The problem of spectral estimation, namely ? recovering the frequency contents of a signal ? arises in various fields of science and engineering, including speech recognition, array imaging and remote sensing. In this talk, I will introduce the MUltiple SIgnal Classification (MUSIC)  algorithm for line spectral estimation and provide a stability analysis of the MUSIC algorithm. Numerical  comparison of MUSIC with other algorithms, such as greedy algorithms and L1 minimization, shows that MUSIC combines the advantages of strong stability and low computational complexity for the detection of well-separated frequencies on a continuum. Moreover, MUSIC truly shines 

when the separation of frequencies drops to one Rayleigh length and below while all other methods fail. This is a joint work with Albert Fannjiang at UC Davis.