CN101984461A - Method for denoising statistical model image based on controllable pyramid - Google Patents
Method for denoising statistical model image based on controllable pyramid Download PDFInfo
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Abstract
The invention discloses a method for denoising statistical model image based on controllable pyramid, mainly solving the problem that the existing denoising technology is lack of partial adaptivity and Gibbs artefact existing in the denoising results. The processing process comprises the following steps: adding the Gaussian white noise in which the space is not changed into the clear image so as to obtain the image containing the noise; respectively performing the controllable pyramid conversion on the image containing the noise and the noise signals; performing the sub-block dividing on conversion sub-band coefficient of the image containing the noise except the low-pass sub-band; performing the Gauss scale mixed mould modeling on the conversion sub-band coefficient sub-block of the image containing the noise; estimating the covariance matrix of the conversion sub-band coefficient sub-block of the image containing the noise and the covariance matrix of the conversion sub-band coefficient sub-block of the clear image in sequence; using Bayes rules to estimate the conversion sub-band coefficient of the clear image; performing the controllable pyramid reconstruction and the total variation operations on the low-pass sub-band and the conversion sub-band coefficient after being denoised in sequence so as to obtain the denosing results. The invention can be used for computer visual and signal processing fields.
Description
Technical field
The invention belongs to image processing field, relate to the method for natural image denoising, can be used for fields such as computer vision and signal Processing.
Technical background
The natural image denoising is crucial technology in fields such as computer vision, pattern-recognition and signal Processing, and the purpose of denoising is to maximize edge and the texture information that as far as possible keeps original image when removing noise.Natural image all contains a large amount of edges and texture information usually, and as the edge of cap and the striped on the clothes etc., and traditional denoising method is relatively more responsive to these complicated information, and this will cause existing in the denoising result serious edge and texture blooming.Again because behind the natural image process multi-scale transform, the distribution of its conversion coefficient presents " high peak heavily trails " shape, and there is very strong correlativity in these coefficients in each yardstick and between yardstick, are a very challenging job and will seek optimumly to describe the true statistical model that distributes of image transformation coefficient.
At the above characteristics of natural image, its denoising method can reduce substantially based on airspace filter with based on transform domain filtering two big class denoising methods.
1. based on the natural image denoising method of airspace filter, mainly comprise following two kinds:
1) based on the level and smooth denoising method of statistics, this method mainly is a pixel of utilizing statistical informations such as the average of image pixel, intermediate value or variance to come smoothed image, and this smoothing technique all can cause the fuzzy of integral image usually.
2) based on the denoising method of threshold process, this method all is to choose a threshold value earlier usually, to keep greater than the pixel of threshold value then, pixel zero setting less than threshold value, though this method can effectively be removed noise, but its denoising relatively blindly, and information losses such as edge are serious, and denoising result is overly dependent upon selected threshold value.
More than these methods all be directly the pixel of natural image to be handled, though all considered the statistical property of image pixel, all insufficient, so can cause denoising result very poor.
2. based on the natural image denoising method of transform domain filtering, comprise following several:
1) based on the denoising method of wavelet transformation:
1a) based on the threshold denoising method of wavelet transformation, this method is being carried out behind the wavelet transformation to image, choose appropriate thresholds according to the statistical property between wavelet coefficient and carry out threshold process, but because wavelet transformation does not possess anisotropic properties, can not make optimum expression to the directional information in the image, thereby the edge fog that has caused denoising result, moreover denoising result also depends on choosing of threshold value to a great extent.
1b) set HMT model denoising method based on the hidden Markov of wavelet transformation, this method is that wavelet subband coefficients of images is set up the HMT model, with this catch wavelet coefficient between yardstick and yardstick in correlativity, this method is except the isotropy defective of wavelet transformation, the training complexity of HMT model parameter is very high, and the quality of parameter training depends on the initialization of parameter to a certain extent.
2) based on the denoising method of profile wave convert: this method is carried out profile wave convert to image earlier, and then selected threshold method or statistical model method come conversion coefficient is processed, though the profile ripple has overcome the isotropic problem of small echo, but because its laplacian decomposition used in decomposable process and down-sampling operation can cause spectral aliasing, and, it is each layer segmentation at frequency domain, and this has just limited its application to a certain extent.
