Abstract
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.
Highlights
The Shannon-Nyquist theorem dictates that to sense features at a particular frequency, we must sample uniformly at twice that rate
We develop a compressive sensing (CS) framework for videos modeled as linear dynamical systems (LDSs), which is motivated, in part, by the extensive use of such models in characterizing dynamic textures [10, 15, 33], activity modeling, and video clustering [37]
We provide a high level overview of our proposed framework for video CS; the goal here is to build a CS framework, implementable on the single pixel camera (SPC), for videos that are modeled as LDSs
Summary
The Shannon-Nyquist theorem dictates that to sense features at a particular frequency, we must sample uniformly at twice that rate. This sampling rate might be too high; in modern digital cameras, invariably, the sensed imaged is compressed immediately without much loss in quality. For other applications, such as high speed imaging and sensing in the nonvisual spectrum, camera/sensor designs based on the Shannon-Nyquist theorem lead to impractical and costly designs. Exploiting the sparsity of s, the signal y can be recovered exactly from M “ OpK logpN {Kqq measurements provided the matrix ΦΨ satisfies the so-called restricted isometry property (RIP) [4]. The signal y can be recovered from z by solving a convex problem of the form min }s}1 subject to }z ΦΨs}2 ď ,
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