Bayesian Approach to Inverse Problems PDF
Jérôme IdierThe goal of this book is to deal with inverse problems and regularized solutions using Bayesian statistical tools, with a particular view to signal and image estimation. Chapters 1-3 cover the theoretical notions that make it possible to cast inverse problems within a mathematical framework. Chapters 4-6 address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. Chapters 9-14 put the main tools introduced in the previous chapters into a practical context in important applicative areas, such as astronomy or medical imaging.
Get this from a library! Bayesian approach to inverse problems. [Jérôme Idier;] -- "The goal of this book is to deal with inverse problems and regularized solutions using Bayesian statistical tools, with a particular view to signal and image estimation."--Jacket.
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Bayesian inference Prior distributions In ill-posed parameter estimation problems, e.g., inverse problems, prior information plays a key role Intuitive idea: assign lower probability to values of that you don’t expect to see, higher probability to values of that you do expect to see Examples 1 Gaussian processes with speci ed covariance kernel The Bayesian Approach to Inverse Problems | …
GitHub - jjx323/VIfIP: Using variational Bayesian ...
In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-tdistribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regular-ization in the form of a prior distribution, and a LASSO type prior distribution is
23/06/2016 · The Bayesian approach to inverse problems In the previous subsection, we constructed the probability measure , which is supported on a given variable-order Besov space . We can now present the following theorem for the well-defined problem.
12 Oct 2018 ... The Bayesian method is a powerful tool that enables inference and ... inverse temperature parameters), on Bayesian inference (Nassar et al., 2010; ... Note that our approach is applicable to variable problem situations and ...