Isotropic random fields on the sphere have applications in environmental models and astrophysics. The classic Karhunen-Lo\`{e}ve expansion in terms of spherical harmonics has a drawback of requiring full observation of the random field over the sphere. Attempting to solve this difficulty, we study decomposition by needlets --- a highly localised basis --- of an isotropic random field on the sphere. We prove the $L_2$ convergence of the needlet  decomposition of a two-weakly isotropic random field. We use a quadrature rule to construct fully discrete needlets for computation and give the truncation error of the discrete needlet approximation for random fields.


Yu Guang Wang

Research Area

School of Mathematics and Statistics, UNSW


Tue, 29/04/2014 - 10:00am


RC-4082, The Red Centre, UNSW