching guidance, survey of deep space.But the speckle noise being brought to image by SAR coherent imaging mechanism, brings adverse effect to post-processed such as target identification and compression of images.Effectively filtering speckle noise has become the important prerequisite of the follow-up decipher of image.

Because SAR image has abundant texture and edge, therefore in effective filtering speckle noise, fully retain texture and the edge of image, be the emphasis of SAR image noise reduction processing.In recent years, due to the superperformance that rarefaction representation has in natural image noise reduction, become just gradually one of effective ways of image noise reduction.But these class methods are in rarefaction representation, the problem that has image detail loss that is difficult to avoid.For improving image detail hold facility, existing method is confined to the image after sparse noise reduction to process mostly, but because the information of losing in rarefaction representation cannot be recovered, its improvement degree is limited, can not significantly repair the edge details of noise reduction image impairment.

Summary of the invention

The present invention is the deficiency that overcomes existing SAR image denoising method and exist image edge details were information loss, to obtain details noise reduction SAR image clearly, provides a kind of SAR image denoising method based on shearing wave coefficient processing.The method fully takes into account the characteristic of shearing wave coefficient, model shearing wave coefficient rarefaction representation noise reduction model, then use TV method further to repair image, not only can well suppress the speckle noise of SAR image, and solved the detail textures maintenance problem of falling spot image, therefore the method can effectively realize SAR image noise reduction.Comprise the following steps:

Step 1, image noise model conversion

Use non-logarithm Additive noise model, it is 0 additive noise that the multiplicative noise that in input SAR image, average is 1 is converted into average.

Step 2, the sparse noise reduction of shearing wave zone

First noise image is carried out to shearing wave and convert the shearing wave coefficient w that obtains image.For realizing the rarefaction representation of coefficient, with measuring matrix Φ, coefficient w is converted i.e. y=Φ w.Further hypothesis y is expressed as z sparse the approaching of measuring under matrix Φ.Obtain following optimization sparse representation model:

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

In the time that formula (1) is got minimum value, corresponding optimum solution z is the rarefaction representation of former coefficient w and rarefaction representation average be clean image cut ripple Coefficient Mean without inclined to one side estimation.Use StOMP Algorithm for Solving formula (1), first y is projected on each atom of measuring matrix Φ, then corresponding the projection value that is greater than threshold value atom is put into indexed set I ₁, after by indexed set Atom, y being approached, obtain residual error R ¹y.For adopting more atom further to approach y, can be to residual error R ¹y adopts in a like fashion and further decomposes.If the residual error of the m time iteration is R ^my, R ^m+1y can be expressed as:

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

Wherein φ _rmwhile representing the m time iteration, the atom of selecting from measure matrix Φ, is incorporated to I by these selected atoms _m-1obtain the I upgrading _m.If meet end condition || R ^my|| ²≤ ε or | I _m| >L iteration finishes, otherwise continues iteration.In the time that finishing, iteration can obtain optimum solution z by through type (3)

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

Optimization solution z is the rarefaction representation of former coefficient w will and the little coefficient abandoning when w 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

According to shearing wave coefficient feature, integrating step two results, set up the TV model based on energy functional:

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

Wherein P _s(u) suc as formula shown in (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)

Wherein M is j, k, and set under l, this set is determined by losing the shearing wave function that coefficient is corresponding in step 2 rarefaction representation, P _s(u) the presentation video u result of reconstruction from projection on shearing wave function space in this section.When the energy functional of up-to-date style (3) is got minimal value, and u is now TV denoising image after treatment.Can be obtained by formula (3) 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)

Formula (6) Section 1 is diffusion term, make ρ (x)=φ ' (x)/x, wherein ρ (x) can control the smoothness in diffusion process.

Use method of steepest descent through type (7) to solve formula (6)

U ^k+1=u ^k+ Δ t[η (Ps (u ^k))-λ (u ^k-u ₀)] formula (7)

Wherein Δ t is iteration step length, and k is the k time iteration, u ₀for original noisy image, iteration initial value is u _s+ Δ t[η (u _d)], finishing iteration in the time that the MAD between the iteration of twice of front and back is less than a certain thresholding, obtains final noise reduction image.

Innovative point of the present invention is the sparse property and the ability of extracting image border of utilizing image cut wave system number, utilize retention factor in rarefaction representation to carry out noise reduction to clean image cut wave system number without the advantage of partially estimating, and for the Edge texture information of image impairment in rarefaction representation process, utilize the distinguishing characteristic of the little coefficient of shearing wave to picture noise and edge details, adopt TV to process for image in the projection result in this space, further realized noise reduction and details reparation to image.

Beneficial effect of the present invention: use based on the optimum noise reduction model of statistics and come rarefaction representation shearing wave coefficient instead of traditional soft and hard threshold disposal route, simultaneously in the time of solving model optimization problem, adopted StOMP algorithm not only to ensure solving precision but also improved operation efficiency, therefore overall noise reduction can reach higher level; And set up the TV processing based on energy functional, and on the basis of noise reduction, further the information of losing in rarefaction representation process is repaired, therefore the method can keep image texture details in noise reduction, also has higher operation efficiency.

The present invention mainly adopts the method for emulation experiment to verify, institute in steps, conclusion all on MATLAB8.0 checking correct.