3) based on the denoising method of Gauss's yardstick mixture model GSM, referring to Javier Portilla, Vasily Strela, Martin J.Wainwrignt, and Eero P.Simoncelli.Image Denoising Using Scale Mixtures of Gaussians in the Wavelet Domain.[J] IEEE Transactions on Image Processing, vol.12, no.11, pp:1338-1351,2003.This method at first carries out handling pyramid SP conversion to image, neighborhood to the conversion coefficient subband carries out the modeling of Gauss's yardstick hybrid GSM then, come denoising with the method for Bayes's least mean-square error at last, but because in the process of carrying out the modeling of Gauss's yardstick hybrid GSM, the covariance matrix of this method hypothesis coefficient is constant in whole subband, this has just caused the covariance matrix of this method not possess adaptivity, and, owing to can handle the multi-direction decomposition transform that pyramid SP conversion is a kind of redundancy, can introduce some cuts unavoidably in its denoising result, be the pseudo-shadow of gibbs, influence denoising effect.
Summary of the invention
The objective of the invention is to overcome above-mentioned existing methods deficiency, on based on the Gauss's yardstick hybrid GSM model based that can handle pyramid SP, a kind of natural image denoising method based on localized mass and total variation TV operation has been proposed, this method realizes adaptivity by the localized mass operation, the pseudo-shadow of gibbs in conjunction with in the total variation TV operation elimination denoising result improves denoising effect.
The concrete scheme that realizes the object of the invention is: at first image is carried out handling pyramid SP conversion, then each the coefficient direction subband after the conversion is divided into the sub-piece of overlapped a certain size, again each sub-piece is carried out the modeling of Gauss's yardstick hybrid GSM, in the process of modeling, consider in the subband simultaneously and the correlativity between adjacent scale subbands, by the processing of Bayes and total variation method, obtained edge and texture information and kept good denoising result at last.Its specific implementation process is as follows:
(1) is that the standard deviation that the clean natural image of L * L adds space invariance is the zero-mean white Gaussian noise of σ to size, obtains noisy image;
(2) respectively noisy image and the noise signal that is added are carried out handling pyramid SP conversion, obtain the conversion sub-band coefficients y of noisy image and the conversion sub-band coefficients n of noise signal, and suppose that the conversion sub-band coefficients of original clean image is x;
(3) except that low pass subband, the change direction sub-band coefficients of noisy image under each yardstick done following processing:
3.1) utilize the conversion sub-band coefficients n estimating noise covariance matrix C of noise signal
n=E{nn
T, T representing matrix transposition wherein, E represents matrix is got expectation;
3.2) the conversion sub-band coefficients y of noisy image is divided into the sub-piece y that overlapped size is B * B
i, i=1,2 ..., N, wherein N represents the number of sub-piece;
3.3) to y
iCarry out the modeling of Gauss's yardstick hybrid GSM, promptly
Z wherein
iBe positive scale factor, u
iBe that covariance matrix is
Zero-mean Gauss vector, x
iThe sub-piece of representing original clean image transformation sub-band coefficients x, n
iBe add the sub-piece of noise signal conversion sub-band coefficients n;
3.4) estimator piece y
iCovariance matrix
Wherein
Be y
iAverage;
3.5) estimate the sub-piece x of original clean image transformation sub-band coefficients x
iCovariance matrix
And order
3.6) utilize Bayes's least estimated x
c=∫ p (z
i| y
i) (∫ x
iP (x
i| y
i, z
i) dx
i) dz
i, estimate x
iIn the center coefficient x of each coefficient neighborhood
c, posterior probability wherein
P (y
i| z
i) be likelihood function, p (z
i) be prior probability, p (y
i) be a normalized constant, second integration is reduced to one Wei Na estimates for simplify calculating, that is:
4) utilize each transformation of coefficient subband and low pass subband after the denoising to carry out earlier handling pyramid SP reconstruct, obtain preliminary denoising image; Utilize total variation TV operation that preliminary denoising image is handled again, obtain final denoising image.
The present invention compared with prior art has the following advantages:
1, the present invention is because when handling noisy image transformation sub-band coefficients, earlier it is divided into overlapped sub-piece, be processing unit with sub-piece then, thereby has a good block adaptive, simultaneously, the overlapped dividing mode of sub-piece can not introduced the local edge blocking effect, improves the local performance of denoising result;
2, the present invention is because when the covariance matrix of calculating noise covariance matrix, the sub-piece of noisy image transformation sub-band coefficients, consider the set membership between adjacent yardstick equidirectional conversion sub-band coefficients, also consider under the yardstick under the high pass subband and a yardstick correlativity of the logical intersubband in adjacent band mutually simultaneously, make the correlativity between the image transformation sub-band coefficients obtain abundant excavation;
3, the present invention is owing to carry out earlier handling pyramid SP reconstruct to each transformation of coefficient subband after the denoising and low pass subband, again reconstructed image has been added total variation TV operation then, eliminated the pseudo-shadow of the gibbs in the denoising result, improve the number of quantitative analysis of denoising result, improved the visual effect of denoising result.
