Primal-dual method for robust spectral estimation of complex valued sequences

A primal-dual method for estimating the spectrum of a complex sequence is provided that minimizes the l_p norm of the complex spectrum for 1<p<2 via solution of the dual problem in complex space. This provides reduced spectral leakage, enhanced spectral resolution, and robustness to missing data samples when compared to the minimum l₂ norm spectral estimate. The optimization of the dual problem converges quickly in a small number of gradient search steps, providing solutions to large problems in very short time. Examples are provided that demonstrate the narrow, spiky nature of the spectrum, the reduced spectral leakage, and robustness to unevenly sampled data.