Adaptive sparse linear prediction: A promising tool for blind deconvolution

Linear prediction is a fundamental theme in signal processing, due to its theoretical relevance and the wide range of applications, which include autoregressive parameters estimation, predictive speech coding, line enhancement, frequency detection and others. Linear prediction can also be employed in blind deconvolution and equalization, which concern one of its earlier application in seismic signal processing. However, the classical predictive techniques fail in the case of blind deconvolution of non minimum-phase systems. In this sense, this work presents some new theoretical results on the application of linear prediction in blind deconvolution. Such results come from the proposal of the mean absolute error criterion (MAE) that exploits the sparse nature of the recovering signal. We discuss the scope and effectiveness of the method by means of a study on the location of the zeros of the obtained optimal filter. In addition, we show how the obtained solution can be accessed in the light of the nonlinear uncorrelation property. Finally, some simulation results are obtained for the sign-error LMS algorithm.