Fixed Point Iterations for SURE-based PSF Estimation for Image Deconvolution

TL;DR

This paper introduces fixed point iteration methods to efficiently optimize SURE-based parameters for blind image deconvolution, significantly reducing computational cost and convergence time compared to brute-force search.

Contribution

The authors propose novel fixed point algorithms for rapid, low-cost estimation of multiple PSF and regularization parameters in SURE-based blind deconvolution.

Findings

Fixed point methods converge in 50-100 iterations

Each iteration has low computational cost

Achieves near-optimal PSF parameters efficiently

Abstract

Stein's unbiased risk estimator (SURE) has been shown to be an effective metric for determining optimal parameters for many applications. The topic of this article is focused on the use of SURE for determining parameters for blind deconvolution. The parameters include those that define the shape of the point spread function (PSF), as well as regularization parameters in the deconvolution formulas. Within this context, the optimal parameters are typically determined via a brute for search over the feasible parameter space. When multiple parameters are involved, this parameter search is prohibitively costly due to the curse of dimensionality. In this work, novel fixed point iterations are proposed for optimizing these parameters, which allows for rapid estimation of a relatively large number of parameters. We demonstrate that with some mild tuning of the optimization parameters, these fixed point methods typically converge to the ideal PSF parameters in relatively few iterations, e.g. 50-100, with each iteration requiring very low computational cost.