Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by means of specific 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 to high-volume and high-dimensional visual data, 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 (e.g., low-rank) representations from data corrupted with noise of unknown magnitude and support, but do not provide a dictionary that respects the structure of the data (e.g., images), 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 a restricted form of tensor factorization, 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.
翻译:字典学习和元件分析模型对于学习与特定任务相关的(地精提取、维维度减低、分解等)的缩略图至关重要。 模型复杂性通过特定的结构(如宽度、低级别或非惯性)进行编码。 不幸的是, K-SVD(通过Singulal value Discomposition(SVD)学习稀疏编码词典)等方法很难推广到数量大和高水平的视觉数据,在外层存在时也十分脆弱。 相反,强健的部件分析方法,如Robust主元件分析(RPCA)等,能够从以未知的音量和支持腐蚀的数据中恢复低复杂性(例如低级别)的(例如低级别)表示。 但是,K-SVDD(通过Singultural Dismation(SVD)学习稀薄的字典,以及昂贵的计算方法。 在本文中,我们提出了一种新颖的Kronecker- decombolable 组件分析模型模型,以Robust Kronecker 小块分析(RronCA)的硬性背景(RCA), 其精度分析(即精度分析) 和精度分析, 其精度分析, 其精度的精度的精度是用来的精度分析,其精度的精度的精度分析,其精度的精度的精度的精度的精度和精度分析,其精度的精度的精度分析,其精度分析,其精度分析,其中的精度分析,其精度,其精度是用于的精度的精度的精度的精度,其精度的精度的精度是用于的精度的精度的精度分析,其中的精度,其中的精度,其中的精度是用于的精度分析,其中的精度是用来的精度分析,其精度分析,其中的精度是用于的精度分析,其精度分析,其精度的精度的精度的精度的精度的精度的精度的精度,其精度分析,其精度分析,其精度的精度的精度分析,其中的精度,其精度分析,其精度