NDLI: Compressed sensing of approximately sparse signals

Content Provider	IEEE Xplore Digital Library
Author	Stojnic, M. Weiyu Xu Hassibi, B.
Copyright Year	2008
Description	Author affiliation: Sch. of Ind. Eng., Purdue Univ., West Lafayette, IN (Stojnic, M.)
Abstract	It is well known that compressed sensing problems reduce to solving large under-determined systems of equations. If we choose the compressed measurement matrix according to some appropriate distribution and the signal is sparse enough the $l_{1}$ optimization can exactly recover the ideally sparse signal with overwhelming probability by Candes, E. and Tao, T., [2], [1]. In the current paper, we will consider the case of the so-called approximately sparse signals. These signals are a generalized version of the ideally sparse signals. Letting the zero valued components of the ideally sparse signals to take the values of certain small magnitude one can construct the approximately sparse signals. Using a different but simple proof technique we show that the claims similar to those of [2] and [1] related to the proportionality of the number of large components of the signals to the number of measurements, hold for approximately sparse signals as well. Furthermore, using the same technique we compute the explicit values of what this proportionality can be if the compressed measurement matrix A has a rotationally invariant distribution of the null-space. We also give the quantitative tradeoff between the signal sparsity and the recovery robustness of the $l_{1}$ minimization. As it will turn out in an asymptotic case of the number of measurements the threshold result of [1] corresponds to a special case of our result.
Starting Page	2182
Ending Page	2186
File Size	242484
Page Count	5
File Format	PDF
ISBN	9781424422562
DOI	10.1109/ISIT.2008.4595377
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-07-06
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sensors Sparse matrices Sufficient conditions Electronic mail USA Councils Rotation measurement Probabilistic logic l1-optimization compressed sensing
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
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
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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