NDLI: Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization

Content Provider	IEEE Xplore Digital Library
Author	Zai Yang Lihua Xie
Copyright Year	1991
Abstract	The mathematical theory of super-resolution developed recently by Candès and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set of uniform time-space samples. This theory was then extended to the cases of partial/compressive samples and/or multiple measurement vectors via atomic norm minimization (ANM), known as off-grid/continuous compressed sensing (CCS). 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) sparse metric is proposed that promotes sparsity to a greater extent than the atomic norm. Using this metric an optimization problem is formulated and a locally convergent iterative algorithm is implemented. The algorithm iteratively carries out ANM with a sound reweighting strategy which enhances sparsity and resolution, and is termed as reweighted atomic-norm minimization (RAM). Extensive numerical simulations are carried out to demonstrate the advantageous performance of RAM with application to direction of arrival (DOA) estimation.
Sponsorship	IEEE Signal Processing Society
Starting Page	995
Ending Page	1006
Page Count	12
File Size	3327538
File Format	PDF
ISSN	1053587X
Volume Number	64
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2016-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Frequency estimation Optimization Minimization Continuous compressed sensing Signal resolution Random access memory reweighted atomic norm minimization (RAM) Continuous compressed sensing (CCS) DOA estimation frequency estimation gridless sparse method high resolution
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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