Optimal representation of images by localized phase

The POCS algorithm (Projection Onto Convex Sets) used for image reconstruction from spectral phase is investigated. The convergence rate of the algorithm is defined and analyzed, and the characteristics of images optimally represented by phase-only information are presented. It is concluded that images of geometric form are most efficiently represented by 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 recently reported advantages of the localized phase representation over the global approach, and suggest possible compression schemes.