Codomain scale space and regularization for high angular resolution diffusion imaging

Regularization is an important aspect in high angular resolution diffusion imaging (HARDI), since, unlike with classical diffusion tensor imaging (DTI), there is no a priori regularity of raw data in the co-domain, i.e. considered as a multispectral signal for fixed spatial position. HARDI preprocessing is therefore a crucial step prior to any subsequent analysis, and some insight in regularization paradigms and their interrelations is compulsory. In this paper we posit a codomain scale space regularization paradigm that has hitherto not been applied in the context of HARDI. Unlike previous (first and second order) schemes it is based on infinite order regularization, yet can be fully operationalized. We furthermore establish a closed-form relation with first order Tikhonov regularization via the Laplace transform.