Compressive acquisition of linear dynamical systems

Aswin C. Sankaranarayanan, Pavan Turaga, Rama Chellappa, Richard G. Baraniuk

Research output: Contribution to journalArticle

21 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)2109-2133
Number of pages25
JournalSIAM Journal on Imaging Sciences
Volume6
Issue number4
DOIs
StatePublished - Oct 22 2013

Fingerprint

Linear Dynamical Systems
Compressive Sensing
Dynamical systems
Recovery
Time-varying Parameters
Accumulate
Instant
Sampling
Imaging techniques
High-dimensional
Imaging
Acquisition
Model
Invariant
Experiments
Estimate
Range of data
Demonstrate
Experiment

Keywords

  • Compressive sensing
  • Linear dynamical system
  • Video compressive sensing

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

Cite this

Sankaranarayanan, A. C., Turaga, P., Chellappa, R., & Baraniuk, R. G. (2013). Compressive acquisition of linear dynamical systems. SIAM Journal on Imaging Sciences, 6(4), 2109-2133. https://doi.org/10.1137/120863307

Compressive acquisition of linear dynamical systems. / Sankaranarayanan, Aswin C.; Turaga, Pavan; Chellappa, Rama; Baraniuk, Richard G.

In: SIAM Journal on Imaging Sciences, Vol. 6, No. 4, 22.10.2013, p. 2109-2133.

Research output: Contribution to journalArticle

Sankaranarayanan, AC, Turaga, P, Chellappa, R & Baraniuk, RG 2013, 'Compressive acquisition of linear dynamical systems', SIAM Journal on Imaging Sciences, vol. 6, no. 4, pp. 2109-2133. https://doi.org/10.1137/120863307
Sankaranarayanan, Aswin C. ; Turaga, Pavan ; Chellappa, Rama ; Baraniuk, Richard G. / Compressive acquisition of linear dynamical systems. In: SIAM Journal on Imaging Sciences. 2013 ; Vol. 6, No. 4. pp. 2109-2133.
@article{925abe7c2f1b49b792d5bac58b19379e,
title = "Compressive acquisition of linear dynamical systems",
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.",
keywords = "Compressive sensing, Linear dynamical system, Video compressive sensing",
author = "Sankaranarayanan, {Aswin C.} and Pavan Turaga and Rama Chellappa and Baraniuk, {Richard G.}",
year = "2013",
month = "10",
day = "22",
doi = "10.1137/120863307",
language = "English (US)",
volume = "6",
pages = "2109--2133",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",

}

TY - JOUR

T1 - Compressive acquisition of linear dynamical systems

AU - Sankaranarayanan, Aswin C.

AU - Turaga, Pavan

AU - Chellappa, Rama

AU - Baraniuk, Richard G.

PY - 2013/10/22

Y1 - 2013/10/22

N2 - 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.

AB - 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.

KW - Compressive sensing

KW - Linear dynamical system

KW - Video compressive sensing

UR - http://www.scopus.com/inward/record.url?scp=84891140838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891140838&partnerID=8YFLogxK

U2 - 10.1137/120863307

DO - 10.1137/120863307

M3 - Article

AN - SCOPUS:84891140838

VL - 6

SP - 2109

EP - 2133

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 4

ER -