Two-dimensional nonparametric spectral analysis in missing data case

We consider two-dimensional (2-D) nonparametric complex spectral estimation (with its 1-D counterpart as a special case) of data matrices with missing samples occurring in arbitrary patterns. Previously, the missing amplitude and phase estimation-expectation maximization (MAPES-EM) algorithms were developed for the general 1-D missing-data problem and shown to have excellent spectral estimation performance. In this correspondence, we present 2-D extensions of MAPES-EM and develop another 2-D 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, which is especially important for long data sequences and 2-D applications such as synthetic aperture radar (SAR) imaging.