Solving Non-negative Linear Inverse Problems with the NeAREst Method

This paper introduces the theoretical development of a numerical method, named NeAREst, for solving nonnegative linear inverse problems, which arise often from physical or probabilistic models, especially, in image estimation with limited and indirect measurements. The Richardson-Lucy (RL) iteration is omnipresent in conventional methods that are based on probabilistic assumptions, arguments and techniques. Without resorting to probabilistic assumptions, NeAREst retains many appealing properties of the RL iteration by utilizing it as the substrate process and provides much needed mechanisms for acceleration as well as for selection of a target solution when many admissible ones exist. Keyword list: non-negative linear inverse problems, nested models at multiple scales, adaptive relaxation, Richardson-Lucy iteration, image estimation