Journal
IET COMMUNICATIONS
Volume 11, Issue 11, Pages 1706-1718Publisher
INST ENGINEERING TECHNOLOGY-IET
DOI: 10.1049/iet-com.2016.1435
Keywords
compressed sensing; singular value decomposition; approximation theory; numerical stability; image reconstruction; computerised tomography; computed tomography reconstruction; numerical stability; orthogonal matching pursuit algorithm; imaging systems; SVD-based weighted equation; RIC; compressed sensing; singular value decomposition-weighted measurement matrix; restricted isometry constant improvement
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Funding
- National Natural Science Foundation of China [61271012, 61671004]
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In compressed sensing, an exact reconstruction depends on the restricted isometry property with a small restricted isometry constant (RIC). Based on singular value decomposition (SVD), the authors improve the RICs of measurement matrices. The proposed weighted measurement matrix method breaks the limit to attain a small RIC and has potential applications in imaging systems. They derive an improvement sufficient condition for the RIC for exact reconstruction using the orthogonal matching pursuit algorithm. The numerical stability of the SVD-based weighted equation is analysed. Simulation results show that the reconstruction results obtained by the proposed SVD-based weighted approach are obviously better than those obtained by the direct reconstruction. In the simulation, they also successfully apply the proposed weighted equation for a computed tomography reconstruction.
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