Combination of Parallel Imaging and Compressed Sensing for high acceleration factor at 7T

Transcription

1 Combination of Parallel Imaging and Compressed Sensing for high acceleration factor at 7T DEDALE Workshop Nice Loubna EL GUEDDARI (NeuroSPin) Joint work with: Carole LAZARUS, Alexandre VIGNAUD and Philippe CIUCIU 06 SEPTEMBER 2017 CEA 10 AVRIL 2012 PAGE 1

2 MRI CONTEXT CEA 10 AVRIL 2012 PAGE 2

3 MRI CONTEXT

4 COMPRESSED SENSING IN MRI Data sampling in the 2D/3D Fourier domain: k-space Non linear reconstruction Acquisition 7Tesla MRI MR Image Spatial frequencies Randomly under-sampled Stakes in MRI: Reduce acquisition time Improve patient comfort Achieve very high resolution in space and time Need very high SNR Limit patient s motion artifact

5 HIGH RESOLUTION NEEDS HIGH SNR

6 PARALLEL IMAGING CEA 10 AVRIL 2012 PAGE 6

7 PARALLEL IMAGING What is parallel imaging? Technique where multiple receiver coils are used to acquire the signal Many small diameter coils measure the NMR signal with higher Signal-to-Noise Ratio (SNR) than a single birdcage coil with a large diameter SOURCE: MRIQUESTION.COM CEA SEPTEMBER 6th 2017 PAGE 7

8 PARALLEL IMAGING What is parallel imaging? Technique where multiple receiver coils are used to acquire the signal Many small diameter coils measure the NMR signal with higher Signal-to-Noise Ratio (SNR) than a single birdcage coil with a large diameter SOURCE: MRIQUESTION.COM CEA SEPTEMBER 6th 2017 PAGE 8

9 PARALLEL MRI BEFORE COMPRESSED SENSING PAGE 9

10 PARALLEL IMAGING BEFORE CS: ACQUISITION First acceleration techniques : Parallel imaging [ SENSE, Pruesman et al., ISMRM 1997] Used since 1997 Reduce the number of phase encoding lines Phase encoding direction Reduce the acquisition time SOURCE: MRIQUESTION.COM CEA SEPTEMBER 6th 2017 PAGE 10

11 PARALLEL IMAGING BEFORE CS: RECONSTRUCTION Image based reconstruction Unfolding the aliased pixels SOURCE: MRIQUESTION.COM [ SENSE, Pruesman et al., MRM 1999] CEA SEPTEMBER 6th 2017 PAGE 11

12 PARALLEL IMAGING BEFORE CS: RECONSTRUCTION K-space based reconstruction Estimating missing data SOURCE: MRIQUESTION.COM [ GRAPPA, Griswold et al., MRM 2002] CEA SEPTEMBER 6th 2017 PAGE 12

13 PARALLEL IMAGING BEFORE CS: RECONSTRUCTION K-space based reconstruction [ GRAPPA, Griswold et al., MRM 2002] SOURCE: MRIQUESTION.COM CEA SEPTEMBER 6th 2017 PAGE 13

14 PARALLEL MRI AND COMPRESSED SENSING PAGE 14

15 CS-PMRI Combination of Compressed Sensing and Parallel Imaging Existing reconstruction algorithm can be divided into three categories: Coil-by-coil image reconstruction [ SPIRIT, Lustig et Pauly, MRM 2010] Need a fully sampled k-space part Hardly applicable to variable density sampling Single image reconstruction [ SparseSENSE, Wu et al., MRM 2008] Applicable to all sampling pattern Dependant on the accuracy of the sensitivity profiles Combination of the two last techniques [ ESPIRIT, Uecker et al., MRM 2014] Need a fully sampled k-space part Hardly applicable to non-cartesian sampling scheme CEA SEPTEMBER 6th 2017 PAGE 15

16 TRAJECTORY CONSTRAINTS Trajectories used: - Non-Cartesian trajectories - Variable density Reconstruction algorithm: Radial Under-sampled Fourier transform (Cartesian or not) Diagonal matrix representing the sensitivity maps of the lth coil Acquired data Sparsifying transform :Reconstructed image CEA SEPTEMBER 6th 2017 PAGE 16

17 TRAJECTORY CONSTRAINTS Trajectories used: - Non-Cartesian trajectories - Variable density Reconstruction algorithm: Radial Under-sampled Fourier transform (Cartesian or not) Block-column matrix each block is a diagonal matrix representing the sensitivity maps of the ith coil Acquired data Sparsifying transform :Reconstructed image CEA SEPTEMBER 6th 2017 PAGE 17

18 SEPARABLE QUADRATIC SURROGATES Upper-bound of the quadratic term with a separable quadratic surrogate: We first rewrite around the current estimate : [Erdogan et al., Phys. Med. Bio. 1999] If we can find a diagonal matrix such that: Then: CEA SEPTEMBER 6th 2017 PAGE 18

19 LIPSCHITZ CONSTANT VS B1-SURROGATE From: the maximum eigenvalue of with: the maximum eigenvalue of is a diagonal matrix with the sum of the squared absolute values on its diagonal Only computable with Power Method If the sampling scheme is Cartesian, the maximum eigenvalue is 1 B1 approach [ BARISTA, Muckley et al., IEEE 2015] CEA SEPTEMBER 6th 2017 PAGE 19

