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We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

Differential cross section measurements are the currency of scientific exchange in particle and nuclear physics. A key challenge for these analyses is the correction for detector distortions, known as deconvolution or unfolding. Binned…

The quantification of myocardial perfusion MRI has the potential to provide a fast, automated and user-independent assessment of myocardial ischaemia. However, due to the relatively high noise level and low temporal resolution of the…

In this paper, we propose a Bayesian spectral deconvolution method for absorption spectra. In conventional analysis, the noise mechanism of absorption spectral data is never considered appropriately. In that analysis, the least-squares…

An analytical solution for the posterior estimate in Bayesian tomography of the unknown quantum state of an arbitrary quantum system (with a finite-dimensional Hilbert space) is found. First, we derive the Bayesian estimate for a pure…

Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is…

We consider the problem of estimation and structure learning of high dimensional signals via a normal sequence model, where the underlying parameter vector is piecewise constant, or has a block structure. We develop a Bayesian fusion…

This paper presents a new Bayesian model and associated algorithm for depth and intensity profiling using full waveforms from time-correlated single-photon counting (TCSPC) measurements in the limit of very low photon counts (i.e.,…

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…

In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework…

In example-based super-resolution, the function relating low-resolution images to their high-resolution counterparts is learned from a given dataset. This data-driven approach to solving the inverse problem of increasing image resolution…

We present a Bayesian Voronoi image reconstruction technique (VIR) for interferometric data. Bayesian analysis applied to the inverse problem allows us to derive the a-posteriori probability of a novel parameterization of interferometric…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Recovering a signal from auto-correlations or, equivalently, retrieving the phase linked to a given Fourier modulus, is a wide-spread problem in imaging. This problem has been tackled in a number of experimental situations, from optical…

We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered…

In many inverse problems, the unknown is composed of multiple components with different regularities, for example, in imaging problems, where the unknown can have both rough and smooth features. We investigate linear Bayesian inverse…

In petroleum well test analysis, deconvolution is used to obtain information about the reservoir system. This information is contained in the response function, which can be estimated by solving an inverse problem in the pressure and flow…

We present in this article the use of probabilistic background constraints in astronomical image deconvolution to approach to a solution as an interval estimate. We elaborate our objective -- the interval estimate of the unknown object from…

In this work we present a new algorithm for data deconvolution that allows the retrieval of the target function with super-resolution with a simple approach that after a precis e measurement of the instrument response function (IRF), the…

Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is…