• Corpus ID: 234470176

Bayesian variational regularization on the ball

@article{Price2021BayesianVR,
  title={Bayesian variational regularization on the ball},
  author={Matthew Alexander Price and Jason D. McEwen},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.05518}
}
We develop variational regularization methods which leverage sparsity-promoting priors to solve severely illposed 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… 
View PDF on arXiv
View With Semantic Reader

Figures from this paper

References

SHOWING 1-10 OF 50 REFERENCES
Sparse image reconstruction on the sphere: a general approach with uncertainty quantification
TLDR
This article considers the Bayesian interpretation of the unconstrained problem which, combined with recent developments in probability density theory, permits rapid, statistically principled uncertainty quantification (UQ) in the spherical setting and linearity is exploited to significantly increase the computational efficiency of such UQ techniques.
Sparse Image Reconstruction on the Sphere: Analysis and Synthesis
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularization, exploiting sparsity in both axisymmetric and directional scale-discretized wavelet space. Denoising,…
Scalable Bayesian Uncertainty Quantification in Imaging Inverse Problems via Convex Optimization
TLDR
A main feature of this work is to leverage probability concentration phenomena and the underlying convex geometry to formulate the Bayesian hypothesis test as a convex problem, that is then efficiently solve by using scalable optimization algorithms.
Maximum-a-Posteriori Estimation with Bayesian Confidence Regions
  • M. Pereyra
  • Mathematics, Computer Science
    SIAM J. Imaging Sci.
  • 2017
TLDR
A new general methodology for approximating Bayesian high-posterior-density credibility regions in inverse problems that are convex and potentially very high-dimensional and which can be computed very efficiently, even in large-scale problems, by using standard convex optimisation techniques.
Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
TLDR
A new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which is solved via convex optimization.
Sparsity Averaging for Compressive Imaging
We discuss a novel sparsity prior for compressive imaging in the context of the theory of compressed sensing with coherent redundant dictionaries, based on the observation that natural images exhibit…
Sparse Bayesian mass-mapping with uncertainties: Full sky observations on the celestial sphere
To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the flat-sky approximation has been sufficiently satisfied. However, with Stage IV…
Sparse Image Reconstruction on the Sphere: Implications of a New Sampling Theorem
TLDR
Through numerical simulations, the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem is verified.
Sparse Bayesian mass mapping with uncertainties: local credible intervals
TLDR
This work draws on the concept of local credible intervals as an extension of the uncertainty quantification techniques previously detailed, and finds that, typically, its recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated with those recovered via Px-MALA.
Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations
Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical…
...
...