An iterative sure-let approach to sparse reconstruction

Abstract

Sparsity-promoting regularization is often formulated as ℓv-penalized minimization (0 <; v ≤ 1), which can be efficiently solved by iteratively reweighted least squares (IRLS). The reconstruction quality is generally sensitive to the value of regularization parameter. In this work, for accurate recovery, we develop two data-driven optimization schemes based on minimization of Stein's unbiased risk estimate (SURE). First, we propose a recursive method for computing SURE for a given IRLS iterate, which enables us to unbiasedly evaluate the reconstruction error, and select the optimal value of regularization parameter. Second, for fast optimization, we parametrize each IRLS iterate as a linear combination of few elementary functions (LET), and solve the linear weights by minimizing SURE. Numerical experiments show that iterating this process leads to higher reconstruction accuracy with remarkably faster computational speed than standard IRLS.