Two-dimensional robust spectrum estimation

Robust estimation is studied of two-dimensional (2-D) power spectra of signals which are adequately represented by Gaussian random field models but for which there are imperfect observations. Two situations of particular interest occur when the contaminating noise is additive and when the contaminating noise appears in the innovations. In these cases, the observed data are not Gaussian and conventional procedures are no longer efficient. To estimate the parameters of the signal model from the contaminated data, two procedures are described which were originally proposed for estimation of scale and location from independent data and adapted to one-dimensional autoregression parameter estimation by previous researchers. The first algorithm is a robustification of least squares and equivalent to an iterated weighted least-squares problem where the weights are data-dependent. The second algorithm is an iterative procedure known as a filter cleaner. Experiments using the robust procedures with synthetic data are reported and the results compared to a conventional method of model-based spectrum estimation