Image reconstruction from localized Fourier magnitude

Fourier transform magnitude is, in many cases, the only measurable data in fields such as optics, x-ray imaging, crystallography and astronomy. Spectral phase information is impractical to obtain in these instances, due to the relatively short wavelength involved. In this paper a new algorithm for image reconstruction from localized spectral magnitude is presented. The algorithm is based on localized Fourier transform magnitudes and a single spatial sample to fully reconstruct an image. The process reconstructs successively larger image blocks, until the entire image is restored, using the spatial sample as initial data. It is shown, that even in cases where the spatial sample is badly corrupted, it has little effect on the reconstructed image. The algorithm is analyzed in the presence of noise, and simulation results are presented.