Efficient correction of adjacency effects for high-resolution imagery: integral equations, analytic continuation, and Padé approximants

This paper deals with the inverse problem of determining surface reflectances from top of atmosphere reflectance measurements when adjacency effects are significant, as is the case with high-resolution imagery. The problem is rigorously formulated as an integral equation of the second kind for the unknown surface reflectance. It is solved by summing the Neumann series associated with the integral equation. Conditions for the convergence of the series are established and, in cases where the Neumann series diverges, analytic continuation by Padé approximants is used to extend the range of applicability of the method. Padé approximants provide very efficient algorithms for the reconstruction of the unknown surface reflectance. In cases where the Neumann series converges Padé approximants yield accurate results at a fraction of the computational cost of the Neumann series. The efficiency of the method is further enhanced by fast FFT-based evaluation of local reflectance averages. The efficiency and versatility of the method are demonstrated on Landsat-based examples.