Two-dimensional nonparametric spectral analysis in the missing data case

We consider two-dimensional (2D) nonparametric complex spectral estimation (with its 1D counterpart as a special case) of data matrices with missing samples occurring in arbitrary patterns. Previously, the MAPES-EM algorithms were developed for the general 1D missing-data problem and shown to have excellent spectral estimation performance. In this paper, we present 2D extensions of MAPES-EM and develop another 2D MAPES algorithm, referred to as MAPES-CM, which solves a maximum likelihood problem iteratively via cyclic maximization (CM). Compared with MAPES-EM, MAPES-CM has similar spectral estimation performance but is computationally much more efficient.