Efficient blind source extraction of noisy mixture utilising a class of parallel linear predictor filters

Abstract

This study presents a novel blind source extraction of a noisy mixture using a class of parallel linear predictor filters. Analysis of a noisy mixture equation is carried out to address new autoregressive source signal model based on the covariance matrix of the whitened data. A method of interchanging the rules of filter inputs is proposed such that this matrix becomes the filter input while the estimated source signals are considered as the parallel filter coefficients. As the matrix has unity norm and unity eigenvalues, the filter becomes independent on the mixture signal norm and eigenvalues variations, thus solving drastically the ambiguity due to the dependency of the filter on the mixture power levels if the mixture is considered as the filter input. Furthermore, the unity eigenvalues of the matrix result in a very fast convergence in two iterations. Simulation results show that the model is capable of extracting the unknown source signals and removing noise when the input signal-to-noise ratio is varied from −20 to 80 dB.

A Null Space-Based Blind Source Separation for Fetal Electrocardiogram Signals

“…In this section, we discus some widely used approaches, such as PCA and FastICA [ 35 , 36 ]. Moreover, the PLP method in [ 12 ] is also included as a recent method to compare with.…”

“…In the FastICA approach, the matrix is equal to , which is the Moore–Penrose inverse of , such that , if [ 12 ]. The resultant estimated sources must be statistically independent.…”

“…In [ 12 ], a BSE based PLP filter was proposed to solve BSS problem using a set of linear predictors that works simultaneously to predict the unknown input sources. The input to the PLP filter is the covariance matrix of the whitened data, denoted by , with the estimated source signals being considered as the PLP filter coefficients.…”

“…In general, the extraction algorithms can be classified as either spatial (non adaptive) or temporal (adaptive) algorithms [ 7 ]. Examples of the BSS/BSE based non-adaptive algorithms include principal component analysis (PCA) [ 8 ], independent component analysis (ICA) [ 8 , 9 ], time scale image (TSI) and singular value decomposition (SVD)/ICA [ 10 ], periodic component analysis [ 11 ], parallel linear predictor (PLP) filters [ 12 , 13 ], template subtraction (TS) [ 14 ], artificial neural network (ANN) [ 15 ], support vector regression (SVR) [ 16 ], tensor decomposition (TD) [ 17 ], deflation [ 18 ], adaptive comb filter (ACF) [ 19 ], and null space component (NCA) [ 20 ]. Examples of the adaptive algorithms include the multi-sensory adaptive noise canceller (MSANC) [ 7 ], fast adaptive orthogonal group ICA [ 21 ], adaptive Volterra filter (AVF) [ 22 ], adaptive neuro fuzzy inference system (ANFIS) and wavelet transform [ 23 ], Kalman filtering [ 24 ], event synchronous canceller [ 25 ], and type-2 adaptive neuro-fuzzy inference systems [ 26 ].…”

“…Some extraction merits were recorded using this method. In [ 12 ], the work presented a novel BSE algorithm using a class of PLP filters whose input is the covariance matrix of the whitened data, while the estimated source signals being considered as the parallel filter coefficients. The method has the merits of solving the power level ambiguity, and has a fast convergence.…”