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 becau se the function is known to have icosahedral symmetry, the data is corrupte d 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 tno sets of basi s functions: the functions implied by a minimum-energy bandlimited exact in terpolation problem and a complete orthonormal set of bandlimited functions . A numerical example of the Cowpea Mosaic Virus is described.