Comparison of model selection techniques for seafloor scattering statistics

Abstract

Acoustic measurements of seafloor backscattering are a source of unwanted sound in seafloor object detection1–3, but also provide a rich set of information regarding the seafloor properties and structure4–7. The intensity in a sonar image (i.e. a spatial map of measured backscattering) is typically characterized by a random process7. There are a variety of metrics, or features, that can be used to describe this random process, including the autocorrelation function, power spectrum8, wavelet decomposition9, gray-level co-occurance matrix6,10, the mean intensity (scattering cross section)11,12 and in general, the intensity probability density function13–15. It was found that for complex scattering environments (such as rocky seafloors, and man-made structures), a mixture pdf was most appropriate14,16, which was justified by the non-stationary character of the acoustic data. Each sample of the data was modeled as being drawn from a finite number of distributions, e.g. either from the seafloor or man-made structure, or from horizontal or vertical facets. In general, the number of components that make up a non-stationary sonar image is unknown, and must be selected prior to choosing a model and estimating the parameters. The more model parameters are used (i.e. more components, or a more complex statistical model for each component), the better the data will be fit, but the parameters may lose meaning. In this work, we explore the use of several model selection techniques based on Bayesian statistics, primarily the Bayesian information criterion (BIC) and Akaike information criterion (AIC). These techniques penalize more complex models in different ways. We also use the log-likelihood (LL) to characterize the model-data fit. This paper is organized as follows. A description of the sonar data used in this work and example images are given in Section 2. The background statistical modeling and model selection techniques are given in Section 3. Results are presented and discussed in Section 4. Conclusions are given in Section 5.