Amplitude spectrum estimation for two-dimensional gapped data

The amplitude and phase estimation (APES) approach to nonparametric spectrum estimation of uniformly sampled data has received considerable interest recently. In this paper, we consider the extension of APES to gapped data, i.e., uniformly sampled data with missing samples. It has recently been shown that the APES estimate of the spectrum is the minimizer of a certain least-squares (LS) criterion, and our extension of APES is based on minimizing this LS criterion with respect to the missing data as well. A computationally efficient method for doing this based on cyclic minimization and the conjugate gradient algorithm is proposed. The new algorithm is called gapped-data APES (GAPES) and is developed for the two-dimensional (2-D) case, with the one-dimensional (1-D) case as a special instance. Numerical examples are provided to demonstrate the performance of the algorithm and to show the advantages of 2-D data processing over 1-D (row or column-wise) data processing, as wen as to show the applicability of the algorithm to synthetic aperture radar (SAR) imaging.