An algorithm for reconstructing positive images from noisy data

In this paper we describe a novel method for finding non-negative solutions to linear inverse problems. Such problems include image reconstruction where one is required to deconvolve a known point spread function from the image to produce a clearer image. The method described here is related to the truncated singular function expansion for solving linear inverse problems. The method consists of choosing the non-negative solution with minimum 2-norm whose singular function expansion agrees with the truncated singular function expansion solution in its first N terms. The fact that only the first N singular function coefficients, which are easily derived from the data, are used gives the method robustness with respect to noise and the method is not computationally very demanding.