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

Abstract

An original algorithm for the detection of small objects in a noisy background is proposed. Its application to underwater objects detection by sonar imaging is addressed. This new method is based on the use of higher-order statistics (HOS) that are locally estimated on the images. The proposed algorithm is divided into two steps. In a first step, HOS (skewness and kurtosis) are estimated locally using a square sliding computation window. Small deterministic objects have different statistical properties from the background they are thus highlighted. The influence of the signal-to-noise ratio (SNR) on the results is studied in the case of Gaussian noise. Mathematical expressions of the estimators and of the expected performances are derived and are experimentally confirmed. In a second step, the results are focused by a matched filter using a theoretical model. This enables the precise localization of the regions of interest. The proposed method generalizes to other statistical distributions and we derive the theoretical expressions of the HOS estimators in the case of a Weibull distribution (both when only noise is present or when a small deterministic object is present within the filtering window). This enables the application of the proposed technique to the processing of synthetic aperture sonar data containing underwater mines whose echoes have to be detected and located. Results on real data sets are presented and quantitatively evaluated using receiver operating characteristic (ROC) curves.

The small target detection based on maximum likelihood estimation and spot detection operator

“…The computation amount will be very large, even unrealistic. So we need to set proper original position and velocity filter to search the small target [7,[12][13][14] . The meanings of the other parameters are as follow:…”

BioSonar: a Bio-Mimetic Approach to Sonar Systems Concepts and Applications

“…Extended research has been done on the subject. Calder et al (1997); Goldman & Cohen (2004); Maussang et al (2007) aim to detect global rarity in the sonar image using the assumption that a mine is a rare event. In Calder et al (1998) Despite the high performances of the new generation of imagery sonars (including SAS systems), ATR using imagery is still at this stage unreliable due to a high false alarm rate and poor performances in heavily cluttered area (Petillot et al (2010)).…”

3D boundary extraction of confocal cellular images using higher order statistics

“…However, very limited information exists about the use of HOS in image processing. To our knowledge, HOS is used for blind source separation, denoising, object/feature detection (Carrato & Ramponi, 1993; Ramponi & Carrato, 1994; Zhao et al , 2002; Rapantzikos et al , 2003; Maussang et al , 2007). The work on Skewness‐of‐Gaussian edge extractor (Carrato & Ramponi, 1993) motivates our present research.…”