Estimation of spatial backscatter power spectra from sonar images

Abstract

Two- and three-dimensional power spectral estimation from sonar backscatter images is an important area of research that has ramifications for understanding the underlying structure of many environmental features. In one case, that of backscatter from groups of animals, the interanimal correlation distances are the inverse Fourier transform of the three-dimensional power spectrum. Estimation of three-dimensional power spectra from sonar data is made difficult because of the spreading of the sonar beams as a function of range which results in a lower resolution image. In multidimensional signal processing parlance, the resulting collected sonar data have been convolved with a spatially variant kernel. Standard signal processing methods have difficulty when applied to these kinds of functions, as the usual assumption is that the data have been obtained from a spatially invariant kernel. A method is proposed to estimate the power spectrum of such images by first starting with an ensemble. It is shown how the spatially variant problem can then be converted into a spatially invariant problem. Straightforward methods for power spectral estimation are then used to determine the spectrum. Examples of the use of the methodology on three-dimensional sonar data will be used to illustrate the method.