Compressed sensing in MRI : mathematical preliminaries and basic examples

• Autorzy: Błaszczyk Ł.

Identyfikatory

DOI

10.1515/nuka-2016-0003

• Konferencja: Proceedings of the Warsaw Medical Physics Meeting 2014 (2014 ; 15-17 May ; Warsaw, Poland)
• Języki publikacji: EN

Abstrakty

EN

In magnetic resonance imaging (MRI), k-space sampling, due to physical restrictions, is very time- -consuming. It cannot be much improved using classical Nyquist-based sampling theory. Recent developments utilize the fact that MR images are sparse in some representations (i.e. wavelet coeffi cients). This new theory, created by Candès and Romberg, called compressed sensing (CS), shows that images with sparse representations can be recovered from randomly undersampled k-space data, by using nonlinear reconstruction algorithms (i.e. l1-norm minimization). Throughout this paper, mathematical preliminaries of CS are outlined, in the form introduced by Candès. We describe the main conditions for measurement matrices and recovery algorithms and present a basic example, showing that while the method really works (reducing the time of MR examination), there are some major problems that need to be taken into consideration.

Słowa kluczowe

EN

compressed sensing; magnetic resonance imaging; sampling theory; sparsity

• Wydawca: Institute of Nuclear Chemistry and Technology
• Czasopismo: Nukleonika
• Rocznik: 2016
• Tom: Vol. 61, No. 1
• Strony: 41--43
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Błaszczyk Ł.

• Institute of Radioelectronics, Warsaw University of Technology, 15/19 Nowowiejska Str., 00-665 Warsaw, Poland, Tel.: [phone]

Bibliografia

• 1. Bernstein, M. A., King, K. F., & Zhou, X. J. (2004).Handbook of MRI pulse sequences. Elsevier.
• 2. Doneva, M., Mutapcic, A., & Lustig, M. (2011). Compressed Sensing (CS) Workshop: Basic Elements of Compressed Sensing. Ohrid.
• 3. Foucart, S., & Rauhut, H. (2013). A mathematical introduction to compressive sensing. Birkhauser.
• 4. Candès, E. J. (2008). The restricted isometry property and its implications for compressed sensing. C. R. Acad. Sci. Paris Ser. I, 346, 589–592. DOI: 10.1016/j.crma.2008.03.014.
• 5. Candès, E. J., & Romberg, J. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theor., 52(2), 489–509. DOI: 10.1109/TIT.2005.862083.
• 6. Vincenti, G., Vincenti, G., Piccini, D., Monney, P.,Chaptinel, J., Rutz, T., Coppo, S., Zenge, M. O.,Schmidt, M., Nadar, M. S., Wang, Q., Chevre, P., Stuber, M., & Schwitter, J. (2014). Preliminary experiences with compressed sensing MultiSlice cine acquisitions for the assessment of left ventricular function: CV_sparse WIP. MAGNETOM Flash., 1, 18–26.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.