Image restoration problems deal with images in which information has been degradedudby blur or noise. In practice, the blur is usually caused by atmospheric turbulence, motion, camera shake, and several other mechanical or physical processes.udIn this study, we present two regularization algorithms for the image deblurring problem.udWe first present a new method based on solving a regularized least-squares (RLS)udproblem. This method is proposed to find a near-optimal value of the regularization parameter in the RLS problems. Experimental results on the non-blind image deblurring problem are presented. In all experiments, comparisons are made with three benchmark methods. The results demonstrate that the proposed method clearly outperforms the other methods in terms of both the output PSNR and structural similarity, as well as the visual quality of the deblurred images. To reduce the complexity of the proposed algorithm, we propose a technique based onudthe bootstrap method to estimate the regularization parameter in low and high-resolution images. Numerical results show that the proposed technique can effectively reduce the computational complexity of the proposed algorithms. In addition, for some cases where the point spread function (PSF) is separable, we propose using a Kronecker product so as to reduce the computations.udFurthermore, in the case where the image is smooth, it is always desirable to replace the regularization term in the RLS problems by a total variation term. Therefore, we propose a novel method for adaptively selecting the regularization parameter in a so-called square root regularized total variation (SRTV). Experimental results demonstrate that our proposed method outperforms the other benchmark methods when applied to smooth images in terms of PSNR, SSIM and the restored image quality.udIn this thesis, we focus on the non-blind image deblurring problem, where the blurudkernel is assumed to be known. However, we developed algorithms that also work in the blind image deblurring. Experimental results show that our proposed methods are robust enough in the blind deblurring and outperform the other benchmark methods in terms of both output PSNR and SSIM values.
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