Advertisement

Optimization of Low-Dose Tomography via Binary Sensing Matrices

  • Theeda PrasadEmail author
  • P. U. Praveen Kumar
  • C. S. Sastry
  • P. V. Jampana
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9448)

Abstract

X-ray computed tomography (CT) is one of the most widely used imaging modalities for diagnostic tasks in the clinical application. As X-ray dosage given to the patient has potential to induce undesirable clinical consequences, there is a need for reduction in dosage while maintaining good quality in reconstruction. The present work attempts to address low-dose tomography via an optimization method. In particular, we formulate the reconstruction problem in the form of a matrix system involving a binary matrix. We then recover the image deploying the ideas from the emerging field of compressed sensing (CS). Further, we study empirically the radial and angular sampling parameters that result in a binary matrix possessing sparse recovery parameters. The experimental results show that the performance of the proposed binary matrix with reconstruction using TV minimization by Augmented Lagrangian and ALternating direction ALgorithms (TVAL3) gives comparably better results than Wavelet based Orthogonal Matching Pursuit (WOMP) and the Least Squares solution.

Keywords

Discrete tomography Compressive sensing WOMP  Binary sensing matrix TVAL3 

Notes

Acknowledgments

One of the authors (CSS) is thankful to CSIR (No. 25(219)/13/ EMR-II), Govt. of India, for its support.

References

  1. 1.
    Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrason. Imaging 6(1), 81–94 (1984)CrossRefGoogle Scholar
  2. 2.
    Badea, C., Gordon, R.: Experiments with the nonlinear and chaotic behaviour of the multiplicative algebraic reconstruction technique (MART) algorithm for computed tomography. Phy. Med. Biol. 49(8), 1455–1474 (2004)CrossRefGoogle Scholar
  3. 3.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)zbMATHCrossRefGoogle Scholar
  4. 4.
    Candes, E.J.: The restricted isometry property and its implications for compressed sensing. C. R. Math. 346, 589–592 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Candes, E.J., Romberg, J.: Practical signal recovery from random projections. In: Proceedings of the SPIE Conference on Wavelet Applications in Signal and Image Processing XI, vol. 5914 (2005)Google Scholar
  6. 6.
    Chen, G.H., Tang, J., Leng, S.: Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets. Med. Phys. 35(2), 660–663 (2008)CrossRefGoogle Scholar
  7. 7.
    Daubechies, I.: Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, Philadelphia (1992)zbMATHCrossRefGoogle Scholar
  8. 8.
    Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Elad, M. (ed.): Sparse and Redundant Representations: from Theory to Applications in Signal Processing. Springer, New York (2010)Google Scholar
  10. 10.
    Foucart, S., Rauhut, H.: A Mathematical Introduction to Compressive Sensing. Birkhauser, Basel (2013)zbMATHCrossRefGoogle Scholar
  11. 11.
    Frush, D.P., Donnelly, L.F., Rosen, N.S.: Computed tomography and radiation risks: what pediatric health care providers should know. Pediatrics 112, 951–957 (2003)CrossRefGoogle Scholar
  12. 12.
    Jan, J.: Medical Image Processing, Reconstruction and Restoration: Concepts and Methods. CRC Press, Boca Raton (2005)CrossRefGoogle Scholar
  13. 13.
    Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. Society for Industrial and Applied Mathematics, Philadelphia (2001)CrossRefGoogle Scholar
  14. 14.
    Kudo, H., Suzuki, T., Rashed, E.A.: Image reconstruction for sparse-view CT and interior CT - introduction to compressed sensing and differentiated backprojection. Quant. Imaging Med. Surg. 3(3), 147–161 (2013)Google Scholar
  15. 15.
    Li, C., Yin, W., Jiang, H., Zhang, Y.: An efficient augmented Lagrangian method with applications to total variation minimization. Comput. Optim. Appl. 56(3), 507–530 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Natterer, F.: The Mathematics of Computerized Tomography. Society for Industrial and Applied Mathematics, Philadelphia (2001)zbMATHCrossRefGoogle Scholar
  17. 17.
    Pan, X.C., Sidky, E.Y., Vannier, M.: Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction? Inverse Prob. 25(12), 1230009 (2009)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Ritschl, L., Bergner, F., Fleischmann, C., Kachelrieß, M.: Improved total variation-based CT image reconstruction applied to clinical data. Phys. Med. Biol. 56(6), 1545–1561 (2011)CrossRefGoogle Scholar
  19. 19.
    Sastry, C.S., Das, P.C.: Wavelet based multilevel backprojection algorithm for parallel and fan beam scanning geometries. Int. J. Wavelets Multiresolut. Inf. Process. 4(3), 523–545 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Proc. 13(4), 600–612 (2004)CrossRefGoogle Scholar
  22. 22.
    Xu, Q., Mou, X., Wang, G., Sieren, J., Hoffman, E., Yu, H.: Statistical interior tomography. IEEE Trans. Med. Imaging 30(5), 1116–1128 (2011)CrossRefGoogle Scholar
  23. 23.
    Yu, H.Y., Wang, G.: Compressed sensing based interior tomography. Phys. Med. Biol. 54(9), 2791–2805 (2009)CrossRefGoogle Scholar
  24. 24.
    Yu, H.Y., Yang, J.S., Jiang, M., Wang, G.: Supplemental analysis on compressed sensing based interior tomography. Phys. Med. Biol. 54(18), N425–N432 (2009)CrossRefGoogle Scholar
  25. 25.
    Zhang, H., Huang, J., Ma, J., Bian, Z., Feng, Q., Lu, H., Liang, Z., Chen, W.: Iterative reconstruction for X-ray computed tomography using prior-image induced nonlocal regularization. IEEE Trans. Biomed. Eng. 61(9), 2367–2378 (2014)CrossRefGoogle Scholar
  26. 26.
    Zhou, W., Cai, J.-F., Gao, H.: Adaptive tight frame based medical image reconstruction: a proof-of-concept study for computed tomography. Inverse Prob. 29, 125006 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

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

Personalised recommendations