HARDI Denoising: Variational Regularization of the Spherical Apparent Diffusion Coefficient sADC

We denoise HARDI (High Angular Resolution Diffusion Imaging) data arising in medical imaging. Diffusion imaging is a relatively new and powerful method to measure the 3D profile of water diffusion at each point. This can be used to reconstruct fiber directions and pathways in the living brain, providing detailed maps of fiber integrity and connectivity. HARDI is a powerful new extension of diffusion imaging, which goes beyond the diffusion tensor imaging (DTI) model: mathematically, intensity data is given at every voxel and at any direction on the sphere. However, HARDI data is usually highly contaminated with noise, depending on the b-value which is a tuning parameter preselected to collect the data. Larger b-values help to collect more accurate information in terms of measuring diffusivity, but more noise is generated by many factors as well. So large b-values are preferred, if we can satisfactorily reduce the noise without losing the data structure. We propose a variational method to denoise HARDI data by denoising the spherical Apparent Diffusion Coefficient (sADC), a field of radial functions derived from the data. We use vectorial total variation regularization, an L1 data fidelity term and the logarithmic barrier function in the minimization. We present experiments of denoising synthetic and real HARDI data.