Tv/l1 Minimization for Hardi Data Denoising with Reduced Constraint

We denoise High Angular Resolution Diffusion Imaging (HARDI) data, a necessary step for reconstruction of fibers and pathways in the living brain. HARDI gives more accurate information than diffusion tensor imaging (DTI) and allows to reconstruct highly complex fiber architecture. Intensity data is given at all voxels and directions on the sphere. A tuning parameter b is used to collect the data. Although larger b values help to more accurately measure the water diffusion in the brain, more noise is generated as well. We directly denoise raw HARDI data and not the pre-processed orientation distribution functions (ODFs). We propose to minimize an energy composed of three terms: vectorial total variation, L data term, and a logarithmic barrier term to realize the constraints imposed by the image formation model. We present experimental results for denoising synthetic and real HARDI data. Using two measures of restoration accuracy, we can conclude that the proposed denoising model improves data quality. The algorithm is simple and relatively fast.