Description of drawings
Fig. 1 is a process flow diagram of the present invention;
Fig. 2 is the simulation result figure of the present invention on natural image.
Embodiment
With reference to Fig. 1, specific implementation step of the present invention is as follows:
Import the clean natural image of width of cloth size L * L, the standard deviation that generates a space invariance size L * L is the zero-mean white Gaussian noise signal of σ, clean natural image to input adds the noise signal that is generated, obtain noisy image, choosing of L and σ value is indefinite, determine that according to the size of image and the restriction of practical application in institute's employing picture library this example L gets 512 and 256, σ gets 20 and 25.
Step 2, to noisy image and the noise signal that added respectively the travel direction sub band number be that the J yardstick of K can be handled pyramid SP conversion.
2a) noisy image is carried out pre-service, obtain a size pre-service low pass subband L identical with noisy image with a decomposition low-pass filter and a decomposition Hi-pass filter
0With a pre-service high pass subband H
0
2b) use K decomposition bandpass filter and a decomposition narrow band filter to pre-service low pass subband L
0Carry out filtering, obtain size K the band logical subband B identical with noisy image
1, lHandle low pass subband L with an arrowband
1,1, l=1 wherein, 2 ..., K;
2c) low pass subband L is handled in the arrowband
1,1Carry out every 2 down-samplings, obtain a size and be half sampling low pass subband L of noisy image
2,1
2d) to sampling low pass subband L
2,1Earlier decompose bandpass filter and a decomposition narrow band filter carries out filtering, obtain size and lead to subband B for half K of noisy image is with K
2, lHandle low pass subband L with an arrowband
2,1Again to resulting narrow-band low pass subband L
2,1Carry out every 2 down-samplings, obtain size and be the sampling low pass subband L of noisy image 1/4th
2,2Use K decomposition bandpass filter and a decomposition narrow band filter to sampling low pass subband L then
2,2Carry out filtering; And the like, obtain the conversion sub-band coefficients y of noisy image under J yardstick;
2e) standard deviation of a space invariance of generation is 1 zero-mean white Gaussian noise, and it is poor to multiply by the noise criteria that will add, and obtains the noise signal that will add;
2f) noise signal is carried out pre-service, obtain a size pre-service low pass subband L identical with noise signal with a decomposition low-pass filter and a decomposition Hi-pass filter
nWith a high pass subband H
n
2g) use K decomposition bandpass filter and a decomposition narrow band filter to pre-service low pass subband L
nCarry out filtering, obtain size K the band logical subband B identical with noise signal
1, l, nHandle low pass subband L with an arrowband
1, l, n, l=1 wherein, 2 ..., K;
2h) low pass subband L is handled in the arrowband
1,1, nCarry out every 2 down-samplings, obtain a size and be half sampling low pass subband L of noise signal
1,2, n
2i) to sampling low pass subband L
1,2, nEarlier decompose bandpass filter and a decomposition narrow band filter carries out filtering, obtain size and lead to subband B for half K of noise signal is with K
2, l, nHandle low pass subband L with an arrowband
2,1, nAgain to resulting narrow-band low pass subband L
2,1, nCarry out every 2 down-samplings, obtain size and be the sampling low pass subband L of noise signal 1/4th
2,2, nUse K decomposition bandpass filter and a decomposition narrow band filter to sampling low pass subband L then
2,2, nCarry out filtering; And the like, obtain the conversion sub-band coefficients n of noise signal under J yardstick, sum up according to practical application experience, K should get the positive integer less than 16, and the value of J should satisfy 2
J＜＜L, this example K gets 8, and J gets 5.
Step 3, utilize the conversion sub-band coefficients n estimating noise covariance matrix C of noise signal
n=E{nn
T.
3a) in the noise signal conversion sub-band coefficients n of big or small M * M, extract earlier (M-2)
2Individual size is the square neighborhood of w * w; Again each square neighborhood is pulled into big or small w
2* 1 column vector; Then all column vectors are placed on a big or small w
2* (M-2)
2Matrix Q in;
3b) carry out C
n=(QQ
T)/(M-2)
2, obtain size and be w
2* w
2Noise covariance matrix C
nThe M value is indefinite, image to size 512 * 512, M is respectively 512,256,128,64 and 32 from 1 yardstick to 5 yardsticks, to the image of size 256 * 256, M is respectively 256,128,64,32 and 16 from 1 yardstick to 5 yardsticks, and relatively w gets 3,5 and 7 denoising result respectively, drawing w, to get 3 denoising result best, so this example w gets 3.
