Due to the constraints of equipments and technical conditions, images obtained from sampling, compressing, and transferring may be degraded, which cause images visually annoying and prevent them from further processing. The degradation is often modeled as a space-invariant low-pass filter with an added random noise. The goal of image restoration is to restore the original true images from the degraded ones. Blind image restoration, where the blur kernel of the degradation is unknown, is a seriously ill-conditioned problem. To identify the blur and restore the true image, the prior information about the blur kernel and the unknown true image must be introduced. In this thesis, the following image restoration problems are studied: First, the generalized Laplacian distribution is proposed to model the motion blurs for the sparseness characteristic of the blurs, which makes a proper tradeoff between high-efficiency and low-complexity. Exploited the sparseness priors of natural image and motion blur, maximum a posterior (MAP) estimation based on Bayesian theory is used to simultaneously identify blurs and restore images. The experimental results demonstrate the effectiveness of the algorithm. Second, in order to restore the images that are degraded simultaneously by various blurs, an image restoration method for the degradation model where the blur kernel is the mixture of defocus and motion blurs is proposed. Given the defocus blur, the statistical characteristic of the motion blur is exploited with generalized Laplacian model, and then the mixed blur is identified using the Expectation/Maximization (EM) algorithm. Finally the degraded image is restored with the help of the estimated blur. The proposed algorithm could identify the blur effectively, and improve visual quality of the degraded images. Third, wavelet shrinkage denoising has been investigated for a long time due to its simplicity and good results. SLT denoising generates mapping functions (MFs), also known as shrinkage functions, which are learned directly from example images using least-squares fitting. In this paper, we design MFs with the prior information properly incorporated in SLT denoising. Since coefficients in the same wavelet subband have different statistic characteristics, we first classify wavelet coefficients into different classes. Then MFs for different regions are deduced with corresponding prior model. The proposed method obtains higher PSNR (Peak Signal to Noise Ratio), a...
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