Developments in Geomathematics, 3: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements focuses on the application of the mathematics of inversion in remote sensing and indirect measurements, including vectors and matrices, eigenvalues and eigenvectors, and integral equations. The publication first examines simple problems involving inversion, theory of large linear systems, and physical and geometric aspects of vectors and matrices. Discussions focus on geometrical view of matrix operations, eigenvalues and eigenvectors, matrix products, inverse of a matrix, transposition and rules for product inversion, and algebraic elimination. The manuscript then tackles the algebraic and geometric aspects of functions and function space and linear inversion methods, as well as the algebraic and geometric nature of constrained linear inversion, least squares solution, approximation by sums of functions, and integral equations. The text examines information content of indirect sensing measurements, further inversion techniques, and linear inversion methods. The publication is a valuable reference for researchers interested in the application of the mathematics of inversion in remote sensing and indirect measurements.

Table of Contents


List of Frequently Used Symbols and their Meanings

Chapter 1. Introduction

1.1. Mathematical Description of the Response of a Real Physical Remote Sensing System

1.2. Examples of Real Inversion Problems


Chapter 2. Simple Problems Involving Inversion

2.1. Algebraic Elimination

2.2. Quadrature, The Reduction of Integral Equations to Systems of Linear Equations


Chapter 3. Theory of Large Linear Systems

3.1. Matrix-Vector Algebra

3.2. Matrix Products

3.3. Inverse of a Matrix

3.4. Transposition and Rules for Product Inversion


Chapter 4. Physical and Geometric Aspects of Vectors and Matrices

4.1. Geometric Vectors

4.2. Norms, Length and Distance

4.3. Orthogonality

4.4. Geometrical View of Matrix Operations

4.5. Eigenvalues and Eigenvectors

4.6. Quadratic Forms, Eigenvalues and Eigenvectors


Chapter 5. Algebraic and Geometric Aspects of Functions and Function Space

5.1. Orthogonality, Norms and Length

5.2. Other Kinds of Orthogonality

5.3. Approximation by Sums of Functions

5.4. Integral Equations

5.5. The Fourier Transform and Fourier Series

5.6. Spectral Form of the Fundamental Integral Equation of Inversion


Chapter 6. Linear Inversion Methods

6.1. Quadrature Inversion

6.2. Least Squares Solution

6.3. Constrained Linear Inversion

6.4. Sample Applications of Constrained Linear Inversion

6.5. Algebraic Nature of Constrained Linear Inversion

6.6. Geometric Nature of Constrained Linear Inversion



© 1977
Elsevier Science
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