Prior knowledge aided super-resolution line spectral estimation: an iterative reweighted algorithm

Abstract

This paper concerns detecting the frequency components from a spectral sparse, undersampled signal. This problem is also called super-resolution line spectral estimation because the frequencies can take arbitrary continuous values. The prior knowledge of the frequency distribution is often available in many applications. To exploit the prior knowledge, a weighting function w(f) designed according to the frequency distribution p(f) is introduced. The prior information can be harnessed through minimizing the corresponding weighted log-sum penalty function. We solve the optimization problem through iteratively decreasing a surrogate function majorizing the original penalty function. Simulation results show that the proposed algorithm outperforms other methods both in noiseless and noisy case, and it also presents superior performance in resolving closely-spaced frequency components.