Reconstruction of aerial images from uniformly sampled magnitude Fourier spectra using spectral statistical models

Statistical Kriging models for spatial data yield optimal linear estimates of unknown samples. In this work, we present a collection of statistical models defined over regions from a dyadic partition of the discrete Fourier spectrum. Spectral covariance models of the 2D Fast Fourier Transform (FFT) of aerial images allow for Kriging interpolation of magnitude and phase spectra from a small number of spectral samples. The reconstructed spectral components are compared to other widely used 2D interpolation algorithms (cubic splines, nearest neighbor, and bilinear interpolators). We approach this problem by exploring the magnitude and phase spectra independently.