Step 4, noisy image transformation sub-band coefficients y is carried out overlapped sub-piece divide.
To size is the noisy image transformation sub-band coefficients y of P * P, divides exactly if P can be divided the big or small B of sub-piece, and then sub-piece adds up to T
1=P/B, otherwise T
1=(P/B)+1; (j, if l) the sub-piece divided of expression is n with y
1=1,2 ..., (T
1-1), n
2=1,2 ..., (T
1-1), (n then
1-1) * (B-c)+1≤j≤n
1* (B-c)+and c, (n
2-1) * (B-c)+1≤l≤n
2* (B-c)+c; If n
1=T
1, n
2≠ T
1, (n then
1-1) * (B-c)+and 1≤j≤P, (n
2-1) * (B-c)+1≤l≤n
2* (B-c)+c); If n
1≠ T
1, n
2=T
1, (n then
1-1) * (B-c)+1≤j≤n
1* (B-c)+and c, (n
2-1) * (B-c)+1≤l≤P; If n
1=T
1, n
2=T
1, (n then
1-1) * (B-c)+and 1≤j≤P, (n
2-1) * (B-c)+1≤l≤P, wherein c represents any two coefficient number that sub-piece is overlapped, c, B and P value are indefinite, according to different c values and the comparison of denoising result down of B value, the value of this example from thin yardstick to thick yardstick c is followed successively by 10,4,2,1,1, image to size 512 * 512, the value of this example from thin yardstick to thick yardstick B is followed successively by 128,32,16,4,4, image to size 256 * 256, the value of this example from thin yardstick to thick yardstick B is followed successively by 128,16,8,4,4, difference according to the image size, image to size 512 * 512, the value of this example from thin yardstick to thick yardstick P is followed successively by 512,256,128,64,32, to the image of size 256 * 256, the value of this example from thin yardstick to thick yardstick P is followed successively by 256,128,64,32,16.
Step 5, to the sub-piece y of noisy image transformation sub-band coefficients
iCarry out the modeling of Gauss's yardstick hybrid GSM.
Rule of thumb histogrammic method draws, and Gauss's yardstick hybrid GSM model profile can be than the sub-piece y of the noisy image transformation sub-band coefficients of accurate match
iTrue histogram distribution, therefore with Gauss's yardstick hybrid GSM model to the sub-piece y of noisy image transformation sub-band coefficients
iModeling, its expression formula is:
Z wherein
iBe positive scale factor, u
iBe that covariance matrix is
Zero-mean Gauss vector, x
iThe sub-piece of representing original clean image transformation sub-band coefficients x, n
iBe add the sub-piece of noise signal conversion sub-band coefficients n, z
iValue be the interval of a regulation, i.e. logz
i∈ [20.5,3.5].
Step 6, the sub-piece y of the noisy image transformation sub-band coefficients of estimation
iCovariance matrix
6a) at the sub-piece y of noisy image transformation sub-band coefficients of big or small B * B
iIn, extract earlier (B-2)
2Individual size is the square neighborhood of w * w; Again each square neighborhood is pulled into big or small w
2* 1 column vector; Then all column vectors are placed on a big or small w
2* (B-2)
2Matrix Y in;
6b) calculate the sub-piece y of noisy image transformation sub-band coefficients
iCovariance matrix
Wherein
Size be w
2* w
2
Step 7, the sub-piece x of the clean image transformation sub-band coefficients of estimation
iCovariance matrix
7a) by the sub-piece y of noisy image transformation sub-band coefficients
iHistogram distribution obtain its Gauss's yardstick hybrid GSM model tormulation formula:
Again by y
iGauss's yardstick hybrid GSM model tormulation formula obtain y
iThe conditional covariance matrix expression formula:
Wherein
Be the sub-piece n of noise signal conversion sub-band coefficients
iCovariance matrix, be the noise signal of space invariance according to the noise that is added, this example is got
7b) to y
iThe conditional covariance matrix expression formula
Expectation is got on both sides, obtains
In order to be without loss of generality, this example is got E{z
i}=1 draws
7c) according to the clean sub-piece x of image transformation sub-band coefficients
iHistogram distribution, obtain its Gauss's yardstick hybrid GSM model tormulation formula and be:
Again by x
iGauss's yardstick hybrid GSM model tormulation formula obtain the sub-piece x of clean image transformation sub-band coefficients
iThe covariance square
Utilize then
With
Obtain the sub-piece x of clean image transformation sub-band coefficients
iThe covariance square
Step 8, utilize Bayes's least mean-square error method of estimation, estimate the sub-piece x of clean image transformation sub-band coefficients
iIn the center coefficient x of each coefficient neighborhood
c
8a) calculate likelihood function p (y
i| z
i), its expression formula is:
