Union of Data-Driven Subspaces via Subspace Clustering for Compressive Video Sampling

Abstract

The standard Compressive Sensing (CS) theory indicates that robust signals recovery can be obtained from just a few collection of incoherent projections. To further decrease the necessary measurements, an alternative to the generic CS framework assumes that signals lie on a union of subspaces (UoS). However, UoS model is limited to the specific type of signal regularity. This paper considers a more general and adaptive model which presumes that signals lie on a union of data-driven subspaces (UoDS). The UoDS model inherits the merit from UoS that signals have structural sparse representation. Meanwhile, it allows to recover signals using fewer degrees of freedom for a desirable recovery quality than UoS. To construct the UoDS model, a subspace clustering method is utilized to form an adaptive group set. The corresponding adaptive basis is learned by applying a linear subspace learning (LSL) method to each group. A corresponding recovery algorithm with provable performance is also given. Experiment results demonstrate that the proposed model for video sampling is valid and applicable.