A natural gradient algorithm for multichannel blind deconvolution: Frequency domain criteria and time domain updates

This paper addresses the problem of blind deconvolution and separation of multiple independent signals. A frequency domain approach is taken wherein a criterion for separating instantaneous linear mixtures is applied at each frequency. To eliminate the permutation and scaling ambiguity across frequencies, time-domain impulse response coefficients are updated instead of weights in the frequency domain. Using techniques of differential geometry, a new natural gradient algorithm is derived for updating the impulse response coefficients of the separation system by pulling back a Riemannian metric from the frequency domain to the time domain. This leads to a technique for resolving permutation and scale ambiguity across frequency bins that agrees with an approach proposed by Parra and Spence[1].