Optimal selection of regularization parameter for l_1-based image restoration based on SURE

摘要

To exploit the sparsity in transform domain (e.g. wavelets), the image deconvolution can be typically formulated as a ?_1-penalized minimization problem, which, however, generally requires proper selection of regularization parameter for desired reconstruction quality. The key contribution of this paper is to develop a novel data-driven scheme to optimize regularization parameter, such that the resultant restored image achieves minimum prediction error (p-error). First, we develop Stein's unbiased risk estimate (SURE)-an unbiased estimate of p-error-for image degradation model. Then, we propose a recursive evaluation of SURE for the basic iterative shrinkage/thresholding (IST), which enables us to find the optimal value of regularization parameter by exhaustive search. The numerical experiments show that the proposed SURE-based optimization leads to nearly optimal deconvolution performance in terms of peak signal-to-noise ratio (PSNR).