Sparse Signal Estimation by Maximally Sparse Convex Optimization


Selesnick I. W., Bayram I.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, cilt.62, sa.5, ss.1078-1092, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 62 Sayı: 5
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1109/tsp.2014.2298839
  • Dergi Adı: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1078-1092
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e. g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.