Sparse signal recovery from nonlinear measurements

We treat the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and coordinate-wise optimality. These conditions are then used to derive three numerical algorithms aimed at finding points satisfying the resulting optimality criteria: the iterative hard thresholding method and the greedy and partial sparse-simplex methods. The theoretical convergence of these methods and their relations to the derived optimality conditions are studied.

1. INTRODUCTION

Sparsity has long been exploited in signal processing, statistics and computer science. Recent years have witnessed a growing interest in algorithms for sparse recovery [3], [2], [16]. Despite the great interest in exploiting sparsity in various applications, most of the work to date has focused on recovering a sparse vector from linear measurements of the form . For example, the rapidly growing field of compressed sensing [7], [6], [10] considers recovery of a sparse from a small set of linear measurements where .