Acoustical signals in applications of acoustical oceanography, such as ocean acoustic tomography and sea-bed classification using acoustic signals emitted from known sources, are optimally exploited if they are noise free. The effect of blur in acoustic signals has not been well studied, although the blurring mechanism might introduce severe problems in the use of the acoustic signals for specific applications, especially, those using the full signal as the carrier of the relevant information. Deblurring of the signals in addition to denoising is therefore essential for the effective use of the signals. In our work, we apply a Statistical Optimal Filtering method that uses the Singular Value Decomposition of a first estimate of the blurring matrix and statistics to deblur the signal in an efficient and effective way and to quantify uncertainty for the recovered signal. In this talk, we will present the method and discuss its effectiveness using as test case, an application of sea-bed classification based on a statistical characterization of an acoustic signal. The statistical characterization is particularly sensitive to noise and blur contamination of the exploitable signal and any attempt for getting a signal clear from noise and blur is absolutely necessary, for obtaining reliable results.

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