Robust Kronecker-Decomposable Component Analysis for Low-Rank Modeling
This work addresses the need for robust and efficient image decomposition methods in computer vision and signal processing, though it appears incremental as it builds on existing techniques like K-SVD and PCP.
The paper tackles the problem of robust low-rank modeling for images by combining sparse dictionary learning and robust component analysis, resulting in a method that is robust to gross corruption and computationally efficient, with demonstrated effectiveness in background subtraction and image denoising compared to state-of-the-art methods.
Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning, the current methods of choice are arguably K-SVD and its variants, which learn a dictionary (i.e., a decomposition) for sparse coding via Singular Value Decomposition. In robust component analysis, leading methods derive from Principal Component Pursuit (PCP), which recovers a low-rank matrix from sparse corruptions of unknown magnitude and support. However, K-SVD is sensitive to the presence of noise and outliers in the training set. Additionally, PCP does not provide a dictionary that respects the structure of the data (e.g., images), and requires expensive SVD computations when solved by convex relaxation. In this paper, we introduce a new robust decomposition of images by combining ideas from sparse dictionary learning and PCP. We propose a novel Kronecker-decomposable component analysis which is robust to gross corruption, 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 a restricted form of tensor factorization. The effectiveness of the proposed approach is demonstrated on real-world applications, namely background subtraction and image denoising, by performing a thorough comparison with the current state of the art.