Skip to main content

Adaptive Sampling and Reconstruction for Sparse Magnetic Resonance Imaging

  • Chapter
  • First Online:
Computational Modeling of Objects Presented in Images


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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others


  1. Arfanakis K, Tamhane AA, Pipe JG, Anastasio MA (2005) K-space undersampling in PROPELLER imaging. Magn Reson Med 53:675–683

    Article  Google Scholar 

  2. Bernstein MA, King KF, Zhou XJ (2004) Handbook of MRI pulse sequences. Elsevier, USA

    Google Scholar 

  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):489–509

    Google Scholar 

  4. Candès EJ, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51(12):4203–4215

    Article  MATH  Google Scholar 

  5. Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52:1289–1306

    Article  MathSciNet  Google Scholar 

  6. Edelstein WA, Hutchison JM, Johnson G, Redpath T (1980) Spin warp NMR imaging and applications to human whole-body imaging. Phys Med Biol 25:751–756

    Article  Google Scholar 

  7. Elad M (2010) Sparse and redundant representations: from theory to applications in signal and image processing. Springer, New York

    Google Scholar 

  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):473–478

    Article  Google Scholar 

  9. Lauterbur EC (1973) Image formation by induced local interactions: examples employing nuclear magnetic resonance. Nature 242:190–191

    Article  Google Scholar 

  10. Lustig M (2008) SPARSE MRI. Ph.D Thesis, Stanford University

    Google Scholar 

  11. Lustig M, Donoho D, Pauly JM (2007) Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 58:1182–1195

    Article  Google Scholar 

  12. Meyer CH (1998) Spiral echo-planar imaging. echo-planar imaging. Springer, Berlin

    Google Scholar 

  13. O’Sullivan J (1985) A fast sinc function gridding algorithm for fourier inversion in computer tomography. IEEE Trans Med Imaging 4(MI-4):200–207

    Google Scholar 

  14. Pipe J (1999) Motion correction with PROPELLER MRI: application to head motion and free-breathing cardiac imaging. Magn Reson Med 42:963–969

    Article  Google Scholar 

  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 134:280–286

    Article  Google Scholar 

  16. Placidi G, Alecci M, Sotgiu A (2000) \(\omega \)-Space adaptive acquisition technique for magnetic resonance imaging from projections. J Magn Reson 143:197–207

    Article  Google Scholar 

  17. Placidi G (2012) MRI: essentials for innovative technologies. CRC Press Inc, Boca Raton, pp 111–160

    Google Scholar 

  18. Trzasko JD, Manduca A (2009) Highly undersampled magnetic resonance image reconstruction via homotopic \({\rm L}_{0}\) - minimization. IEEE Trans Med Imaging 28:106–121

    Google Scholar 

  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 1–11

    Google Scholar 

  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):1163–1176

    Article  Google Scholar 

  21. Wang Z, Arce GR (2010) Variable density compressed image sampling. Trans Image Process 19(1):264–270.

    Google Scholar 

Download references


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.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Giuseppe Placidi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Ciancarella, L., Avola, D., Placidi, G. (2014). Adaptive Sampling and Reconstruction for Sparse Magnetic Resonance Imaging. In: Di Giamberardino, P., Iacoviello, D., Natal Jorge, R., Tavares, J. (eds) Computational Modeling of Objects Presented in Images. Lecture Notes in Computational Vision and Biomechanics, vol 15. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04038-7

  • Online ISBN: 978-3-319-04039-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics