Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 285–303 | Cite as

Reconstruction of sparse-view tomography via preconditioned Radon sensing matrix

  • Prasad TheedaEmail author
  • P. U. Praveen Kumar
  • C. S. Sastry
  • P. V. Jampana
Original Research


Computed Tomography (CT) is one of the significant research areas in the field of medical image analysis. As X-rays used in CT image reconstruction are harmful to the human body, it is necessary to reduce the X-ray dosage while also maintaining good quality of CT images. Since medical images have a natural sparsity, one can directly employ compressive sensing (CS) techniques to reconstruct the CT images. In CS, sensing matrices having low coherence (a measure providing correlation among columns) provide better image reconstruction. However, the sensing matrix constructed through the incomplete angular set of Radon projections typically possesses large coherence. In this paper, we attempt to reduce the coherence of the sensing matrix via a square and invertible preconditioner possessing a small condition number, which is obtained through a convex optimization technique. The stated properties of our preconditioner imply that it can be used effectively even in noisy cases. We demonstrate empirically that the preconditioned sensing matrix yields better signal recovery than the original sensing matrix.


Computed tomography Radon transform Compressive sensing Sparse approximation Preconditioning TVAL3 

Mathematics Subject Classification

94A12 65F50 42A15 68U10 



The second and third authors are thankful to CSIR (No. 25(219)/13/EMR-II), Govt. of India, for its support. Prasad Theeda gratefully acknowledges the support being received from MHRD, Govt. of India.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  • Prasad Theeda
    • 1
    Email author
  • P. U. Praveen Kumar
    • 1
    • 3
  • C. S. Sastry
    • 1
  • P. V. Jampana
    • 2
  1. 1.Department of MathematicsIndian Institute of Technology HyderabadSangareddyIndia
  2. 2.Department of Chemical EngineeringIndian Institute of Technology HyderabadSangareddyIndia
  3. 3.Department of Computer ScienceCHRIST UniversityBengaluruIndia

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