Cardoso's Independent Component Analysis (ICA) with Joint Approximate Diagonalization of Eigenmatrices (JADE) Method

This text describes our implementation of Cardoso's Independent Component Analysis (ICA) using the Joint Approximate Diagonalization of Eigenmatrices (JADE) method. This powerful signal processing technique separates independent components from mixed signals by optimizing fourth-order cumulants through joint diagonalization of eigenmatrices. The algorithm implementation typically involves whitening the input data, computing cumulant matrices, and performing joint diagonalization to maximize statistical independence. Through ICA and JADE, we can accurately estimate original signal components while analyzing their distinctive characteristics using higher-order statistical properties. This method finds extensive applications across multiple domains including speech recognition (separating overlapping voices), image processing (feature extraction and noise removal), and data analysis (dimensionality reduction and pattern discovery). We selected this approach for our research due to its robustness in handling non-Gaussian signals and conducted detailed investigation into its optimization parameters and performance metrics.