The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural symmetries. For such a method to be employed by researchers from a wide range of backgrounds, it is crucial that its reliance on prior knowledge about the system is minimized, and that it is robust under various conditions. Here, we present a method employing band-limited spherical functions to enable the reconstruction of reciprocal space maps of a wide variety of nanostructures. This method has been thoroughly tested and compared to existing methods in its ability to retrieve known reciprocal space maps, as well as its robustness to changes in initial conditions, using both simulations and experimental data. The anchoring of this method in a framework of integral geometry and linear algebra highlights its possibilities and limitations.