Knowledge based blind deconvolution of non-minimum phase FIR systems

We introduce a new concept coined "knowledge based blind deconvolution" as the problem of estimating the input of an unknown non-minimum phase FIR system using only noisy observed output and an initial model of the original input. Here, unlike conventional blind deconvolution where some assumptions on the statistical properties of the white source signal are needed to be made, an initial estimation of the original input, to be identified based on some prior knowledge, is whitened and used instead of the usual I.I.D input. We first justify the basis of our proposed algorithm, using an iterative blind deconvolution method based on Shalvi-Weinstein criterion, in which the deconvolution filter is updated using the previous estimation of the input signal iteratively. Then, the algorithm is further developed by using an initial model, as the first estimation of the input signal, as there are applications such as glottal flow estimation where such a model exists. Furthermore, constrained optimization is used to estimate the deconvolution filter to satisfy more than just one criterion. This optimization contains an objective function that is Shalvi-Weinstein criterion (normalized kurtosis maximization) and, a nonlinear equality in which the mean square error (MSE) between the estimated input and the initial model is kept lower than a limit. The proposed algorithm is applied to simulated cases to assess its performance.