Parametric PSF estimation based on recursive SURE for sparse deconvolution

PSF (point spread function) estimation plays an important role in blind image deconvolution. It has been shown in our previous work that minimization of the Stein’s unbiased risk estimate (SURE) – unbiased estimate of mean squared error (MSE) – could yield an accurate PSF estimate. In this paper, we show that the PSF estimation error is upper bounded by the deconvolution accuracy and the mismatch between the assumed PSF parametric form and the underlying true one. For this reason, we incorporate the {\ell_{1}}-penalized sparse deconvolution into the SURE instead of previously used Wiener filter. In particular, we apply the iterative soft-thresholding algorithms to solve {\ell_{1}}-minimization, and develop recursive evaluations of SURE, which is then shown to converge to the existing theoretical result. In practical implementations with large-scale data, we apply the Monte-Carlo simulation to avoid the explicit matrix operation. Numerical examples demonstrate the improvements of PSF estimate, and the resulting deconvolution performance.