Two-dimensional wavelet variance estimation with application to sea ice SAR images

The surface of Arctic sea ice presents complex patterns of cracks and ridges that change with the seasons according to the external forces acting on the ice and the internal stresses within the ice. We propose a new statistical tool for analysis of these patterns based on a two-dimensional Maximal Overlap Discrete Wavelet Transform (MODWT) of Synthetic Aperture Radar (SAR) images, which can be used to track how ice conditions change over the course of the year. Here we give details on an extended pyramid algorithm that efficiently computes the MODWT coefficients for all combinations of vertical and horizontal scales. We show how to use these coefficients to form mean- and median-based wavelet variance estimates along with confidence intervals for the true unknown variances. We demonstrate the usefulness of the statistical tool on images acquired by the SAR sensor onboard RADARSAT, but the tool is of potential use in other geoscience applications and in other areas (e.g. medical imaging). We provide a Matlab implementation of this tool but also give sufficient details so that it can be encoded in other languages.