We consider mathematical algorithms for the restoration of object information from finitely many measurements of the object's spectrum, with particular emphasis on the development of linear and nonlinear non-iterative methods that can incorporate prior information about object extent and shape. The linear method presented here generalizes the minimum energy bandlimited extrapolation procedure, which is the closed form limit of Gerchberg-Papoulis iteration in this case. The nonlinear method generalizes the maximum entropy method (MEM) of Burg.
Charles L. Byrne,
Raymond M. Fitzgerald,
"Image Restoration And Resolution Enhancement", Proc. SPIE 0413, Inverse Optics I, (22 September 1983); doi: 10.1117/12.935853; https://doi.org/10.1117/12.935853