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Found 13 papers, 6 papers with code
Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimation
Unsupervised learning is a training approach in the situation where ground truth data is unavailable, such as inverse imaging problems.
Scalable Bayesian uncertainty quantification with data-driven priors for radio interferometric imaging
This work proposes a method coined QuantifAI to address UQ in radio-interferometric imaging with data-driven (learned) priors for high-dimensional settings.
Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems
Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty.
Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling
This discretisation is asymptotically unbiased for Gaussian targets and shown to converge in an accelerated manner for any target that is $\kappa$-strongly log-concave (i. e., requiring in the order of $\sqrt{\kappa}$ iterations to converge, similarly to accelerated optimisation schemes), comparing favorably to [M. Pereyra, L. Vargas Mieles, K. C.
Proximal nested sampling with data-driven priors for physical scientists
Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging.
The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution
Additionally, instead of viewing the augmented posterior distribution as an approximation of the original model, we propose to consider it as a generalisation of this model.
Learned reconstruction methods with convergence guarantees
In recent years, deep learning has achieved remarkable empirical success for image reconstruction.
On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent
Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution.
Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms
Bayesian computation is performed by using a parallel tempered version of the preconditioned Crank-Nicolson algorithm on the manifold, which is shown to be ergodic and robust to the non-convex nature of these data-driven models.
Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie
The proposed algorithms are demonstrated on several canonical problems such as image deblurring, inpainting, and denoising, where they are used for point estimation as well as for uncertainty visualisation and quantification.
Wasserstein Control of Mirror Langevin Monte Carlo
In this paper, we consider Langevin diffusions on a Hessian-type manifold and study a discretization that is closely related to the mirror-descent scheme.
Maximum likelihood estimation of regularisation parameters in high-dimensional inverse problems: an empirical Bayesian approach. Part I: Methodology and Experiments
In this work, we propose a general empirical Bayesian method for setting regularisation parameters in imaging problems that are convex w. r. t.
Methodology Computation 62C12, 65C40, 68U10, 62F15, 65J20, 65C60, 65J22
Fast unsupervised Bayesian image segmentation with adaptive spatial regularisation
This paper presents a new Bayesian estimation technique for hidden Potts-Markov random fields with unknown regularisation parameters, with application to fast unsupervised K-class image segmentation.
