Continuous Compressed Sensing With a Single or Multiple Measurement Vectors

Abstract

We consider the problem of recovering a single or multiple frequency-sparse signals, which share the same frequency components, from a subset of regularly spaced samples. The problem is referred to as continuous compressed sensing (CCS) in which the frequencies can take any values in the normalized domain [0,1). In this paper, a link between CCS and low rank matrix completion (LRMC) is established based on an ${\ell }_0$-pseudo-norm-like formulation, and theoretical guarantees for exact recovery are analyzed. Practically efficient algorithms are proposed based on the link and convex and nonconvex relaxations, and validated via numerical simulations.

4 pages, 2 figures, in IEEE Workshop on Statistical Signal Processing (SSP), pp. 308--311, June 2014

References in corpus (4)

• The Convex Geometry of Linear Inverse Problems
• On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data
• A discretization-free sparse and parametric approach for linear array signal processing
• Exact Joint Sparse Frequency Recovery via Optimization Methods

Cited by in corpus (9)

• On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data
• A discretization-free sparse and parametric approach for linear array signal processing
• Atomic Norm Minimization for Modal Analysis from Random and Compressed Samples
• Exact Joint Sparse Frequency Recovery via Optimization Methods
• Vandermonde Decomposition of Multilevel Toeplitz Matrices with Application to Multidimensional Super-Resolution
• Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization
• Achieving High Resolution for Super-resolution via Reweighted Atomic Norm Minimization
• Gridless Line Spectral Estimation with Multiple Measurement Vector via Variational Bayesian Inference
• Grid-less Variational Direction of Arrival Estimation in Heteroscedastic Noise Environment