Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements

In this graduate-level monograph, S. Twomey, a professor of atmospheric sciences, develops the background and fundamental theory of inversion processes used in remote sensing — e.g., atmospheric temperature structure measurements from satellites—starting at an elementary level.
The text opens with examples of inversion problems from a variety of disciplines, showing that the same problem—solution of a Fredholm linear integral equation of the first kind — is involved in every instance. A discussion of the reduction of such integral equations to a system of linear algebraic equations follows. Subsequent chapters examine methods for obtaining stable solutions at the expense of introducing constraints in the solution, the derivation of other inversion procedures, and the detailed analysis of the information content of indirect measurements. Each chapter begins with a discussion that outlines problems and questions to be covered, and a helpful Appendix includes suggestions for further reading.

Sean Twomey (1927–2012) was born in Cork County, Ireland in 1927 and received his academic degrees, including his Ph.D. from the National University of Ireland in Galway. He held research appointments with several institutions in Australia and the United States including the U.S. Weather Bureau and the Naval Research Laboratory, and was a Professor at The University of Arizona's Department of Atmospheric Sciences from 1976 until his retirement in 1990. He was the author of many scientific papers in areas such as atmospheric radiation, aerosol and cloud physics, and inversion mathematics and of another influential textbook, Atmospheric Aerosols, 1979. 

Preface
List of Frequently Used Symbols
1. Introduction
2. Simple Problems Involving Inversion
3. Theory of Large Linear Systems
4. Physical and Geometric Aspects of Vectors and Matrices.
5. Algebraic and Geometric Aspects of Functions and Function Space.
6. Linear Inversion Methods
7. Further Inversion Techniques
8. Information Content of Indirect Sensing Measurements
9.Further Topics
Appendix:
1. Determinants
2. Matrix Properties Involving Determinants
3. Solution by Determinants of a Linear System of Equations.
Suggestions for Further Reading
Name Index
Subject Index