Multichannel blind deconvolution via maximum likelihood estimator: application in neural recordings

Abstract

In many multidimensional data such as radar recordings and astrophotography images, the receiver sensors record a linear mixture of signals propagated by a few activities, and the signal of each activity is repetition of a specific waveform at different times and with different amplitudes. The goal of multichannel blind deconvolution problem is retrieving the characteristics of the mentioned activities from the recorded signals. This problem is ill-posed without additional constraints, hence, different constraints are considered for this problem depending on the considered application. In this study, we propose a maximum likelihood framework for solving multichannel blind deconvolution problem when (1) the waveforms of the activities are time-limited signals, (2) the waveforms occur only a few times in the signal of each activity, or in other words, the occurrence times of the activities are sparse signals, and (3) there is no overlap between two consecutive occurrences of the waveform in the signal of each activity. The considered scenario can be adapted to several applications especially to neural recordings. We verify the efficiency of the proposed framework using simulations. Moreover, we apply the proposed framework on a real neural data set, and show how the obtained results can be employed to analyze the data from signal processing point of view.