Parameterized L1-Minimization Algorithm for Off-the-Gird Spectral Compressive Sensing

Abstract

Spectral compressive sensing is a novel approach that enables extraction of spectral information from a spectral-sparse signal, exclusively from its compressed measurements. Thus, the approach has received considerable attention from various fields. However, standard compressive sensing algorithms always require a sparse signal to be on the grid, whose spacing is the standard resolution limit. Thus, these algorithms severely degenerate while handling spectral compressive sensing, owing to the off-the-grid issue. Some off-the-grid algorithms were recently proposed to solve this problem, but they are either inaccurate or computationally expensive. In this paper, we propose a novel algorithm named parameterized ℓ₁-minimization (PL1), which can efficiently solves the off-the-grid spectral estimation problem with relatively low computational complexity.