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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
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Official URL: https://doi.org/10.1109/TIT.2019.2920640
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 | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of 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: |
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| Volume: | 65 | ||||||||
| Number: | 10 | ||||||||
| Page Range: | pp. 6620-6632 | ||||||||
| DOI: | 10.1109/TIT.2019.2920640 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Publisher Statement: | © 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 |
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