Positive iterative deconvolution with energy conservation

Abstract

An algorithm for solving a convolution-type Fredholm equation of the first kind in the isoplanatic case is presented. The inverse operator is therefore expanded into a geometric sum. Partial sums are calculated analytically to increase convergence. In an iterative scheme, by considering conservation of energy, positivity as a nonlinear constraint is applied. This approach guarantees the exact solution in the case of complete information and leads to stable results for incomplete information and in the presence of noise. Photon noise, readout noise, and noise by computer quantization are considered, and results of one-dimensional computer experiments are discussed. © 1998 American Institute of Physics.