Optimal reconstruction of images from localized phase

The importance of localized phase in signal representation is investigated. The convergence rate of the POCS algorithm (projection onto convex sets) used for image reconstruction from spectral phase is defined and analyzed, and the characteristics of images optimally reconstructed from phase-only information are presented. It is concluded that images of geometric form are most efficiently reconstructed from their spectral phase, whereas images of symmetric form have the poorest convergence characteristics. The transition between the two extremes is shown to be continuous. The results provide a new approach and analysis of the previously reported advantages of the localized phase representation over the global approach, and suggest possible compression schemes.