The sparsity-based signal reconstruction is typically formulated as an \(\ell _1\) regularization (i.e., lasso problem in statistics), and the reconstruction accuracy strongly depends on the regularization parameter. In this paper, we develop two data-driven optimization schemes, based on minimization of Stein’s unbiased risk estimate (SURE). First, a recursive evaluation of SURE is proposed to estimate the mean squared error during the reconstruction iterations, which enables us to optimize the regularization parameter. Second, for fast optimization, we perform the alternating updates between regularization parameter and solution. In particular, we perform the convergence analysis of the recursive SURE and the accompanied Monte Carlo simulation, based on the Jacobian recursion, support identification and proximal point framework. Numerical experiments show that the proposed methods lead to highly accurate estimate of regularization parameter and nearly optimal reconstruction.

基于稀疏性的信号重建通常被公式化为\(\ell _1\)正则化（即lasso统计学中的问题），重建精度强烈依赖于正则化参数。在本文中，我们基于 Stein 的无偏风险估计 (SURE) 的最小化开发了两种数据驱动的优化方案。首先，提出了 SURE 的递归评估来估计重建迭代期间的均方误差，这使我们能够优化正则化参数。其次，为了快速优化，我们在正则化参数和解之间执行交替更新。特别是，我们基于雅可比递归、支持识别和近端点框架，对递归 SURE 和伴随的蒙特卡罗模拟进行收敛分析。