Blind deconvolution and source separation in acoustics

Abstract

Blind deconvolution (BDC) and blind source separation (BSS) are active research topics with many important applications in acoustics. The goal of deconvolution is to recover original input signal from the output of a convolution filter. In blind deconvolution details of the convolution filter and input signals are not known. The fundamental assumption in BDC is that the input signal is a non-Gaussian stochastic process. A topic closely related to BDC is BSS. BSS is a process that is an inverse operation to a mixing process. In BSS it is assumed that inputs to the mixing systems are statistically independent stochastic processes, where only one input may be Gaussian, others must be non-Gaussian. Standard criterion functions for BDC and BSS are reviewed. Limitations of the second-order statistics and need for higher-order statistics (HOS) or information theoretic criteria that lead to nonlinear optimization algorithms are pointed out. Advantages of various information theoretic criteria for BDC and BSS are discussed. Because gradients of these criteria are nonlinear, resulting optimization algorithms are nonlinear. Linear and non-linear algorithms for BDC and BSS are examined. [Work supported by ONR Codes 321US and 333.]