Noncanonical Spectral Model of Multidimensional Uniform Random Fields

Abstract

The estimates for the power spectrum of multidimensional uniform random fields in the form of models of finite mixtures of standard spectra are proposed. The learning algorithm of the models demonstrates improved convergence properties for degenerate spectra and small interclass distances in the frequency space, as well as for small volumes of the experimental data. Based on this, the noncanonical models of uniform random fields are presented as a sum of statistically independent spatial harmonics with random amplitudes and frequencies. The alternative representation of a multidimensional spectrum as a sample of random frequencies allowed us to propose computationally efficient algorithms of digital synthesis of background and underlying surface images with the topology of spectral estimates that are adequate for the experimental data. The algorithms are free from simplifying assumptions regarding the method of discretization of the field and functional form of the power spectral density.