Traditional Principal Component Analysis (PCA) aims to project data onto orthogonal subspaces. However, a limitation of PCA is that it struggles in presence of outliers. Robust Principal Component Analysis (RPCA) improves upon this by effectively handling outliers. Using operations defined with tensor algebra, these methods are further extended to tensor-methods, to handle more complex, multidimensional data. By approximating with low-rank data, these methods are particularly useful for signal denoising. The main goal of this thesis is to examine two such tensor-based algorithms. With emphasis to explain the mathematical background, parameter selection, and performance analysis. To provide visual explanation and validation, we test these algorithms on noisy images.
|
