Multifractal analysis of synthetic aperture radar images using wavelets
Monty Lasserre, Dan Roach, Norman R. Eldridge · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
This paper interprets 1D intensities in images of Synthetic Aperture Radar (SAR) as interwoven sets of mathematically defined singularities, and the spectrum of singularity strengths has been calculated using wavelets. Superposition of spectra from a transect of SAR data from the European Earth Resources Satellite (ERS-1) with the spectra from a SAR simulation based only on local terrain elevation variation shows that there exists a range of singularity strengths in ERS-1 data which are closely described by a topographic model. Modeling the SAR spectra using singularity spectra from Cantor sets and multiplicative cascades only partially helps in defining the SAR signal as a multifractal. The paper proposes that identifying and isolating the singularities in a SAR image for the purposes of classifying images can be assisted by using results from a singularity spectrum. The object of this classification is the resolution of images into regions with stable pixels representing purely a response to topographic relief and distinguishable from responses from land use and terrestrial cover types.