A general theory for subspace-sparse recovery

Abstract

High-dimensional data that often lie in low-dimensional subspaces are ubiquitous in many fields of signal and image processing, pattern recognition, machine learning, etc. Finding sparse representations of data points in a dictionary built by using the collection of data helps to study low-dimensional subspaces. In this paper, we consider the problem of subspace-sparse representation for data composed of two distinct features. Applying different measures to the coefficients of the two distinct features under different dictionaries makes the model used in this paper more general. We present theoretical guarantee for subspace-sparse representation under conditions on the subspaces and data. The program used in this paper can handle data with structured corruption, missing entries, sparse outliers and random bounded noise well.