Blind single channel deconvolution using nonstationary signal processing

Blind deconvolution is fundamental in signal processing applications and, in particular, the single channel case remains a challenging and formidable problem. This paper considers single channel blind deconvolution in the case where the degraded observed signal may be modeled as the convolution of a nonstationary source signal with a stationary distortion operator. The important feature that the source is nonstationary while the channel is stationary facilitates the unambiguous identification of either the source or channel, and deconvolution is possible, whereas if the source and channel are both stationary, identification is ambiguous. The parameters for the channel are estimated by modeling the source as a time-varyng AR process and the distortion by an all-pole filter, and using the Bayesian framework for parameter estimation. This estimate can then be used to deconvolve the observed signal. In contrast to the classical histogram approach for estimating the channel poles, where the technique merely relies on the fact that the channel is actually stationary rather than modeling it as so, the proposed Bayesian method does take account for the channel's stationarity in the model and, consequently, is more robust. The properties of this model are investigated, and the advantage of utilizing the nonstationarity of a system rather than considering it as a curse is discussed.