Least-squares reconstruction of spatially limited objects using smoothness and non-negativity constraints

Abstract

This paper describes an approach to reconstructing an optical object which has been subjected to low pass spatial-frequency filtering. The object is assumed to be of limited and known spatial extent and is further known to be non-negative and reasonably smooth. The smoothness constraint is incorporated into a regularizing matrix in a novel way. This matrix defines a regularized version of the original imaging equation, which is then solved using least-squares estimation under a non-negativity constraint. Combining constraints in this way can lead to reconstructions of very high quality.