Robust Harmonic Retrieval via Block Successive Upper-Bound Minimization

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Pages (from-to)6310-6324
Journal / PublicationIEEE Transactions on Signal Processing
Issue number23
Online published11 Oct 2018
Publication statusPublished - 1 Dec 2018


Harmonic retrieval (HR) is a problem of significance with numerous applications. Many existing algorithms are explicitly or implicitly developed under Gaussian noise assumption, which, however, are not robust against non-Gaussian noise such as impulsive noise or outliers. In this paper, by employing the ℓ ℓ lp- fitting criterion and block successive upper-bound minimization (BSUM) technique, a variant of the classical RELAX algorithm named as BSUM-RELAX is devised for robust HR. It is revealed that the BSUM-RELAX successively performs alternating optimization along coordinate directions, i.e., it updates one harmonic by fixing the other (K - 1) components, such that the whole problem is split into K single-tone HR problems which are then solved by creating a surrogate function that majorizes the objective function of each subproblem. To further refine the frequency component, the Newton's method that takes linear complexity O(N) is derived for updating the frequency estimates. We prove that under the single-tone case, BSUM-RELAX converges to a Karush Kuhn Tucker (KKT) point. Furthermore, the BSUMRELAX is extended to the multidimensional HR case. Numerical results show that the proposed algorithm outperforms the stateof- the-art methods in heavy-tailed noise scenarios.

Research Area(s)

  • Harmonic retrieval, impulsive noise/outliers, majorization minimization, RELAX, robust estimation