Blind Deconvolution via Maximum Kurtosis Adaptive Filtering

Abstract: In this paper, we present an algorithm for identifying a parametrically described destructive unknown system based on a non-gaussianity measure. It is known that under certain conditions the output of a linear system is more gaussian than the input. Hence, an inverse filter is searched, such that its output is minimally gaussian. We use the kurtosis as a measure of the non-gaussianity of the signal. A maximum of the kurtosis as a function of the deconvolving filter coefficients is searched. The search is done iteratively using the gradient ascent algorithm, and the coefficients at the maximum point correspond to the inverse filter coefficients. This filter may be applied to the distorted signal to obtain the original undistorted signal. While a similar approach has been used before, it was always directed at a particular kind of a signal, commonly of impulsive characteristics. In this paper a successful attempt has been made to apply the algorithm to a wider range of signals, such as to process distorted audio signals and destructed images. This innovative implementation required the revelation of a way to preprocess the distorted signal at hand. The experimental results show very good performance in terms of recovering audio signals and blurred images, both for an FIR and IIR distorting filters.