Abstract
A proper selection of regularization parameter is essential for regularization-based image deconvolution. The main contribution of this paper is to propose a new form of generalized cross validation (GCV) as a criterion for this optimal selection. Incorporating a nil-trace non-linear estimate, we develop this new GCV based on Stein's unbiased risk estimate (SURE)-an unbiased estimate of mean squared error (MSE). The key advantage of this GCV over SURE is that it does not require the knowledge of noise variance. We exemplify this criterion with both Tikhonov regularization and l 1 -based sparse deconvolution. In particular, we develop a recursive evaluation of GCV for the l 1 -estimate based on iterative soft-thresholding (IST) algorithm. Numerical experiments demonstrate the nearly optimal parameter selection and negligible loss of its resultant deconvolution quality.
Published Version
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