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Optimal regularization for MR diffusion signal reconstruction

In this paper we address two problems related to the parametric reconstruction of the diffusion signal in the complete 3D Q-space. We propose a modified Spherical Polar Fourier (mSPF) basis to naturally impose the continuity of the diffusion signal on the whole space. This mathematical constraint results in a dimension reduction with respect to the original SPF basis. In addition, we derive the expression of a Laplace regularization operator in this basis, and compute optimal regularization weight using generalized cross validation (GCV). Experiments on synthetic and real data show that this regularization leads to a more accurate reconstruction than the commonly used low-pass filters.