Beam sharpening via multikernel deconvolution

Observation of physical phenomena are made by means of sensors which modify the incoming signals, this modification commonly being modeled by linear convolution with a sensor kernel. This modification limits the resolution that one obtains of the observed objects and brings about the need to reverse the convolution and extract a better object description. We examine a deconvolution problem that is restricted in two ways: the first one assumes that two or more diverse sensor outputs for the same scene at the same viewing angle are available; and second one chooses to look for a deconvolution approach which utilizes the sum of linear convolution filters applied to each of these sensor outputs to produce the deconvolved output being sought. We develop a practical approach to finding optimal deconvolution operators via linear programming. The approach is illustrated by application to the problem of radar beam sharpening using a variety of sensor descriptions.