Rescaled three-mode principal component analysis: An approach to subspace recovery

Abstract

Many tasks, such as image denoising, can be framed within the context of subspace recovery. For its algorithm design, robustness is a critical consideration. In this paper, we propose a novel holistic approach to robust subspace recovery. The fundamental work consists of extending Stein’s unbiased risk estimate to elliptical densities, expanding Gaussian scale mixtures, and estimating error density from the dataset. These advancements serve as the foundation for a rescaled three-mode principal component analysis. By leveraging the majorization–minimization (MM) algorithm, we seamlessly integrate total variation into our model. A key feature of this approach is its inherent robustness to outliers, as demonstrated through our experimental results.