Regularized reconstruction of irregularly sampled scalar light fields

Abstract

This paper addresses the problem of reconstruction of a monochromatic light field based on data points, irregularly distributed within a volume of interest. Such set up is considered to serve a wide area of applications related with three-dimensional display and beam shaping, where physically inconsistent input data is commonly available. Finite-dimensional models of scalar light fields are used to state the reconstruction problem as matrix inversion. Regularized inversion is done by the Tikhonov method, implemented by the iterative algorithm of conjugate gradients. The problem proves to be ill-posed, where the data points inconsistency is fully compensated by the regularized inversion, showing to be attractive for any application.