Diffusion MRI Signal Reconstruction with Continuity Constraint and Optimal Regularization

Emmanuel Caruyer 1 Rachid Deriche 1
1 ATHENA - Computational Imaging of the Central Nervous System
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In diffusion MRI, the reconstruction of the full Ensemble Average Propagator (EAP) provides new insights in the diffusion process and the underlying microstructure. The reconstruction of the signal in the whole Q-space is still extremely challenging however. It requires very long acquisition protocols, and robust reconstruction to cope with the very low SNR at large b-values. Several reconstruction methods were proposed recently, among which the Spherical Polar Fourier (SPF) expansion, a promising basis for signal reconstruction. Yet the reconstruction in SPF is still subject to noise and discontinuity of the reconstruction. In this work, we present a method for the reconstruction of the diffusion attenuation in the whole Q-space, with a special focus on continuity and optimal regularization. We derive a modified Spherical Polar Fourier (mSPF) basis, orthonormal and compatible with SPF, for the reconstruction of a signal with continuity constraint. We also derive the expression of a Laplace regularization operator in the basis, together with a method based on generalized cross validation for the optimal choice of the parameter. Our method results in a noticeable dimension reduction as compared with SPF. Tested on synthetic and real data, the reconstruction with this method is more robust to noise and better preserves fiber directions and crossings.
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Medical Image Analysis, Elsevier, 2012, 16 (6), pp.1113-1120. 〈10.1016/j.media.2012.06.011〉
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Emmanuel Caruyer, Rachid Deriche. Diffusion MRI Signal Reconstruction with Continuity Constraint and Optimal Regularization. Medical Image Analysis, Elsevier, 2012, 16 (6), pp.1113-1120. 〈10.1016/j.media.2012.06.011〉. 〈hal-00711883〉

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