Gradient adaptive algorithms for contrast-based blind deconvolution

This paper presents extensions of stochastic gradient independent component analysis (ICA) methods to the blind deconvolution task. Of particular importance in these extensions are the constraints placed on the deconvolution system transfer function. While unit-norm constrained ICA approaches can be directly applied to the prewhitened blind deconvolution task, an allpass filter constraint within the optimization procedure is more appropriate. We show how such constraints can be approximately imposed within gradient adaptive finite-impulse-response (FIR) filter implementations by proper extensions of gradient techniques within the Stiefel manifold of orthonormal matrices. Both on-line time-domain and block-based frequency-domain algorithms are described. Simulations verify the superior performance behaviors provided by our allpass-constrained algorithms over standard unit-norm-constrained ICA algorithms in blind deconvolution tasks.