Recursive SURE for iterative reweighted least square algorithms

Abstract

Iterative re-weighted least square (IRLS) algorithms for (Formula presented.) -minimization problems require to select proper value of regularization parameter, for which Stein’s unbiased risk estimate (SURE) – an unbiased estimate of prediction error – is often used as a criterion for this selection. In this paper, we propose a recursive SURE to estimate the prediction error during the IRLS iterations. Particularly, we derive the recursion of Jacobian matrix by incorporating matrix splitting scheme into IRLS algorithms. Numerical examples demonstrate that minimizing SURE consistently leads to the nearly optimal reconstructions in terms of prediction error. Theoretical derivations in this work related to the evaluation of Jacobian matrix can be extended, in principle, to other types of regularizers and regularized iterative reconstruction algorithms.