Abstract: A new transform is disclosed, applying methods of group theory, with which the composition of a voxel of three channels comprising isotropic, single fiber and multiple fiber components can be determined, as well as the magnitude and orientation of the diffusion field. Asymmetries produced by experimental artifacts fall into channels distinct from the fiber channels, allowing their separation and a subsequent reduction in noise from the reconstructed fibers.

Abstract: A scratching post assembly for pets comprising a generally C-shaped mounting bracket including a longitudinally extending main body portion and top and bottom flanges extending at approximately right angles from the main body portion, the top and bottom flanges each including an aperture formed therein, an elongated mounting rod including a stop element attached to one end thereof, the mounting rod extending through the flange apertures with the stop element resting upon the top flange, a series of stackable, generally cylindrically-shaped, abrasion resistant cork elements axially mounted on the mounting rod extending between the top and bottom flanges, and the mounting rod being removable for allowing interchanging or replacement of the cork elements.