Criteria for blind deconvolution of multichannel linear time-invariant systems

Blind deconvolution and equalization of linear time-invariant systems have widely received attention in various fields such as data communication, image processing and geophysical data processing. Shalvi and Weinstein (1990) proposed certain criteria for blind deconvolution of nonminimum-phase linear time-invariant systems. Their work is, however, restricted to the single-channel (or scalar) case. This correspondence extends the Shalvi-Weinstein approach to the multichannel case. We propose a multistage maximization criterion and a single-stage maximization criterion for attaining multichannel blind deconvolution. Under the normalized condition specified later, they are shown to be equivalent.