An Iterative Bayesian Algorithm for Sparse Component Analysis in Presence of Noise

• Published in: IEEE transactions on signal processing Vol. 57; no. 11; pp. 4378 - 4390
• Main Authors: Zayyani, H., Babaie-Zadeh, M., Jutten, C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Atomic decomposition; Bayesian analysis; Bayesian methods; Blind source separation; blind source separation (BSS); Complexity; Computer Science; Computer simulation; Convergence; Detection, estimation, filtering, equalization, prediction; Engineering Sciences; Equations; Exact sciences and technology; Gaussian; Gaussian noise; Information, signal and communications theory; Iterative algorithms; Linear equations; Miscellaneous; Noise; Signal and communications theory; Signal and Image Processing; Signal processing; Signal processing algorithms; Signal, noise; Source separation; sparse component analysis (SCA); sparse decomposition; sparse source separation; Studies; Telecommunications and information theory; Additive noise; Performance evaluation; Signal mixing; Parameter estimation; Source separation; Signal estimation; Iterative method; Blind source separation; Algorithm; blind source separation (BSS); Gaussian noise; Linear equation; Algorithm performance; Simulation; A posteriori estimation; sparse decomposition; sparse source separation; Convergence rate; Signal processing; sparse component analysis (SCA); Bayes methods; Low sensitivity; Atomic decomposition; sparse decomposition sparse source separation
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2025154

We present a Bayesian approach for sparse component analysis (SCA) in the noisy case. The algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations with additive Gaussian noise. In general, an underdetermined system of linear equations has infinitely many solutions. However, it has been shown that sufficiently sparse solutions can be uniquely identified. Our main objective is to find this unique solution. Our method is based on a novel estimation of source parameters and maximum a posteriori (MAP) estimation of sources. To tackle the great complexity of the MAP algorithm (when the number of sources and mixtures become large), we propose an iterative Bayesian algorithm (IBA). This IBA algorithm is based on the MAP estimation of sources, too, but optimized with a steepest-ascent method. The convergence analysis of the IBA algorithm and its convergence to true global maximum are also proved. Simulation results show that the performance achieved by the IBA algorithm is among the best, while its complexity is rather high in comparison to other algorithms. Simulation results also show the low sensitivity of the IBA algorithm to its simulation parameters.