Loading...

Sample complexity of total variation minimization

Daei, S ; Sharif University of Technology | 2018

747 Viewed
  1. Type of Document: Article
  2. DOI: 10.1109/LSP.2018.2847051
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2018
  4. Abstract:
  5. This letter considers the use of total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exists a sharp phase transition behavior in TV minimization for the number of measurements necessary to recover the signal in asymptotic regimes. The phase-transition curve specifies the boundary of success and failure of TV minimization for large number of measurements. It is a challenging task to obtain a theoretical bound that reflects this curve. In this letter, we present a novel upper bound that suitably approximates this curve and is asymptotically sharp. Numerical results show that our bound is closer to the empirical TV phase-transition curve than the previously known bound obtained by Kabanava. © 1994-2012 IEEE
  6. Keywords:
  7. Phase transition ; Total variation (TV) minimization ; Curves (road) ; Functions ; Geometry ; Optimization ; Phase measurement ; Phase transitions ; Standards ; Television ; Complexity theory ; Convex functions ; Linear measurements ; Phase transition curves ; Sample complexity ; Theoretical bounds ; Total variation minimization ; Transition behavior ; Image denoising
  8. Source: IEEE Signal Processing Letters ; Volume 25, Issue 8 , 2018 , Pages 1151-1155 ; 10709908 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/8383952