Applied Iterative Methods is a self-contained treatise suitable as both a reference and a graduate-level textbook in the area of iterative algorithms. It is the first book to combine subjects such as optimization, convex analysis, and approximation theory and organize them around a detailed and mathematically sound treatment of iterative algorithms. Such algorithms are used in solving problems in a diverse area of applications, most notably in medical imaging such as emission and transmission tomography and magnetic-resonance imaging, as well as in intensity-modulated radiation therapy. Other applications, which lie outside of medicine, are remote sensing and hyperspectral imaging. This book details a great number of different iterative algorithms that are universally applicable.
Table of Contents
Part I: Preliminaries 1. Introduction 2. Background 3. BasicConcepts 4. Metric Spaces and Norms Part II: Overview 5. Operators 6. Problems and Algorithms Part III: Operators 7. Averaged and Paracontractive Operators Part IV: Algorithms 8. The Algebraic Reconstruction Technique 9. Simultaneous and Block-Iterative ART 10. Jacobi and Gauss-Seidel Methods 11. Conjugate-Direction Methods in Optimization Part V: Positivity in Linear Systems 12. The Multiplicative ART (MART) 13. Rescaled Block-Iterative (RBI) Methods Part VI: Stability 14. Sensitivity to Noise 15. Feedback in Block-Iterative Reconstruction Part VII: Optimization 16. Iterative Optimization 17. Convex Sets and Convex Functions 18. Generalized Projections onto Convex Sets 19. The Split Feasibility Problem 20. Nonsmooth Optimization 21. An Interior-Point Optimization Method 22. Linear and Convex Programming 23. Systems of Linear Inequalities 24. Constrained Iteration Methods 25. Fourier Transform Estimation Part VIII: Applications 26. Tomography 27. Intensity-Modulated Radiation Therapy 28. Magnetic-Resonance Imaging 29. Hyperspectral Imaging 30. Planewave Propagation 31. Inverse Problems and the Laplace Transform 32. Detection and Classification