A parallel algorithm for fast MRI reconstruction

A parallel algorithm for fast MRI reconstruction
Loris Cannelli, Paolo Scarponi, Gesualdo Scutari and Leslie Ying
Dept. of Electrical Engineering, University at Buffalo, The State University of New York
FLEXA[5]: Main Idea
Problem and Motivations
Mathematical Formulation
• The image reconstruction problem can be formulated as
the well-known LASSO problem [6] in which we want to
find x by solving:
• Current
Issues:
• In Dynamic Magnetic Resonance Imaging
(D-MRI) [1], a large amount of data is needed
to obtain good quality images.
• The actual state of the art algorithms [2, 3, 4]
are sequential and they are not fast enough to
allow real-time reconstruction.
min
||d
−
x
(1)
• Figure 4 shows that FLEXA outperforms other
algorithms in terms of Normalized Mean Square Error,
defined as:
Solution:
• Exploit the potential of multi-core architectures
to speed up the reconstruction process.
• Design a novel parallel algorithm with proof of
convergence.
NMSE =
2
||ρ − ρTrue||2
,
2
||ρTrue||2
(2)
Figure 2 : Algorithmic framework intuitive description
where ρ and ρTrue represent the estimated and the true
images in the frequency domain, respectively.
Experiment Description and Discussion
Conclusions
Cardiac Cycle Reconstruction (heart rate 66 bpm, data from a 1.5 T Philips MR scanner)
• Data Structure: 25 time frames, each one stored in a 256 × 256 matrix
• Data Pre-Processing: The fully sampled data are used only for the reference image. The algorithms
rely on a 2/3 Down-Sampling factor to shrink the size of the problem and speed up the calculations.
• Results: as shown in Figure 3 and Figure 4 FLEXA is able to reconstruct a high quality dynamic images
series within one second, while the other tested methods take minutes to achieve similar quality.
Experimental results demonstrate that the proposed
method is able to achieve a lower error in a much
shorter time when compared with other state of the
art algorithms and it also reconstructs in a better
way the dynamic behaviour of the image.
• Impact:
• High
• Task:
(a) Reference frame
(b) FLEXA
Normalized MSE
101
10
(c) kt-FOCUSS
(d) FISTA
Figure 3 : Reconstruction of a single frame from different
algorithms after one second
References
[1] M. Lustig, D. Donoho, and J.M. Pauly.
Sparse mri: The application of compressed sensing for rapid mr
imaging.
Magnetic Resonance in Medicine, 58(6):1182–1195, 2007.
FLEXA
kt-FOCUSS
FISTA
SpaRSA
GRock (P=4)
0
[2] H. Jung, K. Sung, K.S. Nayak, E.Y. Kim, and J.C. Ye.
k-t focuss: A general compressed sensing framework for high resolution
dynamic mri.
Magnetic Resonance in Medicine, 61(1):103–116, 2009.
[3] A. Beck and M. Teboulle.
A fast iterative shrinkage-thresholding algorithm for linear inverse
problems.
SIAM Journal on Imaging Sciences, 2(1):183–202, 2009.
10
−1
10−2
Figure 1 : Block diagram
+ λ||x||1,
where d is the vector which contains the sampled data,
F is the Fourier transform matrix which is related to the
structure of the problem and λ is a regularization factor.
• Proposed
quality images obtained in much less time:
real-time processing is not a dream anymore!
• Possibility to increase the time resolution:
we can now see phenomena otherwise not
observable!
2
Fx||2
[4] S.J. Wright, R.D. Nowak, and M.A. Figueiredo.
Sparse reconstruction by separable approximation.
IEEE Trans. on Signal Processing, 57(7):2479–2493, July 2009.
0
2
4
6
CPU time (sec)
8
Figure 4 : Reconstruction performances of the different
algorithms in terms of Normalized Mean Square Error versus
CPU time
10
[5] L. Cannelli, P. Scarponi, G. Scutari, and L. Ying.
A parallel algorithm for compressed sensing dynamic mri
reconstruction.
23rd annual meeting ISMRM, Toronto, 2015.
[6] R. Tibshirani.
Regression shrinkage and selection via the lasso.
Journal of the Royal Statistical Society. Series B (Methodological),
pages 267–288, 1996.