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.
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