8b) calculate prior probability p (z
i), its expression formula is:
Wherein ∝ represents the reduction symbol, i.e. p (z
i)
Reduction in
8c) calculate normaliztion constant p (y
i), its expression formula is: p (y
i)=∫ p (y
i| z
i) p (z
i) dz
i
8d) utilize the likelihood function p (y of aforementioned calculation
i| z
i), prior probability p (z
i) and normaliztion constant p (y
i) the calculating posterior probability
8d) the integral ∫ x in the calculating Bayes least estimated
iP (x
i| y
i, z
i) dx
i, simple in order to calculate, it is reduced to a Wei Na estimates that expression formula is:
8e) utilize the posterior probability p (z of aforementioned calculation
i| y
i) and Bayes's least estimated in integral ∫ x
iP (x
i| y
i, z
i) dx
i, calculate the sub-piece x of clean image transformation sub-band coefficients
iIn the center coefficient x of each coefficient neighborhood
c, its expression formula is: x
c=∫ p (z
i| y
i) (∫ x
iP (x
i| y
i, z
i) dx
i) dz
i
Step 9, utilize each conversion sub-band coefficients and low pass subband after the denoising to carry out to handle pyramid SP reconstruct and total variation TV operation successively, obtain final denoising image.
9a) to the sampling low pass subband L under the noisy image j yardstick
2, jCarry out every 2 up-samplings, obtain a narrow-band low pass subband L under the j yardstick
1, j, j=J, J-1 ..., 2,1, wherein J is for handling the yardstick of pyramid SP conversion;
9b) to the narrow-band low pass subband L under the j yardstick
1, jThe narrow-band filtering that reverses obtains the counter-rotating narrow-band low pass subband L under the j yardstick
1, i, f, the narrow band filter that wherein reverses differs 180 ° with the decomposition narrow band filter that can handle pyramid SP conversion;
9c) to the K after the denoising under the j yardstick the logical subband D of band
J, lThe bandpass filtering that reverses, promptly the counter-rotating bandpass filter under the j yardstick with can handle the decomposition bandpass filter of pyramid SP conversion under the j yardstick and differ 180 °, under the j yardstick K counter-rotating band lead to subband D
J, l, f, l=1 wherein, 2 ..., K;
9d) with the counter-rotating narrow-band low pass subband L of j yardstick
1, j, fWith K the logical subband D of counter-rotating band
J, l, fBe weighted operation, obtain the sampling low pass subband L under the noisy image j-1 yardstick
2, j-1, make j=j-1, judge whether j equals 1, if j is not equal to 1, forward step (9a) to, otherwise execution in step (9e);
9e) to the sampling low pass subband L under 1 yardstick
2,1Carry out every 2 up-samplings, obtain one the 1 narrow-band low pass subband L under the yardstick
1,1, to the narrow-band low pass subband L under 1 yardstick
1,1The narrow-band filtering that reverses obtains the counter-rotating narrow-band low pass subband L under 1 yardstick
1,1, f
9f) to the K after the denoising under 1 yardstick the logical subband D of band
1, lThe bandpass filtering that reverses, under 1 yardstick K counter-rotating band lead to subband D
1, l, f, l=1 wherein, 2 ..., K;
9g) with the counter-rotating narrow-band low pass subband L of 1 yardstick
1,1, fWith K the logical subband D of counter-rotating band
1, l, fBe weighted operation, obtain the pre-service low pass subband L of noisy image
0, to L
0The low-pass filtering of reversing, pre-service low pass subband L obtains reversing
0, f
9h) to the high-pass filtering of reversing of the pre-service high pass subband after the denoising under 1 yardstick, pre-service high pass subband H obtains reversing
0, f, the pre-service low pass subband of will reversing L
0, fWith counter-rotating pre-service high pass subband H
0, fWeighting obtains preliminary denoising image X
c
9i) according to Rudin-Osher-Fatemi model ROF with preliminary denoising image X
cIn noise X
nTell, by X '
c=X
c-X
n/ λ obtains preliminary useful texture image X '
c, wherein λ is a shrinkage parameters;
9j) shrinkage parameters λ and stopping criterion ξ are set, wherein λ is a positive number arbitrarily, and 0.001≤ξ≤0.01 makes iterated conditional Δ X=|X
c-X '
c|, if Δ X＞ξ, then X
c=X '
c, forward step (9i) to, otherwise with preliminary useful texture image X '
cAs final denoising image, shrinkage parameters λ and stopping criterion ξ value are indefinite, according to the denoising result under different λ values and the ξ value relatively, to the image of size 512 * 512, this example λ gets 1, and ξ gets 0.01, to the image of size 256 * 256, this example λ gets 0.2, and ξ gets 0.01.
