Loading...

Upper bounds on the error of sparse vector and low-rank matrix recovery

Malek Mohammadi, M ; Sharif University of Technology | 2016

838 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.sigpro.2015.09.003
  3. Publisher: Elsevier , 2016
  4. Abstract:
  5. Suppose that a solution x to an underdetermined linear system b=Ax is given. x is approximately sparse meaning that it has a few large components compared to other small entries. However, the total number of nonzero components of x is large enough to violate any condition for the uniqueness of the sparsest solution. On the other hand, if only the dominant components are considered, then it will satisfy the uniqueness conditions. One intuitively expects that x should not be far from the true sparse solution x0. It was already shown that this intuition is the case by providing upper bounds on ||x-x0|| which are functions of the magnitudes of small components of x but independent from x0. In this paper, we tighten one of the available bounds on ||x-x0|| and extend this result to the case that b is perturbed by noise. Additionally, we generalize the upper bounds to the low-rank matrix recovery problem. © 2015 Elsevier B.V. Allrightsreserved
  6. Keywords:
  7. Approximately sparse solutions ; Low-rank matrix recovery ; Restricted isometry property ; Sparse vector recovery ; Linear systems ; Recovery ; Large components ; Low-rank matrix recoveries ; Restricted isometry properties ; Small components ; Sparse solutions ; Sparse vectors ; Underdetermined linear systems ; Upper Bound ; Matrix algebra
  8. Source: Signal Processing ; Volume 120 , 2016 , Pages 249-254 ; 01651684 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0165168415002972