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On the error in phase transition computations for compressed sensing

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Daei, Sajad, Haddadi, Farzan, Amini, Arash and Lotz, Martin (2019) On the error in phase transition computations for compressed sensing. IEEE Transactions on Information Theory, 65 (10). pp. 6620-6632. doi:10.1109/TIT.2019.2920640 ISSN 0018-9448.

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Official URL: https://doi.org/10.1109/TIT.2019.2920640

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Abstract

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and it has become standard to replace it with an upper-bound. Toensure that this technique is suitable, has introduced an upper-bound on the gap between the statistical dimension and its approximation. In this work, we first show that the error bound in in some low-dimensional models such as total variation and 1 analysis minimization becomes poorly large. Next, we develop a new error bound which significantly improves the estimation gap compared to. In particular, unlike the bound in [1] that fails in some settings with overcomplete dictionaries, our bound exhibits a decaying behavior in such cases

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Inverse problems (Differential equations), Gaussian measures
Journal or Publication Title: IEEE Transactions on Information Theory
Publisher: IEEE
ISSN: 0018-9448
Official Date: October 2019
Dates:
DateEvent
October 2019Published
4 June 2019Available
25 May 2019Accepted
Volume: 65
Number: 10
Page Range: pp. 6620-6632
DOI: 10.1109/TIT.2019.2920640
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 6 June 2019
Date of first compliant Open Access: 6 June 2019

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