Image restoration is a complicated process in which the original information can be recovered from the degraded image model caused by lots of factors.Mathematically,image restoration problems are ill-posed inverse pro...Image restoration is a complicated process in which the original information can be recovered from the degraded image model caused by lots of factors.Mathematically,image restoration problems are ill-posed inverse prob-lems.In this paper image restoration models and algorithms based on variational regularization are surveyed.First,we review and analyze the typical models for denoising,deblurring and inpainting.Second,we construct a unified restoration model based on variational regularization and summarize the typical numerical methods for the model.At last,we point out eight diffcult problems which remain open in this field.展开更多
This paper proposes a new image restoration technique, in which the resulting regularized image approximates the optimal solution steadily. The affect of the regular-ization operator and parameter on the lower band an...This paper proposes a new image restoration technique, in which the resulting regularized image approximates the optimal solution steadily. The affect of the regular-ization operator and parameter on the lower band and upper band energy of the residue of the regularized image is theoretically analyzed by employing wavelet transform. This paper shows that regularization operator should generally be lowstop and highpass. So this paper chooses a lowstop and highpass operator as regularization operator, and construct an optimization model which minimizes the mean squares residue of regularized solution to determine regularization parameter. Although the model is random, on the condition of this paper, it can be solved and yields regularization parameter and regularized solution. Otherwise, the technique has a mechanism to predict noise energy. So, without noise information, it can also work and yield good restoration results.展开更多
The nonlinear diffusion filtering in image processing bases on the heat diffusion equations. Its key is the control of diffusion amount. In the previous models, the diffusivity depends on the gradients of images. So i...The nonlinear diffusion filtering in image processing bases on the heat diffusion equations. Its key is the control of diffusion amount. In the previous models, the diffusivity depends on the gradients of images. So it is easily affected by noises. This paper first gives a new multiscale computational technique for diffusivity. Then we proposed a class of nonlinear wavelet diffusion （NWD） models that are used to restore images. The NWD model has strong ability to resist noise. But it, like the previous models, requires higher computational effort. Thus, by simplifying the NWD, we establish linear wavelet diffusion （LWD） models that consist of advection and diffusion. Since there exists the advection, the LWD filter is anisotropic, and hence can well preserve edges although the diffusion at edges is isotropic. The advantage is that the LWD model is easy to be analyzed and has lesser computational load. Finally, a variety of numerical experiments compared with the previous model are shown.展开更多
A satellite image adaptive restoration method was developed that avoids ringing artifacts at the image boundary and retains oriented features. The method combines periodic plus smooth image decom- position with comple...A satellite image adaptive restoration method was developed that avoids ringing artifacts at the image boundary and retains oriented features. The method combines periodic plus smooth image decom- position with complex wavelet packet transforms. The framework first decomposes a degraded satellite im- age into the sum of a ＂periodic component＂ and a ＂smooth component＂. The Bayesian method is then used to estimate the modulation transfer function degradation parameters and the noise. The periodic component is deconvoluted using complex wavelet packet transforms with the deconvolution result of the periodic component then combined with the smooth component to get the final recovered result. Tests show that this strategy effectively avoids ringing artifacts while preserving local image details （especially directional tex- tures） without amplifying the noise. Quantitative comparisons illustrate that the results are comparable with previous methods. Another benefit is that this approach can process large satellite images with parallel processing, which is important for practical use.展开更多
文摘Image restoration is a complicated process in which the original information can be recovered from the degraded image model caused by lots of factors.Mathematically,image restoration problems are ill-posed inverse prob-lems.In this paper image restoration models and algorithms based on variational regularization are surveyed.First,we review and analyze the typical models for denoising,deblurring and inpainting.Second,we construct a unified restoration model based on variational regularization and summarize the typical numerical methods for the model.At last,we point out eight diffcult problems which remain open in this field.
基金This work was supported by the National Natural Science Foundation of China(60204001, 60133010)the Scientific Research Fundation of Hunan Provincial Education Department(02C640)the Youth Chengguang Project of Science and Technology of Wuhan City(
文摘This paper proposes a new image restoration technique, in which the resulting regularized image approximates the optimal solution steadily. The affect of the regular-ization operator and parameter on the lower band and upper band energy of the residue of the regularized image is theoretically analyzed by employing wavelet transform. This paper shows that regularization operator should generally be lowstop and highpass. So this paper chooses a lowstop and highpass operator as regularization operator, and construct an optimization model which minimizes the mean squares residue of regularized solution to determine regularization parameter. Although the model is random, on the condition of this paper, it can be solved and yields regularization parameter and regularized solution. Otherwise, the technique has a mechanism to predict noise energy. So, without noise information, it can also work and yield good restoration results.
文摘The nonlinear diffusion filtering in image processing bases on the heat diffusion equations. Its key is the control of diffusion amount. In the previous models, the diffusivity depends on the gradients of images. So it is easily affected by noises. This paper first gives a new multiscale computational technique for diffusivity. Then we proposed a class of nonlinear wavelet diffusion （NWD） models that are used to restore images. The NWD model has strong ability to resist noise. But it, like the previous models, requires higher computational effort. Thus, by simplifying the NWD, we establish linear wavelet diffusion （LWD） models that consist of advection and diffusion. Since there exists the advection, the LWD filter is anisotropic, and hence can well preserve edges although the diffusion at edges is isotropic. The advantage is that the LWD model is easy to be analyzed and has lesser computational load. Finally, a variety of numerical experiments compared with the previous model are shown.
基金Supported by the National High-Tech Research and Development (863) Program of China (No. 2007AA120408)
文摘A satellite image adaptive restoration method was developed that avoids ringing artifacts at the image boundary and retains oriented features. The method combines periodic plus smooth image decom- position with complex wavelet packet transforms. The framework first decomposes a degraded satellite im- age into the sum of a ＂periodic component＂ and a ＂smooth component＂. The Bayesian method is then used to estimate the modulation transfer function degradation parameters and the noise. The periodic component is deconvoluted using complex wavelet packet transforms with the deconvolution result of the periodic component then combined with the smooth component to get the final recovered result. Tests show that this strategy effectively avoids ringing artifacts while preserving local image details （especially directional tex- tures） without amplifying the noise. Quantitative comparisons illustrate that the results are comparable with previous methods. Another benefit is that this approach can process large satellite images with parallel processing, which is important for practical use.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60073043 70071042+2 种基金60133010 60204001 (国家自然科学基金) the Scientific Research Fund of Hunan Provincial Education Department of China under Grant No.02C640 (湖南省教育
