Robust Spectrum Estimation via Majorization Minimization

In this paper, the robust spectrum estimation problem is revisited through a majorization minimization (MM) based RELAX (MM-RELAX) algorithm. Specifically, MM-RELAX employs the $\ell_{p}$ -fitting criterion to deal with impulsive noise. It alternately optimizes $K$ harmonics by subtracting (K - 1) of them and then updating the remaining one, such that the whole problem is split into $K$ single-tone harmonic retrieval problems which are solved by the MM method. A Newton's method that takes linear time complexity $\mathcal{O}(N)$ is applied for updating the frequency estimates. Numerical results are included to showcase the effectiveness of the MM-RELAX method.