
Sparse image reconstruction on the sphere: a general approach with uncertainty quantification
Inverse problems defined naturally on the sphere are becoming increasing...
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Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization
We propose a Bayesian uncertainty quantification method for largescale ...
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Uncertainty Quantification with Generative Models
We develop a generative modelbased approach to Bayesian inverse problem...
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Bernsteinvon Mises theorems and uncertainty quantification for linear inverse problems
We consider the statistical inverse problem of approximating an unknown ...
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Sparse online variational Bayesian regression
This work considers variational Bayesian inference as an inexpensive and...
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l_1ball Prior: Uncertainty Quantification with Exact Zeros
Lasso and l_1regularization play a dominating role in high dimensional ...
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Invertible Neural Networks for Uncertainty Quantification in Photoacoustic Imaging
Multispectral photoacoustic imaging (PAI) is an emerging imaging modalit...
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Bayesian variational regularization on the ball
We develop variational regularization methods which leverage sparsitypromoting priors to solve severely ill posed inverse problems defined on the 3D ball (i.e. the solid sphere). Our method solves the problem natively on the ball and thus does not suffer from discontinuities that plague alternate approaches where each spherical shell is considered independently. Additionally, we leverage advances in probability density theory to produce Bayesian variational methods which benefit from the computational efficiency of advanced convex optimization algorithms, whilst supporting principled uncertainty quantification. We showcase these variational regularization and uncertainty quantification techniques on an illustrative example. The C++ code discussed throughout is provided under a GNU general public license.
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