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

Abstract

Blind deconvolution is an inverse filtering technique that has received increasing attention from academia as well as 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.

Novel mixing matrix estimation approach in underdetermined blind source separation

“…Set λ ¼ 0:1 to remove low-energy points. The normalized scatter plot after mapping the observed signals to the upper unit hypersphere [20][21] is shown in Fig. 4(b).…”

“…Density-based spatial clustering of applications with noise (DBSCAN) [12][13][14] can overcome the drawbacks of the K-means clustering algorithm, but the parameter selection involved in this method is a challenging task. Further, single source point detection [15][16][17] has been proposed to address the problem of low signal sparsity [18][19][20][21], but it suffers from issues such as high complexity and conditions that are difficult to satisfy.…”

Mixing matrix estimation method for dual‐channel time‐frequency overlapped signals based on interval probability

“…Computing the estimation accuracy of the obtained mixing matrix, NMSE = -65.7254 dB by using (24), indicating high accuracy and great performance.…”

A Fast Converge Dual-Mode Modified Constant Norm Blind Equalization Algorithm

“…The blind equalization is an inequable method according to the traditional equalization method which can equalize the channel by the priori information of the received sequence without the help of the training sequence (Wu, Feng and Zheng, 2014;Fiori, 2013). The blind equalization method can regain the output sequence of the equalizer which is mostly similar to the transmit sequence.…”