Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions

We present an efficient algorithm to solve a class of two- and 2.5-dimensional (2-D and 2.5-D) Fredholm integrals of the first kind with a tensor product structure and nonnegativity constraint on the estimated parameters of interest in an optimization framework. A zeroth-order regularization functional is used to incorporate a priori information about the smoothness of the parameters into the problem formulation. We adapt the Butler-Reeds-Dawson (1981) algorithm to solve this optimization problem in three steps. In the first step, the data are compressed using singular value decomposition (SVD) of the kernels. The tensor-product structure of the kernel is exploited so that the compressed data is typically a…