Constrained Linear Algebraic Deconvolution of Poisson Data
D. D. Dixon, D. Bhattacharya,
T. J. O'Neill, O. T. Tümer, R. S. White, A. D. Zych,
and Wm. A. Wheaton
Astrophysical Journal, 457, 789 (1996)
Abstract
A new method is demonstrated for the deconvolution of Poisson data from
an associated linear instrument response. Building on the method of
Direct Linear Algebraic Deconvolution (DLAD, Wheaton et al 93), the
technique is extended by including the additional
physical constraint that the deconvolved source fluxes be non-negative.
This constraint stabilizes the solution against fluctuations that
appear due to noisy data, and greatly lowers the variances in the
computed fluxes. The uncertainties in the deconvolved fluxes are directly
computable. The algorithm is demonstrated for deconvolution of
Compton double-scatter gamma-ray telescope data.