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Inverse Problems: Inverse Problem, Inverse Problem for Lagrangian Mechanics, Regularization, Tomographic Reconstruction, Seismic Tomography
Chapters: Inverse Problem, Inverse Problem for Lagrangian Mechanics, Regularization, Tomographic Reconstruction, Seismic Tomography, Electrical Resistivity Tomography, Reverse Monte Carlo, Inverse Scattering Problem, Acoustic Source Localization. Source: Wikipedia. Pages: 33. Not illustrated. Free updates online. Purchase includes a free trial membership...
Chapters: Inverse Problem, Inverse Problem for Lagrangian Mechanics, Regularization, Tomographic Reconstruction, Seismic Tomography, Electrical Resistivity Tomography, Reverse Monte Carlo, Inverse Scattering Problem, Acoustic Source Localization. Source: Wikipedia. Pages: 33. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: An inverse problem is the task that often occurs in many branches of science and mathematics where the values of some model parameter(s) must be obtained from the observed data. The inverse problem can be formulated as follows: Data Model parametersThe transformation from data to model parameters is a result of the interaction of a physical system, e.g., the Earth, the atmosphere, gravity etc. Inverse problems arise for example in geophysics, medical imaging (such as computed axial tomography and EEG/ERP), remote sensing, ocean acoustic tomography, nondestructive testing, and astronomy. Inverse problems are typically ill posed, as opposed to the well-posed problems more typical when modeling physical situations where the model parameters or material properties are known. Of the three conditions for a well-posed problem suggested by Jacques Hadamard (existence, uniqueness, stability of the solution or solutions) the condition of stability is most often violated. In the sense of functional analysis, the inverse problem is represented by a mapping between metric spaces. While inverse problems are often formulated in infinite dimensional spaces, limitations to a finite number of measurements, and the practical consideration of recovering only a finite number of unknown parameters, may lead to the problems being recast in discrete form. In this case the inverse problem will typically be ill-conditioned. In these cases, regularization may be used to introduce mild assumptions ...More: http://booksllc.net/?id=203956
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