Compressive Acquisition of Linear Dynamical Systems

Compressive sensing (CS) enables the acquisition and recovery of sparse signals and images at sampling rates significantly below the classical Nyquist rate. Despite significant progress in the theory and methods of CS, little headway has been made in compressive video acquisition and recovery. Video CS is complicated by the ephemeral nature of dynamic events, which makes direct extensions of standard CS imaging architectures and signal models difficult. In this paper, we develop a new framework for video CS for dynamic textured scenes that models the evolution of the scene as a linear dynamical system (LDS). This reduces the video recovery problem to first estimating the model parameters of the LDS from compressive measurements and then reconstructing the image frames. We exploit the low-dimensional dynamic parameters (the state sequence) and high-dimensional static parameters (the observation matrix) of the LDS to devise a novel compressive measurement strategy that measures only the time-varying parameters at each instant and accumulates measurements over time to estimate the time-invariant parameters. This enables us to lower the compressive measurement rate considerably. We validate our approach and demonstrate its effectiveness with a range of experiments involving video recovery and scene classification.