Parametric PSF estimation based on predicted-SURE with $$\ell _1$$ ℓ 1 -penalized sparse deconvolution

Abstract

Point spread function (PSF) estimation plays an important role in blind image deconvolution. It has been shown that incorporating Wiener filter, minimization of the predicted Stein’s unbiased risk estimate (p-SURE)—unbiased estimate of predicted mean squared error—could yield an accurate PSF estimate. In this paper, we provide a theoretical analysis for the PSF estimation error, which shows that the better deconvolution leads to more accurate PSF estimate. It motivates us to incorporate an \(\ell _1\)-penalized sparse deconvolution into the p-SURE minimization, instead of the Wiener-type filtering. In particular, based on FISTA—one of the most popular iterative \(\ell _1\)-solvers, we evaluate the p-SURE for each update, by Jacobian recursion and Monte Carlo simulation. Numerical results of both synthetic and real experiments demonstrate the improvements in PSF estimate, and therefore, deconvolution performance.