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

Wei ZHANG  Feng YU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.9   pp.2026-2030
Publication Date: 2017/09/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Digital Signal Processing
compressive sensing (CS),  spectral compressive sensing,  off-the-grid issue,  parameterized L1-minimization,  

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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.