Effect of the present invention can further specify by following emulation:
1 simulated conditions: utilize the matlab simulation software, under based on the Gauss's yardstick hybrid GSM model natural image denoising framework that can handle pyramid SP, carry out emulation experiment, the natural image of the present invention's test has the lena image, peppers image and house image, wherein the size of lena image is 512 * 512, the size of peppers and house image is 256 * 256, these test pattern references be image library among the http://decsai.ugr.es/～javier/denoise of website, the quantitative denoising result analytical standard that this example is used is Y-PSNR PSNR, and its unit is dB.
The content of 2 emulation and result:
At test pattern, the diplomatic copy inventive method, and application the inventive method compares with the Gauss's yardstick hybrid GSM model method based on handling pyramid SP that has proposed.
2a) the simulation result of lena image, its visual results as shown in Figure 2, wherein Fig. 2 (a) is original clean lena image; Fig. 2 (b) for add standard deviation be 20 noise signal treat denoising lena image; Fig. 2 (c) is for existing based on the denoising result of the Gauss's yardstick hybrid GSM model method that can handle pyramid SP to Fig. 2 (b); Fig. 2 (d) is a denoising result of the present invention.Can see by simulation result, contain more marginal information in the lena image, since existing based on the Gauss's yardstick hybrid GSM model method that can handle pyramid SP in the denoising journey at be whole conversion sub-band coefficients, this has just caused the edge in the denoising result fuzzyyer, and a little sawtooth effect arranged, shoulder profile as the lena image, and the present invention has used the division operation of adaptivity localized mass in the denoising process, be denoising operation at be sub-piece in the whole conversion sub-band coefficients, thereby avoided the fuzzy of local edge, guaranteed the slickness of local edge; The quantitative analysis results of this image is as shown in table 1.
The quantitative analysis results of table 1. the present invention and existing noise-removed technology
By the quantitative analysis results of table 1 as can be seen, because the present invention has adopted total variation TV operation, eliminated the pseudo-shadow of the gibbs in the denoising result, thereby made the bright quantitative analysis results of this law on average improve 0.22dB based on the Gauss's yardstick hybrid GSM model method that can handle pyramid SP than existing.
2b) the simulation result of peppers image, its visual results as shown in Figure 2, wherein Fig. 2 (e) is original clean peppers image; Fig. 2 (f) for add standard deviation be 20 noise signal treat denoising peppers image; Fig. 2 (g) is for existing based on the denoising result of the Gauss's yardstick hybrid GSM model method that can handle pyramid SP to Fig. 2 (f); Fig. 2 (h) is a denoising result of the present invention.Can see by simulation result,, eliminate the pseudo-shadow effect of the gibbs in the denoising result, thereby made the homogeneous area in the denoising result seem more level and smooth, more meet people's visual effect because the present invention has adopted total variation TV operation; Its quantitative analysis results such as table 1 are not.
By the quantitative analysis results of table 1 as can be seen, because the present invention has adopted total variation TV operation, thereby making that quantitative denoising result of the present invention is existing has relatively on average improved 0.24dB based on the Gauss's yardstick hybrid GSM model method that can handle pyramid SP.
2c) the simulation result of house image, its visual results as shown in Figure 2, wherein Fig. 2 (i) is original clean house image; Fig. 2 (j) for add standard deviation be 20 noise signal treat denoising house image; Fig. 2 (k) is for existing based on the denoising result of the Gauss's yardstick hybrid GSM model method that can handle pyramid SP to Fig. 2 (j); Fig. 2 (l) is a denoising result of the present invention.Can see by simulation result, because the present invention has adopted adaptive localized mass operation and total variation TV operation, thereby improve the edge fog phenomenon of denoising result, guaranteed the slickness of local edge, eliminate the pseudo-shadow of the gibbs in the denoising result, improved the flatness of homogeneous area; The quantitative analysis results of this image is as shown in table 1.
Quantitative analysis results by table 1 can be seen, because bright adaptive local block operations and the total variation TV of having adopted of this law operates, improved the edge fog and the pseudo-shadow of gibbs of denoising result, thereby made the bright quantitative result of this law on average improve 0.29dB based on the Gauss's yardstick hybrid GSM model method that can handle pyramid SP than existing.
