Unbiased Bregman-Risk Estimators: Application to Regularization Parameter Selection in Tomographic Image Reconstruction

TL;DR

This paper introduces unbiased estimators for Bregman divergences to improve regularization parameter selection in tomographic image reconstruction, demonstrating promising numerical results and theoretical insights.

Contribution

It develops a new class of unbiased estimators for Bregman divergences and applies them to regularization parameter selection in inverse problems.

Findings

Effective parameter selection method demonstrated in experiments

Observation of measure concentration phenomena

Implications for inverse problem regularization

Abstract

Unbiased estimators are introduced for averaged Bregman divergences which generalize Stein's Unbiased (Predictive) Risk Estimator, and the minimization of these estimators is proposed as a regularization parameter selection method for regularization of inverse problems. Numerical experiments are presented in order to show the performance of the proposed technique. Experimental results indicate a useful occurence of a concentration of measure phenomena and some implications of this hypothesis are analyzed.