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access icon free Restricted isometry constant improvement based on a singular value decomposition-weighted measurement matrix for compressed sensing

  • Author(s): Qian Wang 1  and  Gangrong Qu 1, 2
    • View affiliations
  • Source: Volume 11, Issue 11, 03 August 2017, p. 1706 – 1718
    DOI:  10.1049/iet-com.2016.1435 , Print ISSN 1751-8628, Online ISSN 1751-8636
© The Institution of Engineering and Technology
Received 15/12/2016, Accepted 10/03/2017, Revised 19/02/2017, Published 24/03/2017

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.

Inspec keywords: singular value decomposition; approximation theory; compressed sensing; numerical stability; computerised tomography; image reconstruction

Other keywords: RIC; SVD-based weighted equation; orthogonal matching pursuit algorithm; compressed sensing; numerical stability; imaging systems; computed tomography reconstruction; singular value decomposition-weighted measurement matrix; restricted isometry constant improvement

Subjects: Linear algebra (numerical analysis); Optical, image and video signal processing; Linear algebra (numerical analysis); Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Computer vision and image processing techniques

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