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.