20 PROXIMAL OPTIMIZED GRADIENT METHOD [ POGM, Taylor et al., SIAM 2017] Extension of the Optimized Gradient Method proposed by Kim: [ OGM, Kim et Fessler., Math. Prog. 2016] Twice faster than First Order method with momentum such as: Nesterov s method FISTA [Nesterov, Sov. Math. Dokl. 1983] [ FISTA, Teboule et al., SIAM. 2009] That are known to have an upper bound equal to: [Drior, Teboule, Math. Prog. 2014] The POGM is supposed to have an upper bound equal to: CEA SEPTEMBER 6th 2017 PAGE 20

21 POGM: THE ALGORITHM CEA SEPTEMBER 6th 2017 PAGE 21

22 EXPERIMENTS: SETUP RETROSPECTIVE SIMULATION Materials: From fully acquired image at the 3T and using a 32 channel receiver coil Using a Cartesian sampling scheme: R=4 Variable density Gaussian Reference Sampling CEA SEPTEMBER 6th 2017 PAGE 22

23 EXPERIMENTS: SETUP RETROSPECTIVE SIMULATION Materials: From fully acquired image at the 3T and using a 32 channel receiver coil Using a Cartesian sampling scheme: R=4 Variable density Gaussian Smap CEA SEPTEMBER 6th 2017 PAGE 23

24 EXPERIMENTS: RESULTS FISTA POGM Lipschitz B1 approach CEA SEPTEMBER 6th 2017 PAGE 24

25 EXPERIMENTS: RESULTS Metric: Residual: CEA SEPTEMBER 6th 2017 PAGE 25

26 EXPERIMENTS: SETUP FOR PROSPECTIVE ACQUISITION Materials: Multi-channel coil: Nova (1Tx/32Rx) was used at 7T: MR pulse sequence: from latest Lazarus Sparkling development: Sequence parameters: - CS-GRE (2D) - T2*-weighted - N = FOV = 200x200 mm² - TR = 250 ms - TE = 32ms - α = 30 - Slice thickness: 3 mm - AF = 8 -R=2 Ex-vivo Baboon brain imaging [Lazarus et al, ISMRM 2017 #8] CEA SEPTEMBER 6th 2017 PAGE 26

27 EXPERIMENTS: REFERENCE AND SENSITIVITY MAPS Reference Smap CEA SEPTEMBER 6th 2017 PAGE 27

28 EXPERIMENTS: RESULTS FISTA POGM Lipschitz B1 approach CEA SEPTEMBER 6th 2017 PAGE 28

29 EXPERIMENTS: RESULTS Metric: Residual: CEA SEPTEMBER 6th 2017 PAGE 29

30 CONCLUSION / DISCUSSION POGM is faster than FISTA for both case prospective and retrospective The B1 surrogate depends on the accuracy of the sensitivity maps : Regarding the retrospective simulation it seems that the B1 approach is faster Concerning the prospective acquisition the result are not settled The computation time of the surrogate is lower for the B1 solution compared to the Lipschitz constant solution CEA SEPTEMBER 6th 2017 PAGE 30

31 PAGE 31 CEA 10 AVRIL 2012 Commissariat à l énergie atomique et aux énergies alternatives Centre de Saclay Gif-sur-Yvette Cedex T. +33 (0)1 XX XX XX XX F. +33 (0)1 XX XX XX XX Etablissement public à caractère industriel et commercial RCS Paris B Direction Département Service

32 REFERENCES Beck, A., & Teboulle, M. (2009). A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems. SIAM Journal on Imaging Sciences, 2(1), Griswold, M. A., Jakob, P. M., Heidemann, R. M., Nittka, M., Jellus, V., Wang, J., Haase, A. (2002). Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA). Magnetic Resonance in Medicine. Kim, D., & Fessler, J. A. (2016). Optimized first-order methods for smooth convex minimization. Mathematical Programming, 159(1 2), Lustig, M., & Pauly, J. M. (2010). SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space. Magnetic Resonance in Medicine, 64(2), Muckley, M. J., Noll, D. C., & Fessler, J. A. (2015). Fast parallel MR image reconstruction via B1-based, adaptive restart, iterative soft thresholding algorithms (BARISTA). IEEE Transactions on Medical Imaging, 34(2), CEA SEPTEMBER 6th 2017 PAGE 32

33 REFERENCES Pruessmann, K. P., Weiger, M., Scheidegger, M. B., & Boesiger, P. (1999).._SENSE sensitivity encoding for fast MRI.pdf. Magnetic Resonance in Medicine: Official Journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine. Taylor, A. B., Hendrickx, J. M., & Glineur, F. (2017). Exact worst-case convergence rates of the proximal gradient method for composite convex minimization. Retrieved from Uecker, M., Lai, P., Murphy, M. J., Virtue, P., Elad, M., Pauly, J. M., Lustig, M. (2014). ESPIRiT An Eigenvalue Approach to Autocalibrating Parallel MRI: Where SENSE Meets GRAPPA. Magnetic Resonance in Medicine, 71, Nesterov, Y. (1983, February). A method for unconstrained convex minimization problem with the rate of convergence O (1/k2). In Doklady an SSSR (Vol. 269, No. 3, pp ). Drori, Y., & Teboulle, M. (2014). Performance of first-order methods for smooth convex minimization: A novel approach. Mathematical Programming, 145(1 2), CEA SEPTEMBER 6th 2017 PAGE 33

34 REFERENCES Erdogan, H., & Fessler, J. A. (1999). Monotonic algorithms for transmission tomography. IEEE Transactions on Medical Imaging, 18(9), Stucht, D., Danishad, K. A., Schulze, P., Godenschweger, F., Zaitsev, M., & Speck, O. (2015). Highest resolution in vivo human brain MRI using prospective motion correction. PLoS ONE, 10(7), e CEA SEPTEMBER 6th 2017 PAGE 34