Blind deconvolution by a Newton method on the non-unitary hypersphere

Blind deconvolution is an inverse filtering technique that has received increasing attention from academia as well industry because of its theoretical implications and practical applications, such as in speech dereverberation, nondestructive testing and seismic exploration. An effective blind deconvolution technique is known as Bussgang , which relies on the iterative Bayesian estimation of the source sequence. Automatic gain control in blind deconvolution keeps constant the energy of the inverse filter impulse response and controls the magnitude of the estimated source sequence. The aim of the present paper is to introduce a class of Newton-type algorithms to optimize the Bussgang cost function on the inverse-filter parameter space whose geometrical structure is induced by the automatic-gain-control constraint. As the parameter space is a differentiable manifold, the Newton-like optimization method is formulated in terms of differential-geometrical concepts. The present paper also discusses convergence issues related to the introduced Newton-type optimization algorithms and illustrates their performance on a comparative basis.