Wavelet-based bootstrapping of spatial patterns on a finite lattice

A semi-parametric bootstrap procedure is proposed for two-dimensional spatial processes on a finite lattice (images). Discrete wavelet transforms are used to produce coefficients that are approximately uncorrelated in space. For illustration, realizations of spatial processes from the Matérn class of spectral density functions are analyzed. The goal is to obtain bootstrap realizations by applying the näıve bootstrap to the approximately uncorrelated wavelet coefficients. The methodology is shown to be effective at reproducing moderate levels of spatial covariance on several simulated data sets as well as images taken from a functional MRI experiment. An application to testing functional connectivity in fMRI is also presented.