Image restoration by the method of generalized projections with application to restoration from magnitude

Image restoration problems which involve nonconvex constrains such as the restoration from magnitude problem (RFM) cannot be solved by the method of projections onto convex sets (POCS). An algorithm known as generalized projections is derived and its properties are discussed. We introduce a performance criterion which can be used to measure the performance of the algorithm at any iteration. A method of optimizing (via control of relaxation parameters) the algorithm is described. Comparisons with other RFM methods are furnished.