Lecture 01 Describing Inverse Problems
Lecture 02 Probability
and Measurement Error, Part 1
Lecture 03 Probability
and Measurement Error, Part 2
Lecture 04 The
L2 Norm and Simple Least Squares
Lecture 05 A
Priori Information and Weighted Least Squared
Lecture 06 Resolution
and Generalized Inverses
Lecture 07 Backus-Gilbert
Inverse and the Trade Off of Resolution and Variance
Lecture 08 The
Principle of Maximum Likelihood
Lecture 09 Inexact
Theories
Lecture 10 Prior
Covariance and Gaussian Process Regression
Lecture 11 Non-uniqueness
and Localized Averages
Lecture 12 Vector
Spaces and Singular Value Decomposition
Lecture 13 Equality
and Inequality Constraints
Lecture 14 L1
, L∞ Norm Problems and Linear Programming
Lecture 15 Nonlinear
Problems: Grid and Monte Carlo Searches
Lecture 16 Nonlinear
Problems: Newton’s Method
Lecture 17 Nonlinear
Problems: MCMC and Bootstrap Confidence
Intervals
Lecture 18 Factor
Analysis
Lecture 19 Varimax
Factors, Empirical Orthogonal Functions
Lecture 20 Backus-Gilbert
Theory for Continuous Problems; Radon’s Problem
Lecture 21 Linear
Operators and Their Adjoints
Lecture 22 Fréchet
Derivatives
Lecture 23 Estimating
a Parameter in a Differential Equation
Lecture 24 Exemplary
Inverse Problems, incl. Filter Design
Lecture 25 Exemplary
Inverse Problems, incl. Earthquake Location
Lecture 26 Exemplary
Inverse Problems, incl. Vibrational Problems