Reconstruction of compact binary images from limited Fourier amplitude data.

The problem of reconstructing a binary image from undersampled Fourier amplitude data is considered. This problem maps to an image reconstruction problem in x-ray crystallography. The binary constraint is sufficient to overcome the undersampling and enforce uniqueness, but is insufficient in the case of the additional loss of data that can occur in practice. An iterative projection algorithm is developed that uses binary, connectivity, and compactness constraints to solve the image reconstruction problem. Simulations show the utility of the reconstruction algorithm.