MATLAB Code Implementation for Blind Source Separation

Blind source separation (BSS) is a technique for recovering original independent source signals from mixed observations without prior knowledge of the mixing process. The Information Maximization (Infomax) algorithm, a classical approach in BSS, achieves signal separation by maximizing the entropy of output signals. Implementing this algorithm in MATLAB typically involves the following key steps: First, preprocessing of mixed signals is essential. This includes centering and whitening operations to eliminate signal correlations and improve algorithm convergence. Centering zero-means the signals by subtracting their averages, while whitening transforms signals linearly so their covariance matrix becomes an identity matrix. In MATLAB, this can be implemented using functions like mean() for centering and eig() or svd() for whitening calculations. Second, the core of the Infomax algorithm involves adjusting the separation matrix to maximize output signal entropy. This is typically optimized using the natural gradient method, where separation matrix parameters are iteratively updated. During each iteration, the algorithm computes the gradient of output signals and adjusts parameters based on a learning rate until convergence. MATLAB implementations often use while/for loops for iterations and matrix operations for gradient calculations. Finally, evaluating separation performance is crucial. Metrics like correlation coefficients or signal-to-noise ratios can quantify the similarity between separated signals and original sources. If results are unsatisfactory, hyperparameters such as learning rate or iteration count can be adjusted to optimize performance. MATLAB's corr() function can calculate correlation coefficients for performance assessment. When implementing this algorithm in MATLAB, parameters can be flexibly adjusted for different mixed-signal scenarios. By modifying parameter configurations in the main program or optimizing processing steps, the algorithm's applicability can be extended to handle non-stationary signals or nonlinear mixing problems through additional preprocessing or nonlinear activation functions in the separation network.