An MCMC method for uncertainty quantification in nonnegativity constrained inverse problems

DOI10.1080/17415977.2011.637208zbMath1254.65009OpenAlexW2037277678MaRDI QIDQ3167885

Johnathan M. Bardsley, Colin D. Fox

Publication date: 29 October 2012

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2011.637208

zbMATH Keywords

algorithmregularizationcomputed tomographynumerical examplesinverse problemsMarkov chain Monte Carloimage reconstructionuncertainty quantificationimage deconvolutionbound constrained optimizationquadratic minimization

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Ill-posedness and regularization problems in numerical linear algebra (65F22) Monte Carlo methods (65C05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Numerical analysis or methods applied to Markov chains (65C40) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Inverse problems in linear algebra (15A29)

Related Items (7)

Bayesian Inference with Projected Densities ⋮ Large-Scale Bayesian Spatial-Temporal Regression with Application to Cardiac MR-Perfusion Imaging ⋮ MCMC Algorithms for Computational UQ of Nonnegativity Constrained Linear Inverse Problems ⋮ Sampling-based uncertainty quantification in deconvolution of X-ray radiographs ⋮ Uncertainty Quantification of Density Reconstruction Using MCMC Method in High-Energy X-ray Radiography ⋮ Bayesian Abel Inversion in Quantitative X-Ray Radiography ⋮ A statistical reconstruction model for absorption CT with source uncertainty ^*

Uses Software

• GMRFLib

Cites Work

• A generalized conjugate gradient algorithm for solving a class of quadratic programming problems
• An Iterative Method for Edge-Preserving MAP Estimation When Data-Noise Is Poisson
• Hypermodels in the Bayesian imaging framework
• Sampling-Based Analysis of a Spatially Distributed Model for Liver Metabolism at Steady State
• Projected gradient methods for linearly constrained problems
• On the Solution of Large Quadratic Programming Problems with Bound Constraints
• Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography
• Projected Newton Methods for Optimization Problems with Simple Constraints
• Computational Methods for Inverse Problems
• A Limited Memory Algorithm for Bound Constrained Optimization

This page was built for publication: An MCMC method for uncertainty quantification in nonnegativity constrained inverse problems