Brief description of the drawings

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

Fig. 2 is the true noisy hills SAR image that emulation of the present invention is used;

Wherein white rectangle region is the homogeneity district of selecting;

Fig. 3 is the noise reduction result figure of KSVD method to Fig. 2;

Fig. 4 is the noise reduction result figure of KSVD_TV method to Fig. 2;

Fig. 5 is the noise reduction result figure of the inventive method to Fig. 2.

Embodiment

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

Step 1, image noise model conversion

SAR image Multiplicative noise model is converted into Additive noise model by the non-logarithm noise of employing formula (8) transformation model

I=RX=X+ (R-1) X=X+N formula (8)

Wherein I is that R represents coherent speckle noise by the image intensity of noise pollution, and X represents the real backscatter intensity of atural object, the additive noise that N=(R-1) X is zero-mean.

Step 2, the sparse noise reduction of shearing wave zone

Noise image is carried out to shearing wave conversion, obtain level cone and vertical shearing wave coefficient of boring under each 5 yardsticks, carry out by row sparse to the coefficient under each yardstick.First construct random measurement matrix Φ={ φ _r} _{r ∈ Γ}, then to its normalization.Suppose that w represents the row of coefficient, with measuring matrix Φ, w is converted, i.e. y=Φ w, then sets up optimization sparse representation model and use the sparse model of StOMP Algorithm for Solving.StOMP algorithm is the sparse value of approaching z when initial ₀=0, residual error R ⁰y=y, selected atom subscript indexed set I ₀for sky.In the time of iterations m=1, first ask R ⁰the inner product of y and the each atom of Φ, i.e. R ⁰the projection of y on each atom, then introduces hard-threshold t ₁and select and R by (9) formula ⁰several atoms that y mates most

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

Orthogonalization selected atom, again by R ⁰y projects on the atom after orthogonalization, obtains the residual error R after sparse approaching for the first time ¹y, judges whether indexed set Atom subscript number is less than the degree of rarefication L of setting, if be less than continuation iteration.In the time that circulation finishes, through type (3) calculates final z _m.The size of L is the element number that is greater than threshold value in w, and threshold value is the value between 0.3-0.8 that do not coexist according to noise size.Reconstruct the image u after noise reduction by shearing wave inverse transformation _d.Find the shearing wave of the little coefficient that abandons in rarefaction representation process and their correspondences according to the coefficient after sparse under, gather M, and will after this part little coefficient reconstruct, obtain residual image u _s.

Step 3, TV noise reduction and details reparation

The TV model of model based on energy functional, in the time that the derivative of F (u) equals 0, this energy functional is obtained minimum value.The discrete form of formula (6) is suc as formula (7), wherein iteration step length Δ t=0.1, λ=0.15.Pass through u ⁰=u _s+ Δ t[η (u _d)] try to achieve iteration initial value u ⁰, by u ⁰bring formula (7) iterative loop into, the Ps (u in cyclic process ^k) through type (5) tries to achieve.The mean absolute deviation of through type (10) computed image before each circulation

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

Wherein N is image pixel value size; When MAD is less than when thresholding ε is set, stop iteration, obtain image u after final reparation ^k, otherwise continue to repair u ^k, wherein thresholding ε is set to 2.5e-04.

Effect of the present invention can further illustrate by following emulation experiment:

One, experiment condition and content

Experiment condition: the input picture that experiment is used is Fig. 2, and pixel size is 512 × 512.In test, each noise reduction algorithm all uses MATLAB Programming with Pascal Language to realize.

Experiment content: under above-mentioned experiment condition, KSVD_TV method and the inventive method of using KSVD method, KSVD and general T V to combine are carried out contrast experiment.The homogeneity district average μ for objective evaluation result of denoising effect, variances sigma ², equivalent number ENL weighs.

Experiment 1: respectively Fig. 2 is carried out to noise reduction by the inventive method and existing KSVD and KSVD_TV method, wherein KSVD method superimposed images block size is 8 × 8, and dictionary size is 64 × 256; KSVD_TV method TV iterations is 10, and step-length is 0.2, and between diffusion term and fidelity item, weight λ is 0.15, and the noise reduction obtaining respectively as shown in Figure 3 and Figure 4; In the present invention β=5, λ=0.15, iteration step length Δ t=0.1, iterations is 20, noise reduction result is as shown in Figure 5.Comparison diagram 3 and Fig. 4 can find out that noise reduction of the present invention is stronger, have abundanter edge details information simultaneously.

Experiment 2: select two rectangle homogeneous regions in Fig. 2, use the present invention and KSVD and KSVD_TV method to they denoisings respectively.Use average μ, variances sigma ², equivalent number ENL is as the evaluation index of denoising effect, and is listed in table 1.

The performance parameter of table 1 homogeneity district 1,2 different noise reduction algorithms

The result of table 1 shows, before and after the inventive method noise reduction, the average change amount of image is minimum in several his methods, keeps radar radiation characteristic ability stronger when noise reduction is described; The reduction of variance and NEL significantly improve and have shown that the inventive method has very strong noise reduction capability.

Above-mentioned experiment shows, all better in the visual effect of noise-reduction method of the present invention image after noise reduction and objective evaluation index, the present invention is effective to SAR image noise reduction as can be seen here.

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.