Smoothing Fields of Frames Using Conjugate Norms on Reproducing Kernel Hilbert Spaces

Diffusion tensor imaging provides structural information in medical images in the form of a symmetric positive matrix that provides, at each point, the covariance of water diffusion in the tissue. We here describe a new approach designed for smoothing this tensor by directly acting on the field of frames provided by the eigenvectors of this matrix. Using a representation of fields of frames as linear forms acting on smooth tensor fields, we use the theory of reproducing kernel Hilbert spaces to design a measure of smoothness based on kernels which is then used in a denoising algorithm. We illustrate this with brain images and show the impact of the procedure on the output of fiber tracking in white matter.