点击显示 收起
【摘要】 图像复原是图像分析、识别和理解的重要因素。对于模糊加噪图像，在抑制噪声能力方面约束最小二乘法最强；在保护细节方面，约束最小二乘法比盲目图像复原法和维纳滤波法要差一些。
【关键词】 影像重建；盲区影像重建；滤法；改良过滤法；最小二乘法滤过方法
The processing of the medical digital imaging restoration
TANG Jing-tian， YANG Xiao-li, TANG Yan,et al.
Info-Physics Engineering College of CSU Central South University, Changsha 410083, China
【Abstract】 Image restoration is the important factor that influencesimage’s analysis, recognitionand comprehension. Image restoration act noise-up pressing blind worst side constrained least squares method of filtering noise filtering capacity of the strongest restoration, In the protection of image detail, constrained least squares methodthan the blind image restoration and rehabilitation Wiener filter method to recover the better.
【Key words】 Image restoration; Blind image restoration; Wiener filtering; improved wiener filtering; least square filtering
In the image processing,some details will be strengthened in image degradation，and some other details willbe weaken. In the actual operation, it is possible to use the detailswhich would be weakened, so we had to use the image restoration. Image restoration is the inverse process of image degradation through various restorationcriteria for the resumption of the original image, toimproveimage qualityand be facilitatetoimage analysis, recognitionandcomprehension. Different criteria, different image restoration methods can be derived, just as showing in the paper［3］and paper ［4］. So we study of blindimage restoration, rehabilitation Wiener filter, Wiener filter improved recovery and rehabilitation of constrained least squares filtering. In the end of the paper, we compare the four methods and select the better method to recover the degraded medical digital image.
1 Blind image restoration
If image degradation is unknown, it is necessary to observe the image in a certain way through degradationto identify image restoration methods. This method is the so-called blind image restorationas the paper ［7］. Suppose g(x,y) asa noisy image, n(x,y)asnoise, f(x,y) asthe original image. The gi expressed by the following equation: gi(x,y)=fi(x,y)+ ni(x,y). So we can get: fi(x,y)=1 MM i=1gi（x,y)-1 M1 i=1ni(x,y)
(1)When the M is larger, the right side of equation above the noise value of the mathematical expectation is that it tends to E｛n(x,y)｝ . Under normal circumstances all the mathematicalexpectation of white Gausses noise is zero, so it can be written as :fi(x,y)=1 MM i=1gi（x,y)
(2)There is a imaging system, which has been relatively stable images with the goal of degradation, Such degradation is different because every image is a linear function of displacement impact unchanged h(x,y) of the project. The degraded images can be expressed as :gi(x,y)=fi(x,y)*hi(x,y)
(3)In the formula gi(x,y) is the degenerated image,fi(x,y) is original image,hi(x,y) is the proliferation function, * represents the convolution, i=1,2……M.Fourier transform for image degradation:Gi(u,v)=Fi(u,v)Hi(u,v)
(4)Put the original image spectrum and degradation function separately: In［Gi(u,v)］=1n［Fi(u,v)］+In［Hi(u,v)］
(5)If the images are not related to the impulse response, and it can be below: M i=11n［Gi(u,v)］=M1n［Fi(u,v)］+M i=11n［Hi(u,v)］
(6)When M is large, the transfer function of the number and type is close to a constant value:KH(u,v)=lim M→∞M i=11n［Hi(u,v)］
(7)Therefore, the estimated image:F^ i(u,v)=exp｛KH(u,v) M｝M i=1［Gi(u,v)］1 M
(8)In the above analysis, we didn’t consider the weight of additive noise. In considering a noise component, we can remove noise at first by the filter, and then according to the above method, the image can be analyzed.
2 Wiener filter and Wiener filter improved restoration
Wiener filteringrestoration in paper［5］ and ［6］is to find a filter, making restorationin the image f^ (x,y) and the original image is the smallest Standard deviation. According to the principle of least squares, wecan find a least squares estimatedvalue (post-recovery image) f^ (x,y) forthe degradation of the image g(x,y) and makethe standard deviation the smallest.e2=E｛［(f(x,y)-f^ =(x,y))］2｝
(9)If the original image f(x,y) and the noise n(x,y) is not relevant, and n(x,y) is zero mean, Wiener filter can be drawn from the above conditions, the transfer function M(u,v) M(u,v)=｜H(u,v)｜2+H*(u,v) Pn(u,v)/Pf(u,v)
(10)In the Wiener filter, the power spectrum can be approximated as a constant. Pn(ω)≈A(constant).
