Iterative reconstruction of space-limited scenes from noisy frequency-domain measurements

An iterative projection approach is introduced, which aims specifically at removing a priori information and constraint incompatibility due to noisy measurements. There to a soft frequency domain measurement constraint is proposed. The softness refers to accepting an algorithm iterate whenever it is "close enough" (depending on expected noise level) to the noisy measurements. The scene limitation constraint is softened by providing a smooth transition region between the known extent and zeroed regions of the scene domain. The operators involved are shown to be nonexpansive, and the iterative algorithm may naturally have many solutions, all of which are compatible with the a priori information.