Constrained LMMSE-based object-specific reconstruction in compressive sensing

In many applications like surveillance, it is essential to detect the presence of specific objects by seeing an image or video without being concerned about details of the scene. The reconstruction algorithms proposed in the compressive sensing literature try to iteratively reconstruct the full imag...

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Veröffentlicht in:	IET signal processing Jg. 11; H. 9; S. 1122 - 1127
Hauptverfasser:	Tripathy, Soumya Ranjan, Panda, Ganapati, Majhi, Babita
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	The Institution of Engineering and Technology 01.12.2017
Schlagworte:	closed‐form reconstruction algorithm compressed sensing compressive sensing constrained LMMSE‐based object‐specific reconstruction ill‐conditioned matrix inversion problem image reconstruction linear minimum mean square error estimator matrix inversion mean square error methods modified Euler method regularization method Research Article regularization method modified Euler method compressed sensing matrix inversion image reconstruction constrained LMMSE-based object-specific reconstruction linear minimum mean square error estimator mean square error methods closed-form reconstruction algorithm compressive sensing ill-conditioned matrix inversion problem
ISSN:	1751-9675, 1751-9683, 1751-9683
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Abstract	In many applications like surveillance, it is essential to detect the presence of specific objects by seeing an image or video without being concerned about details of the scene. The reconstruction algorithms proposed in the compressive sensing literature try to iteratively reconstruct the full image. Hence, those are computationally expensive. If some prior knowledge of the object is available, then a closed-form reconstruction algorithm can be formulated. The goal is to reconstruct the object of interest efficiently without being bothered about the quality of reconstruction of the scene. To address this situation, a constraint is formulated and incorporated into linear minimum mean square error (LMMSE) estimator to form a closed-form solution. This compact solution is capable of meaningfully reconstructing the object relative to the scene. In the proposed method, an ill-conditioned matrix inversion problem has been faced and overcome by regularization method. To boost the speed of the algorithm, a modified Euler method is proposed for finding the regularization parameter. To further speedup the reconstruction process, larger images are divided into several pieces and each piece is reconstructed separately using constrained LMMSE. For a given number of measurements, the simulation-based results demonstrate acceptable quality of reconstruction with minimal computational effort.
AbstractList	In many applications like surveillance, it is essential to detect the presence of specific objects by seeing an image or video without being concerned about details of the scene. The reconstruction algorithms proposed in the compressive sensing literature try to iteratively reconstruct the full image. Hence, those are computationally expensive. If some prior knowledge of the object is available, then a closed‐form reconstruction algorithm can be formulated. The goal is to reconstruct the object of interest efficiently without being bothered about the quality of reconstruction of the scene. To address this situation, a constraint is formulated and incorporated into linear minimum mean square error (LMMSE) estimator to form a closed‐form solution. This compact solution is capable of meaningfully reconstructing the object relative to the scene. In the proposed method, an ill‐conditioned matrix inversion problem has been faced and overcome by regularization method. To boost the speed of the algorithm, a modified Euler method is proposed for finding the regularization parameter. To further speedup the reconstruction process, larger images are divided into several pieces and each piece is reconstructed separately using constrained LMMSE. For a given number of measurements, the simulation‐based results demonstrate acceptable quality of reconstruction with minimal computational effort.
Author	Panda, Ganapati Majhi, Babita Tripathy, Soumya Ranjan
Author_xml	– sequence: 1 givenname: Soumya Ranjan surname: Tripathy fullname: Tripathy, Soumya Ranjan email: st11@iitbbs.ac.in organization: 1School of Electrical Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India – sequence: 2 givenname: Ganapati surname: Panda fullname: Panda, Ganapati organization: 1School of Electrical Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India – sequence: 3 givenname: Babita surname: Majhi fullname: Majhi, Babita organization: 2Department of CSIT, Guru Ghasidas Vishwavidyalay, Central University, Bilaspur, India
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Cites_doi	10.1109/JSTARS.2013.2263309 10.1137/S1064827596304010 10.1016/j.acha.2008.07.002 10.1137/1034115 10.1109/ICASSP.2007.366874 10.1109/TIT.2007.909108 10.7848/ksgpc.2013.31.6-2.577 10.1109/TIT.2005.862083 10.1109/MSP.2007.914729 10.1109/TAES.2009.5259191 10.1109/TIT.2006.871582 10.1109/IGARSS.2013.6723499 10.1109/MSP.2007.4286571
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Keywords	regularization method modified Euler method compressed sensing matrix inversion image reconstruction constrained LMMSE-based object-specific reconstruction linear minimum mean square error estimator mean square error methods closed-form reconstruction algorithm compressive sensing ill-conditioned matrix inversion problem
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SubjectTerms	closed‐form reconstruction algorithm compressed sensing compressive sensing constrained LMMSE‐based object‐specific reconstruction ill‐conditioned matrix inversion problem image reconstruction linear minimum mean square error estimator matrix inversion mean square error methods modified Euler method regularization method Research Article
Title	Constrained LMMSE-based object-specific reconstruction in compressive sensing
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