Advanced magnetic resonance imaging (MRI) systems play a significant role in informing diagnostic and treatment plans. Reducing the acquisition time while improving the imaging quality of these systems is receiving great interest from the scientific community, as it represents a key imaging technique to probe soft tissues (e.g., the brain). To achieve this goal, parallel imaging (PI) has been introduced in the late 90s to accelerate the acquisition by undersampling the k-space in a deterministic way with the help of spatial complementary of multi-receiver coils. Another strategy is based on the use of Compressed Sensing (CS) theory for decreasing even more acquisition times while providing theoretical guarantees of exact reconstruction in some particular cases. This theory is based on three main steps: (i) sparsity or compressibility of MR images in a given dictionary (e.g., wavelets, curvelets, ...), (ii) incoherence between sensing and sparsity bases leading to pseudo-random sampling schemes and (iii) nonlinear image reconstruction for promoting image sparsity in the wavelet domain.

Many algorithms have been developed to reconstruct MR images from the combination of PI and CS techniques (cf e.g. [1–4]). Such algorithms generally aim at jointly estimating the reconstructed image and the sensitivity maps associated with the multiple receivers. The latter maps can be either extracted as a preprocessing step [5] to reduce the computing time dedicated to MR image reconstruction or jointly inferred with the image itself [6]. Although faster, the former approach has the disadvantage to be less reliable in case of patient’s motion.

The proposed internship will combine these two approaches by proposing a robust estimation of the reconstruction image while accounting for possible artefacts due to the poor estimation of the sensitivity maps. The project will build on our recent work and will be based on three main steps: (i) the generalization of the observation model to account for data statistics and known properties of the MR images of interest, (ii) the design and use of a state-of-the-art optimization algorithm (alternating direction method of multipliers [7,8]) to estimate the parameters of interest, (iii) validation of the proposed strategy on available real data prospectively collected in a compressed manner at 7 Tesla and comparison with competitive algorithms, (iv) generalization of the proposed strategy to cutting-edge sensing techniques as multi-parametric quantitative MRI (e.g. Magnetic Resonance Fingerprinting).

Skills: We look for candidates strongly motivated by challenging research topics at the crossroad between applied mathematics, MR physics and computer science. Applicants should possess a solid background in signal processing including wavelet theory and optimization and possess demonstrated skills in software programming. Proficiency in Matlab is expected and preliminary experience in Python programming is very desirable as the successful developments will be integrated in the open-source Pysap software. Basic knowledge in MRI would be a plus.

Keywords: Computational imaging, reconstruction, optimization, compressed sensing, MRI.

References:

[1] L. Ying and J. Sheng, “Joint image reconstruction and sensitivity estimation in SENSE (JSENSE),” Magnetic Resonance in Medicine, vol. 57, no. 6, pp. 1196–1202, 2007.

[2] B. Liu, Y. M. Zou, and L. Ying, “Sparsesense: application of compressed sensing in parallel MRI,” in Information Technology and Applications in Biomedicine, 2008. ITAB 2008. International Conference on. IEEE, 2008, pp. 127– 130.

[3] M. Uecker, T. Hohage, K. T. Block, and J. Frahm, “Image reconstruction by regularized nonlinear inversion—joint estimation of coil sensitivities and image content,” Magnetic Resonance in Medicine, vol. 60, no. 3, pp. 674–682, 2008.

[4] R. Otazo, D. Kim, L. Axel, and D. K. Sodickson, “Combination of compressed sensing and parallel imaging for highly accelerated first-pass cardiac perfusion mri,” Magnetic Resonance in Medicine, vol. 64, no. 3, pp. 767–776, 2010.

[5] L. E. Gueddari, C. Lazarus, H. Carrie, A. Vignaud, and P. Ciuciu, “Self-calibrating nonlinear reconstruction al- gorithms for variable density sampling and parallel reception MRI,” in 10th IEEE SAM workshop, 7 2018, pp. 1–5.

[6] M. Uecker, P. Lai, M. J. Murphy, P. Virtue, M. Elad, J. M. Pauly, S. S. Vasanawala, and M. Lustig, “ESPIRiT – an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA,” Magnetic Resonance in Medicine, vol. 71, no. 3, pp. 990–1001, 2014.

[7] A. Halimi, J. M. Bioucas-Dias, N. Dobigeon, G. S. Buller, and S. McLaughlin, “Fast hyperspectral unmixing in presence of nonlinearity or mismodeling effects,” IEEE Transactions on Computational Imaging, vol. 3, no. 2, pp. 146–159, 6 2017.

[8] M. Afonso, J. Bioucas-Dias, and M. Figueiredo, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Trans. Image Processing, vol. 20, no. 3, pp. 681–695, March 2011.

Supervisor name:

Dr Abderrahim Halimi and Dr Philippe Ciuciu

Supervisor and Deputy email addresses:

a.halimi@hw.ac.uk

philippe.ciuciu@cea.fr