NDLI: Compressed Sensing with uncertainty - the Bayesian estimation perspective

Content Provider	IEEE Xplore Digital Library
Author	Bernhardt, S. Boyer, R. Marcos, S. Larzabal, P.
Copyright Year	2015
Description	Author affiliation: L2S, Univ. Paris-Sud, Gif-sur-Yvette, France (Bernhardt, S.; Boyer, R.; Marcos, S.) \|\| SATIE, ENS Cachan, Cachan, France (Larzabal, P.)
Abstract	The Compressed Sensing (CS) framework outperforms the sampling rate limits given by Shannon's theory. This gap is possible since it is assumed that the signal of interest admits a linear decomposition of few vectors in a given sparsifying Basis (Fourier, Wavelet, ...). Unfortunately in realistic operating systems, uncertain knowledge of the CS model is inevitable and must be evaluated. Typically, this uncertainty drastically degrades the estimation performance of sparse-based estimators in the low noise variance regime. In this work, the Off-Grid (OG) and Basis Mismatch (BM) problems are compared in a Bayesian estimation perspective. At first glance, we are tempted to think that these two acronyms stand for the same problem. However, by comparing their Bayesian Cramèr-Rao Bounds (BCRB) for the estimation of a L-sparse amplitude vector based on N measurements, it is shown that the BM problem has a lower BCRB than the OG one in a general context. To go further into the analysis we provide for i.i.d. Gaussian amplitudes and in the low noise variance regime an interesting closed-form expression of a normalized 2-norm criterion of the difference of the two BCRB matrices. Based on the analysis of this closed-form expression, we obtain two conclusions. Firstly, the two uncertainty problems cannot be confused for a non-zero mismatch error variance and with finite N and L. Secondly, the two problems turn to be similar for any mismatch error variance in the large system regime, i.e., for N, L → ∞ with constant aspect ratio N/L → ρ.
Starting Page	421
Ending Page	424
File Size	362712
Page Count	4
File Format	PDF
e-ISBN	9781479919635
DOI	10.1109/CAMSAP.2015.7383826
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-12-13
Publisher Place	Mexico
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Context Reactive power Dictionaries Uncertainty Bayesian estimation Estimation Compressed Sensing with Uncertainty Off-Grid effect and Basis Mismatch Bayes methods 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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