Application of higher order spectra to multi-scale deconvolution of sensor array signals

We present a solution to the multi-scale deconvolution problem using higher order spectra where the data to be deconvolved consist of noise corrupted sensor array measurements. The model assumes that the data are generated as a convolution of an unknown wavelet with linearly time-scaled versions of an unknown signal (reflectivity sequence). This type of data occurs in many signal processing applications, including radar, sonar and seismic processing. Our approach relies on exploiting the redundancy in the measurements due to time-scaling, and does not require knowledge of the wavelet or the signal. We formulate and solve the deconvolution problem as a quadratic minimization subject to a quadratic constraint in the sum-of-cumulants domain. The formulation using higher-order spectra reduces the effect of additive Gaussian noise on the accuracy of the results when compared to the standard time-domain formulation.