Image Reconstruction Based On Sure Regularization Theory Research

Image denosing, image deblurring and image super resolution are very common problem in image field. However, they are ill-posed inverse problem, regularization method is useful strategy which can stabilize the problem and obtain a useful and stable solution. However, when applying this method, the user is faced with the difficult task of adjusting regularization parameter to obtain best performance. In this paper, we focus on regularization parameter selection of image restoration and the details are as follows:Firstly, we solve inverse problem is to use regularization techniques in conjunction with least square objective. Parameter choice is crucial to regularization-based image process, the effect of reconstructed image is measured by minimizing mean square error (MSE), however, the MSE depends on the original signal which is generally is unavailable or unknown a priori, a practical approach Stein’s unbiased risk estimate (SURE) is proposed, we derive the unbiased risk estimate of MSE, which depends on the given data, provides a mean for unbiased risk estimate of the true MSE.Secondly, in this paper, we extend the SURE method to image blurring and image super resolution problems, The SURE criterion has been employed in variety of denosing problems for choosing regularization parameters, in the case of denosing algorithms that can not be expressed analytically. We present novel Monte-Carlo technique which enables the user to calculate SURE, The proposed algorithm is suitable for the exact restoration algorithm as well as those of not being expressed analytically. We justify our claims by presenting experimental result for SURE-based optimization of two different regularization algorithms such as Tikhonov and total variation regularization. We demonstrate numerically that SURE computed using the Monte-Carlo approach accurately predicts the true MSE for several different algorithms.Thirdly, the SURE method can also be used in the choice of the parameters for some denoising algorithms, such as the width of smooth kernel of Non-local means (NLM) denosing algorithm and the threshold parameter of sparse representation regularization denosing algorithm. We use SURE to monitor the MSE of two algorithms for the restoration of an image corrupted by additive white Gaussian noise. Experiment results show the validity of the proposed algorithm, which can confirm the optimality of the proposed parameter selection.