Image Recovery

Abstract

Image Recovery: Theory and Application. Front Cover; Image Recovery: Theory and Application; Copyright Page; Table of Contents; Preface; Acknowledgments; Chapter 1. Signal Restoration, Functional Analysis, and Fredholm Integral Equations of the First Kind; 1.1 Introduction; 1.2 Hilbert Spaces and Linear Operators; 1.3 Existence of Solutions; 1.4 Least-Squares Solutions and the Operator Pseudoinverse; 1.5 Regularization; 1.6 The Truncated SVD Expansion and Filtering; 1.7 The Iterative Algorithm of Landweber; 1.8 Alternating Orthogonal Projections; 1.9 Regularized Iterative Algorithms; 1.10 Moment Discretization. 1.11 Summary and ConclusionsReference; Chapter 2. Mathematical Theory of Image Restoration by the Method of Convex Projections; 2.1 Introduction; 2.2 Some Properties of Convex Sets in Hilbert Space; 2.3 Nonexpansive Maps and Their Fixed Points-Basic Theorems; 2.4 Iterative Techniques for Image Restoration in a Hilbert Space Setting; 2.5 Useful Projections; 2.6 Summary and New Developments; References; Chapter 3. Bayesian and Related Methods in Image Reconstruction from Incomplete Data; 3.1 Introduction; 3.2 Measurement Space-Null Space; 3.3 Deterministic Solutions; 3.4 The Bayesian Approach. 3.5 Use of Other Kinds of Prior Knowledge3.6 MAP Solutions; 3.7 FAIR-Fit and Iterative Reconstruction; 3.8 Comparison of MAP and FAIR Results; 3.9 A Generalized Bayesian Method; 3.10 Discussion; 3.11 Summary; References; Chapter 4. Image Restoration Using Linear Programming; 4.1 Image Restoration; 4.2 Numerical Example of the Matrix Diagonalization of H; 4.3 Linear Programming; 4.4 Norms of the Error; 4.5 Numerical Example of Minimum L1 Norm Method; 4.6 Computation Considerations; 4.7 Spatial Resolution; 4.8 Results; 4.9 Summary and Conclusions; References. Chapter 5. The Principle of Maximum Entropy in Image Recovey5.1 Introduction; 11.1 Introduction; 5.2 Frieden's Approach; 5.3 Burch, Gull, and Skilling's Approach; 5.4 A Differential Equation Approach to Maximum Entropy Image Restoration; 5.5 Conclusion; References; Chapter 6. The Unique Reconstruction of Multidimensional Sequences from Fourier Transform Magnitude or Phase; 6.1 Introduction; 6.2 Fourier Synthesis from Partial Information; 6.3 The Algebra of Polynomials in Two or More Variables; 6.4 The Magnitude Retrieval Proble; 6.5 The Phase Retrieval Problem; 6.6 Summary and Other Problems.