On Nonparametric Estimation of 2-D Smooth Spectra

We consider the problem of smoothed nonparametric estimation of two-dimensional (2-D) spectra. In the one-dimensional (1-D) scenario, several methods have been developed in the past for the computation of nonparametric spectral estimates with lower variance than that of the standard periodogram. Some of these techniques can also be extended to the 2-D case. However, such methods usually require a careful selection of certain design parameters, which can be hard to make. The spectral estimator proposed here is based on cepstrum thresholding and is shown to have significantly lower variance than the standard 2-D periodogram. Moreover, the thresholding is performed in a simple and practically automatic manner without the requirement of extensive prior knowledge about the signal of interest.