  This work considers the multi-channel blind deconvolution problem under the
assumption that the channels are short. First, we investigate the ill-posedness
issues inherent to blind deconvolution problems and sufficient and necessary
conditions on the channels that guarantee well-posedness are derived. Following
previous work on blind deconvolution, the problem is then reformulated as a
low-rank matrix recovery problem and solved by nuclear norm minimization.
Numerical experiments show the effectiveness of this algorithm under a certain
generative model for the input signal and the channels, both in the noiseless
and in the noisy case.

Signal Processing