Introduction to the Mathematics of Inversion in Remote Sensing and Indirecting Measurements (Developments in Geomathematics, Vol 3) (Development in Geomathematics)

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. Content: Inside Front Cover Page II Front Matter Page III Copyright page Page IV Preface Pages V-VI S. TWOMEY List of frequently used symbols and their meanings Pages IX-X Chapter 1 - Introduction Pages 1-25 Chapter 2 - Simple problems involving inversion Pages 27-36 Chapter 3 - Theory of large linear systems Pages 37-52 Chapter 4 - Physical and geometric aspects of vectors and matrices Pages 53-81 Chapter 5 - Algebraic and geometric aspects of functions and function space Pages 83-113 Chapter 6 - Linear inversion methods Pages 115-149 Chapter 7 - Further inversion techniques Pages 151-184 Chapter 8 - Information content of indirect sensing measurements Pages 185-212 Chapter 9 - Further topics Pages 213-230 Appendix Pages 231-234 Suggestions for further reading Pages 235-237 Name index Page 239 Subject index Pages 241-243 This Graduate-level Monograph Develops The Background And Fundamental Theory Of Inversion Processes Used In Remote Sensing. The Treatment Starts At An Elementary Level And Is Largely Self-contained; Each Chapter Begins With An Elementary Discussion Outlining Problems And Questions To Be Covered And Concludes With A Bibliography. After An Introductory Chapter, The Text Progresses To Simple Problems Involving Inversion, The Theory Of Large Linear Systems, Physical And Geometric Aspects Of Vectors And Matrices, And Algebraic And Geometric Aspects Of Functions And Function Space. Subsequent Chapters Explore Linear Inversion Methods, Information Content Of Indirect Sensing Measurements, And Additional Topics. A Helpful Three-part Appendix And Suggestions For Further Reading Conclude The Text.