Phase Retrieval and Zero Crossings: Mathematical Methods in Image Reconstruction

1 Introduction.- 2 Polynomials: A Review.- 3 Entire Functions and Signal Recovery.- 4 Homometric Distributions.- 5 Analytic Signals and Signal Recovery from Zero Crossings.- 6 Signal Representation by Fourier Phase and Magnitude in One Dimension.- 7 Recovery of Distorted Band-Limited Signals.- 8 Compact Operators, Singular Value Analysis and Reproducing Kernel Hilbert Spaces.- 9 Kaczmarz Method, Landweber Iteration, Gerchberg-Papoulis and Regularization.- 10 Two Dimensional Signal Recovery Problems.- 11 Reconstruction Algorithms in Two Dimensions.- 12 Nonexpansive Maps and Signal Recovery.- 13 Projections on Convex Sets in Signal Recovery.- 14 Method of Generalized Projections and Steepest Descent.- 15 Closed Form Reconstruction of the Support and the Object.- 16 Fienup's Input-Output Algorithms and Variations on this Theme.- 17 Topics and Applications of Signal Recovery.- A The Geometry of Projections on Convex Sets.- B Reference Summary.- C References.