Introduction to the mathematics of inversion in remote sensing and indirect measurements

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Orthogonality, norms and length 5. Other kinds of orthogonality 5.

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Approximation by sums of functions 5. Integral equations 5. The Fourier transform and Fourier series 5. Quadrature inversion 6.

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Least squares solution 6. Constrained linear inversion 6. Sample applications of constrained linear inversion 6. Algebraic nature of constrained linear inversion 6. More elaborate treatments of error components in linear inversions 7. The synthesis approach to inversion 7.

Solution in terms of kernels 7. The Prony algorithm — a non-linear inversion method 7. Landweber iteration 7. How many measurements? Interdependence of kernels 8. Extrema of quadratic forms 8. Application to the interdependence problem for the kernels 8. Information content 8.

Independence analysis applied to measured quantities 8. Further examples of inversions and their behavior 9. Beneficial aspects of kernel interdependence 9. Inference of more unknowns than there are measurements 9. Inversions in which the unknown is a matrix 9. Determinants 2. Matrix properties involving determinants 3. Solution by determinants of a linear system of equations Suggestions for further reading Name Index Subject index List of frequently used symbols and their meanings CHAPTER 1 Introduction Many, indeed most, of our everyday methods of measurement are indirect.

Forward and inverse modeling

Convolution If the blurring functions or contribution functions shown in Fig. If, for example, we take the following sequence of values for a variable which we shall call y : by averaging the y , represents a smoothing of the y data and can be written as the convolution of the y data, regarded as a suitably defined distribution of y with respect to a continuous variable x , with a smoothing function which is rectangular in shape, of unit area and width 3 i. Delta function To convert the tabulated y -values in the last paragraph to running means is a very simple process, but to describe it rigorously by an integral we have a problem, since the values y 1, y 2, y 3, etc.

Some physical inversion problems in fact can be reduced to the inversion of the Laplace transform: One might at first sight believe that all that is needed here is a swift perusal of the appropriate textbook and extraction of a suitable inversion formula. Start your free 30 days.

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Introduction to the mathematics of inversion in remote sensing and indirect measurements

Anderson TW. Zhu J, Ting K. A Mathematical Theory. Shannon CE. Bell Syst. Poggio T, Koch C. Quasi-perodic climate change on Mars, Mars. University of Arizona Press, Jacquemart D, Barbe A. Birk M. Brown LR, et al. Dudhia A. Microwindow selection for high-spectralresolution sounders.

Dinelli BM. Gaia M, Santurri L. Weidmann D. Information content and optimisation of high spectral resolution remote Measurement London Adv. Space Res. Tristan S. L, Gabriel P, Leesman K. Part I Liquid.

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

J Appl Meteo Climatology ;45 Includes: diagrams, index, bibliography. Seller Inventory ABE. First Edition - may be Reissue.

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