The typical form of the power spectrum is approximation as:
Pf(ω)=Be-αω
(11)B and a are all constants. The improved Wiener filter transfer function can be written as: Meω(ω)=H*(ω) ｜H(ω)｜2+Ceαω
(12)ω=w=u2+v2,C=A BAssuming the Gaussian function of the system degraded, the one-dimensional PSF: h(x)=1 2πσ2e-x2 2σ2
(13)There σ reflects the expansion of Point Imaging. Its Fourier transform ：H（ω）=eσ2 2ω2
(14)We can come to the one-dimensional Gaussian filter inverse transfer function:M(ω)=eσ2 2ω2
(15)Wiener filter can be drawn by：M(ω)=1 eσ2 2ω2+kex2 2σ2ω2
(16)Improved Wiener filter ：Meω(ω)=1 eσ2 2ω2+Ceσ2 2+αω
(17)Through many experiments, we can get the better effect when σ=0.16，k=0.002,C=0.05. Then the transfer function of the Wiener filter and the improved Wiener filter figure as:
Fig1 The Frequency Response of the Wiener filter(dotted) and the Frequency
Response of the Improved The Wiener filtercan go a god result in paper［1］, but by selecting parameters, the high-frequency end of the Wiener filter improved bandwidth to be wilderthan the wienerfilter’s. Image recovery is conducive to high-frequency details.
3 Rehabilitation of constrained least squares filtering
If we only know a priori knowledge of the noise standard deviation, we can adopt least squares method such as showing in paper［2］to recover. Using Lagrangian optimization theory, the minima of the problem turns into a non-binding extreme problems, these problems become the objective function: E(f,g,a)≈‖g-Hf‖2+a‖Df‖2(18) The discrete form is: D=0 -1 0
-1 4 -10 -1 0(19) If evaluating partial derivative and make it equal to 0: E(f,g,a) f=0(20) f=(HTH+aDTD)-1HTg(21)
4 Experiment and result
We integrates four method of image restoration mentioned above to process medical digital image filled with noise. The step of the method is given as follows:
1) Applying blind image restoration, Wiener filter improved restorationand restorationof constrained least squares filteringto process medical digital image filled with noise.
2) For the image that comes from the first step, obtaining one-line gray-scale curve of image withprogrammer. The breast X-picture and the result can be seen fromFig2.
Fig2. (a)Original image figure, (c)original image with noise, (e) blind image recovery, (g) Wiener filtering recovery，（i)least square recovery，（b）the one-line gray-scale curve of image(a), (d) the one-line gray-scale curve of image(c), (f) the one-line gray-scale curve of image(e), (h) the one-line gray-scale curve of image(g), (j) the one-line gray-scale curve of image(i)
5 Comparison and conclusion
1) Fuzzy-noise image of his gray curve graph, the result of fuzzy gray curve has been completely unable to discern. This shows serious degradation.
2) The image comes from the processing of blind image for image. Image characteristics of a clear division are still not clear, although the image resolution vague, but images are subject to serious noise pollution.
3) The image comesfrom the processing of the wiener filtering recovery for image. Image characteristics more clearly defined, the clearer image change, but it still has a certain degree of image noise pollution
4) The image comesfrom the processing of the least square for image. It suppressing noise and eliminate blurred imagesandachieved fairly good results. At the same time it has lost the noiseofimage details.
5) Image Restoration Act noise-suppressing blind worst side constrained least squares method of filtering noise filtering capacity of the strongest recovery ; In the protection of image detail, constrained least squares method than the blind side filter image restoration and rehabilitation Wiener filter method to recover the better.
【参考文献】
1 Zeng Sanyo,Ding Li xi,Kang Lisha，et al.A Method to approach optimal restoration in image restoration problems without noise energy information. Actia mathem atica scientia. 2003，23B(4)：512- 520.
2 Masashi Sugiyama, Hidemitsu Ogawa.A Unified Method for Optimizing Linear Image Restoration Filters. Signal Processing. 2002，82(11)：1- 22.
3 Markr.Banham, Aggelosk. Katsaggelos, et al.Digital image restoration. IEEE signal processing magazine. 1997，97：24- 41.
4 Michael E. Kuhl, Halim Damerdji, James R. Wilson. Least SquaresEstimation of Nonhomation of Nonhomogeneous Poinesson Processes. Proceedings of the 1998 Winter Simulation Conference. 1998:637-645.
5 许泉平. 图像中的噪声及复原方法研究. 山西焦煤科技,2006，7（7）16-17.
6 芳顾亚. 图像中的噪声及复原方法研究. 大众科技,2005，76（2）40-41.
7 薛梅,邹采荣,杨娟. 一种空间自适应正则化图像盲复原算法. 中国图像图形学报,2002，7（4）:356-362.
作者单位：1 410083 Info-Physics Engineering College of CSU Central South University, China（中南大学信息物理工程学院）2 Ji lin Tumour Hospital,China（吉林省肿瘤医院）