Deconvolution of sensor array signals using scale transform properties

In this paper, we present the extension of solutions to the multiscale deconvolution problem which appears in sensor array applications. The sensor outputs are assumed to be generated as a convolution of the unknown source signal, the so-called wavelet, with various time-scaled versions of an unknown impulse response of the medium, namely reflectivity sequences. Methods to deconvolve these signals are available if the scaling effects, referred to as time-scale factors, are truly known. Here we show that time-scale factors between the system impulse responses can be obtained from the sensor array measurements by using the Scale Transform properties which yield `absolutely blind' multiscale deconvolution scheme.