Statistical Image Processing and Multidimensional Modeling

Paul Fieguth

List of Examples (see also Table of Contents, List of Code Samples)

The book contains a number of examples, interspersed throughout the text, with applications at the end of every chapter. Although the applications are too complex to develop in detail, the intent is to show the illustration of the concepts of the chapter to a more substantial problem of practical interest:

Application 2: Ocean Acoustic Tomography
Application 3: Atmospheric Temperature Inversion
Application 4: Temporal Interpolation of Ocean Temperature
Application 5: Synthetic Aperture Radar Interferometry
Application 6: Texture Classification
Application 7: Image Segmentation
Application 8: Global Data Assimilation
Application 9: Surface Reconstruction
Application 10: Video Denoising
Application 11: Multi-Instrument Fusion of Porous Media

The goal of the text is to take concepts of inverse problems, estimation theory, and random fields beyond their mathematical definition, and to try to develop some degree of insight and intuition. The large number of examples in the text are designed as asides, to numerically explore certain small topics. As a sample, links are provided to the first two examples.

Example 2.1 Root Finding is an Inverse Problem
Example 2.2 Interpolation and Posedness
Example 2.3 Regression and Posedness
Example 2.4 Measurement Models and Conditioning
Example 2.5 Matrix Conditioning
Example 2.6 Interpolation and Regularization
Example 2.7 Interpolation and Smoothness Models
Example 2.8 Interpolation and Cross Validation
Example 2.9 State Estimation and Sampling
Example 3.1 Linear Regression is Least Squares
Example 3.2 Simple Scalar Estimation
Example 3.3 Prior Mean Removal
Example 3.4 Static Estimation and Sampling
Example 4.1 Dynamic Estimation and Sampling
Example 4.2 Kalman Filtering and Interpolation
Example 4.3 Recursive Smoothing and Interpolation
Example 5.1 Multidimensional Interpolation
Example 5.2 Model Inference
Example 6.1 Example Markov Kernels
Example 6.2 Robust Estimation
Example 6.3 Markov Model Inference and Model Order
Example 6.4 Model Inference and Conditioning
Example 7.1 Multiple Hidden Fields
Example 8.1 Principal Components for Remote Sensing
Example 8.2 Overlapped Local Processing
Example 8.3 FFT and Spatial Statistics
Example 8.4 Hierarchical Bases
Example 9.1 Iterative Solutions to Interpolation
Example 9.2 Eigendistributions of Iterative Interpolators
Example 10.1 Interpolation by Marching
Example 11.1 Annealing and Energy Barriers

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