Subspace Learning in The Presence of Sparse Structured Outliers and Noise

Abstract: Subspace learning is an important problem, which has many applications in image and video processing. It can be used to find a low-dimensional representation of signals and images. But in many applications, the desired signal is heavily distorted by outliers and noise, which negatively affect the learned subspace. In this work, we present a novel algorithm for learning a subspace for signal representation, in the presence of structured outliers and noise. The proposed algorithm tries to jointly detect the outliers and learn the subspace for images. We present an alternating optimization algorithm for solving this problem, which iterates between learning the subspace and finding the outliers. This algorithm has been trained on a large number of image patches, and the learned subspace is used for image segmentation, and is shown to achieve better segmentation results than prior methods, including least absolute deviation fitting, k-means clustering based segmentation in DjVu, and shape primitive extraction and coding algorithm.