Generalized quadratic minimization and blind multichannel deconvolution

This paper deals with the problem of quadratic minimization subject to linear equality constraints. Unlike the standard formulation, we assume the most general case of a possibly singular quadratic form. We explain that the existing formal solution to this problem has several drawbacks. Our new approach is free from most of these drawbacks. In particular, it has a simple interpretation and is relatively easy to implement. The practical importance of this result lies in its numerous applications: filter design, spectral analysis, direction finding, and blind deconvolution of multiple FIR channels. Here, we focus on the blind deconvolution application for which we present a novel solution with enhanced performance.