Robust Kronecker component analysis - Bahri,M; Panagakis,Y; Zafeiriou,SP (IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019)
Dictionary learning and component analysis models are fundamental for learning compact representations relevant to a given task. The model complexity is encoded by means of structure, such as sparsity, low-rankness, or nonnegativity. Unfortunately, approaches like K-SVD that learn dictionaries for sparse coding via Singular Value Decomposition (SVD) are hard to scale, and fragile in the presence of outliers. Conversely, robust component analysis methods such as the Robust Principal Component Analysis (RPCA) are able to recover low-complexity representations from data corrupted with noise of unknown magnitude and support, but do not provide a dictionary that respects the structure of the data, and also involve expensive computations. In this paper, we propose a novel Kronecker-decomposable component analysis model, coined as Robust Kronecker Component Analysis (RKCA), that combines ideas from sparse dictionary learning and robust component analysis. RKCA has several appealing properties, including robustness to gross corruption; it can be used for low-rank modeling, and leverages separability to solve significantly smaller problems. We design an efficient learning algorithm by drawing links with tensor factorizations, and analyze its optimality and low-rankness properties. The effectiveness of the proposed approach is demonstrated on real-world applications, namely background subtraction and image denoising and completion, by performing a thorough comparison with the current state of the art.