  We demonstrate a novel approach to the reconstruction of scanning probe x-ray
diffraction tomography data with anisotropic poly crystalline samples. The
method involves reconstructing a voxel map containing an orientation
distribution function in each voxel of an extended 3D sample. This method
differs from existing approaches by not relying on a peak-finding and is
therefore applicable to sample systems consisting of small and highly mosaic
crystalline domains that are not handled well by existing methods. Samples of
interest include bio-minerals and a range of small-graines microstructures
common in engineering metals. By choosing a particular kind of basis functions,
we can effectively utilize non-negativity in orientation-space for samples with
sparse texture. This enables us to achieve stable solutions at high angular
resolutions where the problem would otherwise be under determined. We
demonstrate the new approach using data from a shot peened martensite sample
where we are able to map the twinning micro structure in the interior of a bulk
sample without resolving the individual lattice domains. We also demonstrate
the approach on a piece of gastropods shell with a mosaic micro structure.
