On numerical orientation averaging with spherical Fibonacci point sets and compressive scheme

For light scattering computations, we propose to perform orientation averaging with spherical Fibonacci point sets. Furthermore, a compressive scheme is introduced to recover light scattering quantities for all orientations based on the compressive sensing theory that exploits the priori information that these scattering quantities are sparse in the spherical harmonic domain. The scheme solves convex optimization problem by minimizing the l1-norm of spherical harmonic expansion coefficients of light scattering quantities. Combining with spherical Fibonacci point sets, this compressive scheme can achieve highly accurate recovery results with fewer orientations than conventional orientation averaging schemes. It is indicated that the proposed compressive orientation averaging scheme with Fibonacci point sets is straightforward to implement and shows good performance in error convergence.