arXiv subjects

Robert G. Aykroyd

Publications and source records attributed to Robert G. Aykroyd.

3 recordsLinked to original sources

arXiv2024

A variational inference framework for inverse problems

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model fitting times. The message passing and factor graph fragment approach to variational Bayes that is also described facilitates streamlined implementation of approximate inference algorithms and allows for supple inclusion of numerous response distributions and penalizations into the inverse problem model. Models for one- and two-dimensional response variables are examined and an infrastructure is laid down where efficient algorithm updates based on nullifying weak interactions between variables can also be derived for inverse problems in higher dimensions. An image processing application and a simulation exercise motivated by biomedical problems reveal the computational advantage offered by efficient implementation of variational Bayes over Markov chain Monte Carlo.

stat.ME↗

arXiv2022

Image Reconstruction by Splitting Expectation Propagation Techniques from Iterative Inversion

Reconstructing images from downsampled and noisy measurements, such as MRI and low dose Computed Tomography (CT), is a mathematically ill-posed inverse problem. We propose an easy-to-use reconstruction method based on Expectation Propagation (EP) techniques. We incorporate the Monte Carlo (MC) method, Markov Chain Monte Carlo (MCMC), and Alternating Direction Method of Multiplier (ADMM) algorithm into EP method to address the intractability issue encountered in EP. We demonstrate the approach on complex Bayesian models for image reconstruction. Our technique is applied to images from Gamma-camera scans. We compare EPMC, EP-MCMC, EP-ADMM methods with MCMC only. The metrics are the better image reconstruction, speed, and parameters estimation. Experiments with Gamma-camera imaging in real and simulated data show that our proposed method is convincingly less computationally expensive than MCMC and produces relatively a better image reconstruction.

eess.IV↗

arXiv2018

Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment

The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this paper, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimised implementation is provided in Python.

stat.AP↗