Denoising approach to multichannel signal estimation

Multichannel sensor array processing has received considerable attention in many important areas of signal processing. Almost all data recorded by multisensor instruments contain various amounts of noise, and much work has been done in developing optimal processing structures for estimating the signal source from the noisy multichannel observations. The techniques developed so far assume the signal and noise processes are at least wide-sense-stationary so that optimal linear estimation can be achieved with a set of linear, time-invariant filters. Unfortunately, nonstationary signals arise in many important applications and there is no efficient structure with which to optimally deal with them. While wavelets have proven to be useful tools in dealing with certain nonstationary signals, the way in which wavelets are to be used in the multichannel setting is still an open question. Based on the structure for optimal linear estimation of nonstationary multichannel data and statistical models of spatial signal coherence, we propose a method to obtain an efficient multichannel estimator based on the wavelet transform.