Related papers: Sparse image reconstruction on the sphere: a gener…

This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…

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 surveys this inverse problem is ill-posed…

In this paper, we propose a local squared Wasserstein-2 (W_2) method to solve the inverse problem of reconstructing models with uncertain latent variables or parameters. A key advantage of our approach is that it does not require prior…

With increasing deployment of machine learning systems in various real-world tasks, there is a greater need for accurate quantification of predictive uncertainty. While the common goal in uncertainty quantification (UQ) in machine learning…

We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…

In context-specific applications such as robotics, telecommunications, and healthcare, artificial intelligence systems often face the challenge of limited training data. This scarcity introduces epistemic uncertainty, i.e., reducible…

In the first part, we develop a general framework for projection structures and study several inference problems within this framework. We propose procedures based on data dependent measures (DDM) and make connections with empirical Bayes…

We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions on the sphere which speed up computations by a factor \order{\sqrt{N}} compared to present methods where $N$ is the number of pixels. No…

The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…

Uncertainty Quantification (UQ) is a key discipline for computational modeling of complex systems, enhancing reliability of engineering simulations. In crashworthiness, having an accurate assessment of the behavior of the model uncertainty…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational…

We present a general approach to visualizing uncertainty in static 2-D statistical graphics. If we treat a visualization as a function of its underlying quantities, uncertainty in those quantities induces a distribution over images. We show…

Uncertainty in physical parameters can make the solution of forward or inverse light scattering problems in astrophysical, biological, and atmospheric sensing applications, cost prohibitive for real-time applications. For example, given a…

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic interpretation.…

Recent advances in deep learning have led to its widespread adoption across diverse domains, including medical imaging. This progress is driven by increasingly sophisticated model architectures, such as ResNets, Vision Transformers, and…

Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…

We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ…

Climate models are generally calibrated manually by comparing selected climate statistics, such as the global top-of-atmosphere energy balance, to observations. The manual tuning only targets a limited subset of observational data and…