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Fast methods for recovering sparse parameters in linear low rank models

Esmaeili, A ; Sharif University of Technology | 2017

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  1. Type of Document: Article
  2. DOI: 10.1109/GlobalSIP.2016.7906072
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2017
  4. Abstract:
  5. In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion to the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To this end, we employ a technique to initially approximate the support of the sparse vector. We further propose to unify the partial matrix completion and sparse vector recovery into an augmented four-step problem. Simulation results reveal that the augmented approach achieves the best performance, while both proposed methods outperform the natural two-step technique with substantially less computational requirements. © 2016 IEEE
  6. Keywords:
  7. IMAT ; Lasso ; Matrix completion ; Missing data ; Sparse ; Big data ; Recovery ; Vectors ; Matrix algebra
  8. Source: 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016, 7 December 2016 through 9 December 2016 ; 2017 , Pages 1403-1407 ; 9781509045457 (ISBN)
  9. URL: https://ieeexplore.ieee.org/document/7906072