Claims (5)
1. one kind based on the Gauss's yardstick hybrid GSM model natural image denoising method that can handle pyramid SP, comprises the steps:
(1) is that the standard deviation that the clean natural image of L * L adds space invariance is the zero-mean white Gaussian noise of σ to size, obtains noisy image;
(2) respectively noisy image and the noise signal that is added are carried out handling pyramid SP conversion, obtain the conversion sub-band coefficients y of noisy image and the conversion sub-band coefficients n of noise signal, and suppose that the conversion sub-band coefficients of original clean image is x;
(3) except that low pass subband, the change direction sub-band coefficients of noisy image under each yardstick done following processing:
3.1) utilize the conversion sub-band coefficients n estimating noise covariance matrix C of noise signal
n=E{nn
T, T representing matrix transposition wherein, E represents matrix is got expectation;
3.2) the conversion sub-band coefficients y of noisy image is divided into the sub-piece y that overlapped size is B * B
i, i=1,2 ..., N, wherein N represents the number of sub-piece;
3.3) to y
iCarry out the modeling of Gauss's yardstick hybrid GSM, promptly
Z wherein
iBe positive scale factor, u
iBe that covariance matrix is
Zero-mean Gauss vector, x
iThe sub-piece of representing original clean image transformation sub-band coefficients x, n
iBe add the sub-piece of noise signal conversion sub-band coefficients n;
3.4) estimator piece y
iCovariance matrix
Wherein
Be y
iAverage;
3.5) estimate the sub-piece x of original clean image transformation sub-band coefficients x
iCovariance matrix
And order
3.6) utilize Bayes's least estimated x
c=∫ p (z
i| y
i) (∫ x
iP (x
i| y
i, z
i) dx
i) dz
i, estimate x
iIn the center coefficient x of each coefficient neighborhood
c, posterior probability wherein
P (y
i| z
i) be likelihood function, p (z
i) be prior probability, p (y
i) be a normalized constant, second integration is reduced to one Wei Na estimates for simplify calculating, that is:
4) utilize each transformation of coefficient subband and low pass subband after the denoising to carry out earlier handling pyramid SP reconstruct, obtain preliminary denoising image; Utilize total variation TV operation that preliminary denoising image is handled again, obtain final denoising image.
2. according to claim 1 based on the Gauss's yardstick hybrid GSM model natural image denoising method that can handle pyramid SP, wherein step (2) is described carries out handling pyramid SP conversion to noisy image, carries out as follows:
(2.1) with a decomposition low-pass filter and a decomposition Hi-pass filter noisy image is carried out pre-service, obtain a size pre-service low pass subband L identical with noisy image
0With a pre-service high pass subband H
0
(2.2) use K decomposition bandpass filter and a decomposition narrow band filter to pre-service low pass subband L
0Carry out filtering, obtain size K the band logical subband B identical with noisy image
1, lHandle low pass subband L with an arrowband
1,1, l=1 wherein, 2 ..., K;
(2.3) low pass subband l is handled in the arrowband
1,1Carry out every 2 down-samplings, obtain a size and be half sampling low pass subband L of noisy image
2,1
(2.4) to sampling low pass subband L
2,1Decompose bandpass filter and a decomposition narrow band filter carries out filtering with K, obtain size and lead to subband B for half K band of noisy image
2, lHandle low pass subband L with an arrowband
2,1, then to resulting narrow-band low pass subband L
2,1Carry out every 2 down-samplings, obtain size and be the sampling low pass subband L of noisy image 1/4th
2,2, and then decompose bandpass filter and a decomposition narrow band filter to sampling low pass subband L with K
2,2Carry out filtering, and the like.
3. according to claim 1 based on the Gauss's yardstick hybrid GSM model natural image denoising method that can handle pyramid SP, wherein step (2) is described carries out handling pyramid SP conversion to the noise signal that is added, and carries out as follows:
(2a) standard deviation of a space invariance of generation is 1 zero-mean white Gaussian noise, multiply by the noise criteria difference σ that will add, and obtains the noise signal that will add;
(2b) noise signal is carried out pre-service, obtain a size pre-service low pass subband L identical with noise signal with a decomposition low-pass filter and a decomposition Hi-pass filter
nWith a high pass subband H
n
(2c) use K decomposition bandpass filter and a decomposition narrow band filter to pre-service low pass subband L
nCarry out filtering, obtain size K the band logical subband B identical with noise signal
1, l, nHandle low pass subband L with an arrowband
1,1, n, l=1 wherein, 2 ..., K;
(2d) low pass subband L is handled in the arrowband
1,1, nCarry out every 2 down-samplings, obtain a size and be half sampling low pass subband L of noise signal
1,2, n
(2e) to sampling low pass subband L
1,2, nDecompose bandpass filter and a decomposition narrow band filter carries out filtering with K, obtain size and lead to subband B for half K band of noise signal
2, l, nHandle low pass subband L with an arrowband
2,1, n, to resulting narrow-band low pass subband L
2,1, nCarry out every 2 down-samplings, obtain size and be the sampling low pass subband L of noise signal 1/4th
2,2, n, and then decompose bandpass filter and a decomposition narrow band filter to sampling low pass subband L with K
2,2, nCarry out filtering, and the like.
