This paper describes mathematical tools applicable to the reconstruction of anisotropic velocity distributions through the unfolding of data coming from techniques like collective Thomson scattering or laser induced fluorescence, where one-dimensional projections of the velocity space along a "scattering" direction are measured. Salient details of gyrotropic distributions can be reproduced when using simultaneous measurements from two or three scattering directions. The mathematical framework can also be used to optimize instrumental geometry for maximal resolution of the velocity distribution. An example is given based on alpha particle distribution in the Joint European Torus tokamak [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)]. (C) 2004 American Institute of Physics.