Blind source separation algorithm for biomedical signal based on lie group manifold

Independent Component Analysis (ICA) is a powerful tool for solving blind source separation problem in biomedical engineering. The traditional ICA algorithm ignores the Lie group structure of constrained matrix manifold. In this paper, a gradient descent algorithm on Lie group manifold is proposed based on the geometric framework of optimization algorithm on Riemann manifold. Firstly, the orthogonal constraint separation matrices are regarded as a Lie group manifold, and the gradient of ICA objective function on the Lie group manifold is given by using Riemann metric; Secondly, the geodesic equation of the current iteration point along the gradient descent direction is calculated; Finally, a new iteration point is obtained by moving a certain step along the geodesic line, meanwhile, the step length can be adjusted adaptively. Simulation results show that the gradient algorithm on Lie group manifold is feasible for blind Source Separation, and its performance (convergence speed, stability and error) is better than other algorithms.