4. according to claim 1 based on the Gauss's yardstick hybrid GSM model natural image denoising method that can handle pyramid SP, wherein step (4) is described carries out handling pyramid SP conversion reconstruct earlier to each transformation of coefficient subband after the denoising and low pass subband, carries out as follows:
(4.1) to the sampling low pass subband L under the noisy image j yardstick
2, jCarry out every 2 up-samplings, obtain a narrow-band low pass subband L under the j yardstick
1, j, j=J, J-1 ..., 2,1, wherein J is for handling the yardstick of pyramid SP conversion;
(4.2) to the narrow-band low pass subband L under the j yardstick
1, jThe narrow-band filtering that reverses obtains the counter-rotating narrow-band low pass subband L under the j yardstick
1, j, f, the narrow band filter that wherein reverses differs 180 ° with the decomposition narrow band filter that can handle pyramid SP conversion;
(4.3) to the K after the denoising under the j yardstick the logical subband D of band
J, lThe bandpass filtering that reverses, promptly the counter-rotating bandpass filter under the j yardstick with can handle the decomposition bandpass filter of pyramid SP conversion under the j yardstick and differ 180 °, under the j yardstick K counter-rotating band lead to subband D
J, l, f, l=1 wherein, 2 ..., K;
(4.4) with the counter-rotating narrow-band low pass subband L of j yardstick
1, j, fWith K the logical subband D of counter-rotating band
J, l, fBe weighted operation, obtain the sampling low pass subband L under the noisy image j-1 yardstick
2, j-1, make j=j-1, judge whether j equals 1, if j is not equal to 1, forward step (4.1) to, otherwise execution in step (4.5);
(4.5) to the sampling low pass subband L under 1 yardstick
2,1Carry out every 2 up-samplings, obtain one the 1 narrow-band low pass subband L under the yardstick
1,1, to the narrow-band low pass subband K under 1 yardstick
1,1The narrow-band filtering that reverses obtains the counter-rotating narrow-band low pass subband L under 1 yardstick
1,1, f
(4.6) to the K after the denoising under 1 yardstick the logical subband D of band
1, lThe bandpass filtering that reverses, under 1 yardstick K counter-rotating band lead to subband D
1, l, f, l=1 wherein, 2 ..., K;
(4.7) with the counter-rotating narrow-band low pass subband L of 1 yardstick
1,1, fWith K the logical subband D of counter-rotating band
1, l, fBe weighted operation, obtain the pre-service low pass subband L of noisy image
0, to L
0The low-pass filtering of reversing, pre-service low pass subband L obtains reversing
0, f
(4.8) to the high-pass filtering of reversing of the pre-service high pass subband after the denoising under 1 yardstick, pre-service high pass subband H obtains reversing
0, f, the pre-service low pass subband of will reversing L
0, fWith counter-rotating pre-service high pass subband H
0, fWeighting obtains reconstructed image.
5. according to claim 1 based on the Gauss's yardstick hybrid GSM model natural image denoising method that can handle pyramid SP, wherein step (4) is described utilizes total variation TV operation that preliminary denoising image is handled, and carries out as follows:
(4a) according to Rudin-Osher-Fatemi model ROF with preliminary denoising image X
cIn noise X
nTell, by X '
c=X
c-X
n/ λ obtains preliminary useful texture image X '
c, wherein λ is a shrinkage parameters;
(4b) shrinkage parameters λ and stopping criterion ξ are set, wherein λ is a positive number arbitrarily, and 0.001≤ξ≤0.01 makes iterated conditional Δ X=|X
c-X '
c|, if Δ X＞ξ, then X
c=X '
c, forward step (4a) to, otherwise with preliminary useful texture image X '
cAs final denoising image.
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| CN107369143A (en) * | 2017-07-03 | 2017-11-21 | 南京觅踪电子科技有限公司 | A kind of image denoising method based on continuous bandpass filtering and reconstruction |
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| CN111091511A (en) * | 2019-12-17 | 2020-05-01 | 广西科技大学 | Broad-spectrum denoising method for microscopic image |
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