Robust Harmonic Retrieval via Block Successive Upper-Bound Minimization
Cheng Qian, Yunmei Shi, Lei Huang, Hing Cheung So · IEEE Transactions on Signal Processing · 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 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 point. Furthermore, the BSUM-RELAX is extended to the multidimensional HR case. Numerical results show that the proposed algorithm outperforms the state-of-the-art methods in heavy-tailed noise scenarios.