Structured Sparse Representation With Union of Data-Driven Linear and Multilinear Subspaces Model for Compressive Video Sampling

The standard compressive sensing (CS) theory can be improved for robust recovery with fewer measurements under the assumption that signals lie on a union of subspaces (UoS). However, the UoS model is restricted to specific types of signal regularities with predetermined topology for subspaces. This paper proposes a generalized model which adaptively decomposes signals into a union of data-driven subspaces (UoDS) for structured sparse representation. The proposed UoDS model leverages subspace clustering to derive the optimal structures and bases for the subspaces conditioned on the sample signals. For multidimensional signals with various statistics, it supports linear and multilinear subspace learning for compressive sampling. As an improvement for generic CS model, the basis which represents the sparsity of sample signals is adaptively generated via linear subspace learning method. Furthermore, a generalized model with multilinear subspace learning is considered for CS to avoid vectorization of high-dimensional signals. In comparison to UoS, the UoDS model requires fewer degrees of freedom for a desirable recovery quality. Experimental results demonstrate that the proposed model for video sampling is promising and applicable.