3D Reconstruction from spherical harmonic coefficients?

I am working on a project to reconstruct a 3D object from rotation invariant shape descriptors. So far I have worked in the process of converting a 3D object to a harmonic map and calculating the spherical harmonic coefficients and inturn the rotation invariant shape descriptors which is the norm of all spherical harmonic coefficients. I have basically implemented the works of the following research paper. I would like to reconstruct the 3D object back from the shape descriptors. I am unable to find any methods for the reconstruction and would like to know whether there are any methods for the reconstruction from the shape descriptors.