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Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…
We develop a computational framework to quantify uncertainty in shear elastography imaging of anomalies in tissues. We adopt a Bayesian inference formulation. Given the observed data, a forward model and their uncertainties, we find the…
This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computational method combines an image domain technique and…
Recently, a new probabilistic "data fusion" framework based on Bayesian principles has been developed on JET and W7-AS. The Bayesian analysis framework folds in uncertainties and inter-dependencies in the diagnostic data and signal…
This paper presents a new Bayesian spectral unmixing algorithm to analyse remote scenes sensed via sparse multispectral Lidar measurements. To a first approximation, in the presence of a target, each Lidar waveform consists of a main peak,…
In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic…
Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates…
The motivation of this work is the detection of cerebrovascular accidents by microwave tomographic imaging. This requires the solution of an inverse problem relying on a minimization algorithm (for example, gradient-based), where successive…
We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…
Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…
Deep learning-based image reconstruction approaches have demonstrated impressive empirical performance in many imaging modalities. These approaches usually require a large amount of high-quality paired training data, which is often not…
A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contains numerous peaks corresponding to surface atoms. The method, based on the relevance vector machine with $\mathrm{L}_1$…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
Deep learning is having a profound impact in many fields, especially those that involve some form of image processing. Deep neural networks excel in turning an input image into a set of high-level features. On the other hand, tomography…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…
The sparse-driven radar imaging can obtain the high-resolution images about target scene with the down-sampled data. However, the huge computational complexity of the classical sparse recovery method for the particular situation seriously…
Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…
In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…