Journal ArticleDOI
Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion
Albert Tarantola,Bernard Valette +1 more
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TLDR
In this article, a general definition of the nonlinear least squares inverse problem is given, where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodierentia l equations).Abstract:
We attempt to give a general definition of the nonlinear least squares inverse problem. First, we examine the discrete problem (finite number of data and unknowns), setting the problem in its fully nonlinear form. Second, we examine the general case where some data and/or unknowns may be functions of a continuous variable and where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodierentia l equations). As particular cases of our nonlinear algorithm we find linear solutions well known in geophysics, like Jackson’s (1979) solution for discrete problems or Backus and Gilbert’s (1970) a solution for continuous problems.read more
Citations
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Geophysical inversion with a neighbourhood algorithm—I. Searching a parameter space
TL;DR: In this article, a derivative-free search method for finding models of acceptable data fit in a multidimensional parameter space is presented, which falls into the same class of method as simulated annealing and genetic algorithms, which are commonly used for global optimization problems.
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Monte Carlo sampling of solutions to inverse problems
Klaus Mosegaard,Albert Tarantola +1 more
TL;DR: In inverse problems, obtaining a maximum likelihood model is usually not sucient, as the theory linking data with model parameters is nonlinear and the a posteriori probability in the model space may not be easy to describe.
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Redfield ratios of remineralization determined by nutrient data analysis
TL;DR: A nonlinear inverse method is applied to nutrient data upon approximately 20 neutral surfaces in each of the South Atlantic, Indian, and Pacific basins, between 400 and 4000 m depth by accounting for the gradient in nutrients due to the mixing of [open quotes]preformed[close quotes] concentrations of the major water masses, the nutrient changes due to biological activity are examined, and the time-mean, basinwide Redfield ratios calculated.
Journal Article
Inverse problems = Quest for information
Albert Tarantola,Bernard Valette +1 more
TL;DR: The inverse problem may be formulated as a problem of combination of information: the experimental information about data, the a priori information about parameters, and the theoretical information, and it is shown that the general solution of the non-linear inverse problem is unique and consistent.
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Radio Tomographic Imaging with Wireless Networks
Joey Wilson,Neal Patwari +1 more
TL;DR: A linear model for using received signal strength (RSS) measurements to obtain images of moving objects and mean-squared error bounds on image accuracy are derived, which are used to calculate the accuracy of an RTI system for a given node geometry.
References
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Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and Its Applications.
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Uniqueness in the Inversion of Inaccurate Gross Earth Data
George E. Backus,Freeman Gilbert +1 more
TL;DR: In this article, it was shown that a given set G of measured gross Earth data permits such a construction of localized averages, and if so, how to find the shortest length scale over which G gives a local average structure at a particular depth if the variance of the error in computing that local average from G is to be less than a specified amount.
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The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.
TL;DR: In this paper, the discrete general linear inverse problem is reduced to a set of m equations in n unknowns and a linear combination of the eigenvectors of the coefficient matrix can be used to determine parameter resolution and information distribution among the observations.