Title :
A Linear Source Recovery Method for Underdetermined Mixtures of Uncorrelated AR-Model Signals Without Sparseness
Author :
Benxu Liu ; Reju, V.G. ; Khong, Andy W. H.
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, Singapore
Abstract :
Conventional sparseness-based approaches for instantaneous underdetermined blind source separation (UBSS) do not take into account the temporal structure of the source signals. In this work, we exploit the source temporal structure and propose a linear source recovery solution for the UBSS problem which does not require the source signals to be sparse. Assuming the source signals are uncorrelated and can be modeled by an autoregressive (AR) model, the proposed algorithm is able to estimate the source AR coefficients from the mixtures given the mixing matrix. We prove that the UBSS problem can be converted into a determined problem by combining the source AR model together with the original mixing equation to form a state-space model. The Kalman filter is then applied to obtain a linear source estimate in the minimum mean-squared error sense. Simulation results using both synthetic AR signals and speech utterances show that the proposed algorithm achieves better separation performance compared with conventional sparseness-based UBSS algorithms.
Keywords :
Kalman filters; autoregressive processes; blind source separation; linear programming; mean square error methods; sparse matrices; speech processing; state-space methods; Kalman filter; instantaneous UBSS problem; linear source estimation; linear source recovery method; minimum mean squared error sense; mixing matrix; source autoregressive coefficient estimation; source temporal structure; sparseness-based approach; speech utterances; state-space model; synthetic AR signal separation; uncorrelated AR-model signal underdetermined mixtures; underdetermined blind source signal separation; Kalman filters; Mathematical model; Signal processing algorithms; Source separation; Speech; State-space methods; Time-frequency analysis; Kalman filter; Underdetermined blind source separation; autoregressive model; matrix rank; source recovery;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2014.2329646