A spatial regularization framework of orientation diffusion functions using total variation and wavelet

We introduce a variational framework and a numerical method for simultaneous reconstruction and regularization of orientation distribution functions (ODF). The regularization is performed both angularly and spatially. The spatial regularization is based on the sparsity of MR images in finite difference domain and wavelet domain. The angular regularization is performed using Laplace-Beltrami operator on the unit sphere. The modified primal-dual hybrid gradient scheme is applied to solve the model efficiently. We apply the framework on two ODF reconstruction models. The experimental results indicate that with spatial and angular regularization in the process of reconstruction, we can get better directional structures of reconstructed ODFs.