On the error in phase transition computations for compressed sensing

Daei, S ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1109/TIT.2019.2920640
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2019
  4. Abstract:
  5. 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. To ensure that this technique is suitable, [1] 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 [1] in some low-dimensional models such as total variation and ell _{1} analysis minimization becomes poorly large. Next, we develop a new error bound which significantly improves the estimation gap compared to [1]. In particular, unlike the bound in [1] that fails in some settings with overcomplete dictionaries, our bound exhibits a decaying behavior in such cases. © 1963-2012 IEEE
  6. Keywords:
  7. Error estimate ; Low-complexity models ; Statistical dimension ; Compressed sensing ; Asymptotic phase ; Error bound ; Error estimates ; Low-dimensional models ; Over-complete dictionaries ; Statistical dimension ; Total variation ; Upper Bound ; Errors
  8. Source: IEEE Transactions on Information Theory ; Volume 65, Issue 10 , 2019 , Pages 6620-6632 ; 00189448 (ISSN)
  9. URL: https://ieeexplore.ieee.org/abstract/document/8730348