Multi-scale deconvolution of sensor array signals

We present a novel solution to a 'hands-off' deconvolution problem in which the data to be deconvolved consist of sensor array measurements. The aim is to find the original source signal (wavelet) and signature of the medium (reflectivity sequence) from the available sensor measurements. Our model assumes that the data are generated as a convolution of an unknown wavelet with various time-scaled versions of an unknown reflectivity sequence. This type of data occurs in many array signal processing applications, including radar, sonar and seismic processing. Our approach relies on exploiting the redundancy in the measurements due to time-scaling which is introduced by the geometry and the sensor placement, and does not require knowledge of the wavelet or reflectivity sequence. Furthermore, we make no assumptions on the statistical properties of these signals. We formulate and solve the deconvolution problem as a quadratic minimization subject to a quadratic constraint. We also illustrate the performance of the technique using simulation examples.