Evaluation and verification of bottom acoustic reverberation statistics predicted by the point scattering model

Abstract

The point scattering model offers a parameterization of the reverberation probability density function (pdf) in terms of the coefficient of excess (kurtosis) and a coherent component represented by a harmonic process with random phase. In this paper the potential utility of this parametrization is investigated in the context of seafloor characterization. The problem of separating out the effect of each parameter is discussed. Computer simulations are used to verify model predictions on the reverberation quadrature, envelope, and phase pdf. As part of the verification study, the scatterer density was determined from the kurtosis of the reverberation quadrature pdf. A statistical analysis of this procedure points to reduced estimate accuracy with decreasing kurtosis. Additional computer simulations show that the chosen pdf family, developed under the assumption of a Poisson scatterer distribution, is flexible enough to fit reverberation data generated by non-Poisson scatterer distributions exhibiting a degree of clustering or regularity. A computer experiment demonstrates how this parametrization can be used in conjunction with a simple sonar geometry to generate acoustic signatures for seafloor classification. In addition, real reverberation data collected by a Sea Beam sonar system in two different seafloor areas are interpreted according to the chosen parametrization. PACS numbers: 43.30.Hw, 43.30.Gv, 43.20.Fn INTRODUCTION Acoustic reverberation is usually modeled as a Gaussian stochastic process. Equivalently, its envelope and phase are assumed to have a Rayleigh and uniform probability density function (pdf), respectively. However, real reverberation data often exhibit deviations from this nominal model. •'2 More general and flexible pdf families are then needed to describe the statistical behavior of reverberation. 3 If rever- beration is viewed as interference, incorporating its non-Gaussian nature into the design of a detection/estimation processor will lead closer to optimum performance. If reverberation is viewed as an information-bearing signal, deviations from normal statistics convey useful information about the scatterer distributions in the medium and ultimatelyabout the nature of the medium.In this paper, we adopt the latter viewpoint and concentrate on the problem of seafloor characterization. We focus our attention on a reverberation pdf family supported by the point-scattering model. 4-•ø This pdf family is parametrized by (1) the coefficient of excess, that is associated with the average number of scatterers contributing to the return and (2) a "coherent component" coefficient. Under certain conditions it is possible to relate these parameters to seafloor characteristics such as rms roughness and correlation area. TM However, the point-scattering theory has been developed for random (Poisson) scatterer distributions. Therefore, direct analytical connections to seafloor parameters cannot be obtained when non-Poisson distributions are present. In general, scatterers in the ocean exhibit clustering...

Higher-Order Statistics for the Detection of Small Objects in a Noisy Background Application on Sonar Imaging

“…That explains the shape of the square structures observed in the result images and the decreasing values along the edges and inside the square. From (18) and (19), for low values of p, skewness can be approximated by 1/ √ p and kurtosis by 1/ p. This explains that for a 21 × 21 window, the highest values in the skewness image is close to 21 (corresponding to p = 1/(21 × 21)) and 441 for the kurtosis. As a consequence, the higher is the size of the computation window, the higher is the value of the maximum on the skewness and the kurtosis image.…”

“…(i) In a noisy background, the HOS have small values. This corresponds to the nullity of the HOS for the Gaussian distribution (note that in this specific case, the approximations proposed in (18) and (19) do not hold anymore).…”

“…This method uses the crossing of a skewness operator by zero (corresponding to a symmetric distribution) to detect edges in images with good performances and robustness [17]. The most interesting paper regarding our application is proposed by Alexandrou et al [18]: a coefficient of excess, the kurtosis (4thorder statistical value), is studied in order to model the non-Gaussian reverberation hypothesis. But, as raised by the authors, it is difficult to differentiate this excess, induced by an inaccurate modeling of the background with a Gaussian law, from a potential coherent component embedded in the reverberation.…”

Evaluation of the method based on PSR techniques for target detection in reverberation

“…In the shallow-water environment, the detection of targets on the sea floor is often limited by the bottom reverberation [17]. According to the point-scattering theory [18][19][20], the reverberation arises from a multitude of scatterers distributed independently on the sea floor. On the assumptions of a very large number of reflectors, the reverberation process has a Gaussian probability density function (PDF) and thus Rayleigh envelope.…”

“…On the assumptions of a very large number of reflectors, the reverberation process has a Gaussian probability density function (PDF) and thus Rayleigh envelope. However, non-Rayleigh reverberation can occur when the conditions of the central limit theory (CLT) are violated [18,[20][21][22]. For example, there may be too few scatterers in the resolution cell of the high-resolution active sonar systems, or the scatterers may not be identically distributed.…”