<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In magnetic resonance imaging (MRI), <italic>k</italic>-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 coefficients). This new theory, created by Candès and Romberg, called compressed sensing (CS), shows that images with sparse representations can be recovered from randomly undersampled <italic>k</italic>-space data, by using nonlinear reconstruction algorithms (i.e. <italic>l</italic><sub>1</sub>-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.</p></abstract>

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 coefficients). 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.

Compressed sensing in MRI – mathematical preliminaries and basic examples

Institute of Radioelectronics, Warsaw University of Technology, 15/19 Nowowiejska Str., 00-665 Warsaw, Poland, Tel.: +48 22 234 7647

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{"article-title":"Compressed sensing in MRI \u2013 mathematical preliminaries and basic examples"}

In magnetic resonance imaging (MRI), k-space sampling, due to physical restrictions, is very time-consuming. It cannot be much improved using classical...

Compressed sensing in MRI – mathematical preliminaries and basic examples

Publié en ligne: 17 mars 2016

Pages: 41 - 43

Reçu: 02 juil. 2014

Accepté: 05 août 2015

DOI: https://doi.org/10.1515/nuka-2016-0003

Mots clés
compressed sensing, magnetic resonance imaging, sampling theory, sparsity

© 2016 Łukasz Błaszczyk, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Compressed sensing in MRI – mathematical preliminaries and basic examples

Publié en ligne: 17 mars 2016

Pages: 41 - 43

Reçu: 02 juil. 2014

Accepté: 05 août 2015

DOI: https://doi.org/10.1515/nuka-2016-0003

Mots cléscompressed sensing, magnetic resonance imaging, sampling theory, sparsity

© 2016 Łukasz Błaszczyk, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
compressed sensing, magnetic resonance imaging, sampling theory, sparsity