Symmetry-constrained 3-D interpolation of viral X-ray crystallography data

A three-dimensional (3-D) interpolation problem that is important in viral X-ray crystallography is considered. The problem requires new methods because the function is known to have icosahedral symmetry, the data is corrupted by experimental errors and therefore lacks the symmetry, the problem is 3-D, the measurements are irregularly spaced, and the number of measurements is large (10^4). A least-squares approach is taken using two sets of basis functions: the functions implied by a minimum-energy bandlimited exact interpolation problem and a complete orthonormal set of bandlimited functions. A numerical example of the Cowpea Mosaic Virus is described.