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Continuous compressed sensing with a single or multiple measurement vectors
 in Proceedings of IEEE Workshop on Statistical Signal Processing (SSP
"... We consider the problem of recovering a single or multiple frequencysparse 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 ..."
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We consider the problem of recovering a single or multiple frequencysparse 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 `0pseudonormlike 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. Index Terms — Continuous compressed sensing, multiple measurement vectors (MMV), atomic norm, DOA estimation. 1.
ACHIEVING HIGH RESOLUTION FOR SUPERRESOLUTION VIA REWEIGHTED ATOMIC NORMMINIMIZATION
"... The superresolution theory developed recently by Candès and FernandesGranda aims to recover fine details of a sparse frequency spectrum from coarse scale information only. The theory was then extended to the cases with compressive samples and/or multiple measurement vectors. However, the existing ..."
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The superresolution theory developed recently by Candès and FernandesGranda aims to recover fine details of a sparse frequency spectrum from coarse scale information only. The theory was then extended to the cases with compressive samples and/or multiple measurement vectors. However, the existing atomic norm (or total variation norm) techniques succeed only if the frequencies are sufficiently separated, prohibiting commonly known high resolution. In this paper, a reweighted atomicnorm minimization (RAM) approach is proposed which iteratively carries out atomic norm minimization (ANM) with a sound reweighting strategy that enhances sparsity and resolution. It is demonstrated analytically and via numerical simulations that the proposed method achieves high resolution with application to DOA estimation. 1.
SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization
"... Abstract—The mathematical theory of superresolution developed recently by Candès and FernandesGranda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set of regularly spaced timespace samples. This theory w ..."
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Abstract—The mathematical theory of superresolution developed recently by Candès and FernandesGranda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set of regularly spaced timespace samples. This theory was then extended to the cases with partial/compressive samples and/or multiple measurement vectors via atomic norm minimization (ANM), known as offgrid/continuous compressed sensing. However, a major problem of existing atomic norm methods is that the frequencies can be recovered only if they are sufficiently separated, prohibiting commonly known high resolution. In this paper, a novel nonconvex optimization method is proposed which guarantees exact recovery under no resolution limit and hence achieves high resolution. A locally convergent iterative algorithm is implemented to solve the nonconvex problem. The algorithm iteratively carries out ANM with a sound reweighting strategy which enhances sparsity and resolution, and is termed as reweighted atomicnorm minimization (RAM). Extensive numerical simulations are carried out to demonstrate the performance of the proposed method with application to direction of arrival (DOA) estimation. Index Terms—Continuous compressed sensing (CCS), DOA estimation, frequency estimation, gridless sparse method, high resolution, reweighted atomic norm minimization (RAM). I.