Robust Principal Component Analysis (RPCA) MATLAB Implementation
Robust PCA, derived from low-rank matrix recovery problems by Wright et al. [13], has gained significant attention in recent years as one of the most popular RPCA methods. Low-rank matrix recovery aims to reconstruct original low-rank data from noisy observations - a concept analogous to PCA which identifies low-dimensional subspaces while treating deviations as noise. The core innovation lies in simultaneously requiring L0 to be low-rank while S0 must be sparse with arbitrarily large elements, enabling effective outlier handling through mathematical optimization. This implementation demonstrates how to separate corruptions (even extreme pixel noises) into sparse components using convex optimization techniques.