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.
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