Recover the phase of a complex signal from its amplitude in two domains. The algorithm alternately enforces amplitude constraints in image and Fourier domains until convergence.
Target image
Recovered image
Fourier amplitude
Error history
Gerchberg-Saxton (1972): alternating projections between image-domain and Fourier-domain amplitude constraints recover the missing phase. Fundamental to crystallography (X-ray phase problem), electron microscopy, and holography.