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Adaptive Sampling and Reconstruction for Sparse Magnetic Resonance Imaging

  • Laura Ciancarella
  • Danilo Avola
  • Giuseppe Placidi
Chapter
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 15)

Abstract

An adaptive acquisition sequence for Sparse 2D Magnetic Resonance Imaging (MRI) is presented. The method combines random sampling of Cartesian trajectories with an adaptive 2D acquisition of radial projections. It is based on the evaluation of the information content of a small percentage of the k-space data collected randomly to identify radial blades of k-space coefficients having maximum information content. The information content of each direction is evaluated by calculating an entropy function defined on the power spectrum of the projections. The images are obtained by using a non linear reconstruction strategy, based on the homotopic \(\mathrm{L}_{0}\)-norm, on the sparse data. The method is tested on MRI images and it is also compared to the weighted Compressed Sensing. Some results are reported and discussed.

Keywords

Magnetic resonance imaging (MRI) Compressed sensing (CS) \(\mathrm{L}_{1}\)-norm Radial adaptive acquisition Homotopic \(\mathrm{L}_{0}\)-norm. 

Notes

Acknowledgments

We gratefully acknowledge Abruzzo Region for the financial con-tribution to the project through the European Social Fund (FSE). In addition, we acknowledge Dr. Joshua Trzasko, for having pro-vided useful details to implement the homotopic L0-norm minimiza-tion, and the other members of Computer Vision Laboratory and of AAVI Laboratory for their helpful contribution, in particular Mrs Carmelita Marinelli for technical assistance.

References

  1. 1.
    Arfanakis K, Tamhane AA, Pipe JG, Anastasio MA (2005) K-space undersampling in PROPELLER imaging. Magn Reson Med 53:675–683CrossRefGoogle Scholar
  2. 2.
    Bernstein MA, King KF, Zhou XJ (2004) Handbook of MRI pulse sequences. Elsevier, USAGoogle Scholar
  3. 3.
    Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509Google Scholar
  4. 4.
    Candès EJ, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51(12):4203–4215CrossRefMATHGoogle Scholar
  5. 5.
    Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52:1289–1306CrossRefMathSciNetGoogle Scholar
  6. 6.
    Edelstein WA, Hutchison JM, Johnson G, Redpath T (1980) Spin warp NMR imaging and applications to human whole-body imaging. Phys Med Biol 25:751–756CrossRefGoogle Scholar
  7. 7.
    Elad M (2010) Sparse and redundant representations: from theory to applications in signal and image processing. Springer, New YorkGoogle Scholar
  8. 8.
    Jackson JI, Meyer CH, Nishimura DG, Macovski A (1991) Selection of a convolution function for fourier inversion using gridding. IEEE Trans Med Imaging 10(3):473–478CrossRefGoogle Scholar
  9. 9.
    Lauterbur EC (1973) Image formation by induced local interactions: examples employing nuclear magnetic resonance. Nature 242:190–191CrossRefGoogle Scholar
  10. 10.
    Lustig M (2008) SPARSE MRI. Ph.D Thesis, Stanford UniversityGoogle Scholar
  11. 11.
    Lustig M, Donoho D, Pauly JM (2007) Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 58:1182–1195CrossRefGoogle Scholar
  12. 12.
    Meyer CH (1998) Spiral echo-planar imaging. echo-planar imaging. Springer, BerlinGoogle Scholar
  13. 13.
    O’Sullivan J (1985) A fast sinc function gridding algorithm for fourier inversion in computer tomography. IEEE Trans Med Imaging 4(MI-4):200–207Google Scholar
  14. 14.
    Pipe J (1999) Motion correction with PROPELLER MRI: application to head motion and free-breathing cardiac imaging. Magn Reson Med 42:963–969CrossRefGoogle Scholar
  15. 15.
    Placidi G, Alecci M, Colacicchi S, Sotgiu A (1998) Fourier reconstruction as a valid alternative to filtered back projection in iterative applications: implementation of fourier spectral spatial EPR imaging. J Magn Reson 134:280–286CrossRefGoogle Scholar
  16. 16.
    Placidi G, Alecci M, Sotgiu A (2000) \(\omega \)-Space adaptive acquisition technique for magnetic resonance imaging from projections. J Magn Reson 143:197–207CrossRefGoogle Scholar
  17. 17.
    Placidi G (2012) MRI: essentials for innovative technologies. CRC Press Inc, Boca Raton, pp 111–160Google Scholar
  18. 18.
    Trzasko JD, Manduca A (2009) Highly undersampled magnetic resonance image reconstruction via homotopic \({\rm L}_{0}\) - minimization. IEEE Trans Med Imaging 28:106–121Google Scholar
  19. 19.
    Trzasko JD, Manduca A (2008) A fixed point method for homotopic \({\rm L}_{0 }\)—minimization with application to MR image recovery.In: Proc SPIE 6913, Medical Imaging 2008: Phys Med Imaging, 6913F, pp 1–11Google Scholar
  20. 20.
    Usman M, Prieto C, Schaeffter T, Batchelor PG (2011) k-t group sparse: a method for accelerating dynamic MRI. Magn Reson Med 1176(4):1163–1176CrossRefGoogle Scholar
  21. 21.
    Wang Z, Arce GR (2010) Variable density compressed image sampling. Trans Image Process 19(1):264–270. http://overcode.yak.net/15?width=1600&size=XS Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Laura Ciancarella
    • 1
  • Danilo Avola
    • 1
  • Giuseppe Placidi
    • 1
  1. 1.Department of Life, Health and Environmental SciencesUniversity of L’AquilaL’AquilaItaly

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