A family of risk estimators as criteria for psf estimation: From sureto GCV

Abstract

Stein's unbiased risk estimate (SURE) has been proven as a valid criterion for PSF (point spread function) estimation [1], which is essential to blind image deconvolution. In this paper, we develop a family of risk estimators as the criteria for blur identification. We first provide a direct proof of the validity of SURE. From this new perspective, we develop generalized cross validation (GCV) as a novel criterion and interpret it as a variant of SURE. A key advantage of GCV over SURE is that it does not depend on noise variance: we do not need to estimate it in advance. We also provide a theoretical error analysis for the regularizer approximation within this SURE-type framework, by which we show that the error of PSF estimate is upper bounded by the approximation error. We further introduce a novel adaptive regularizer, which yields more accurate PSF estimate than other choices by extensive experimental tests.