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In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Learning an energy-based model from data samples is a central problem in machine learning. Many recent and popular methods, such as denoising score matching for training energy-based diffusion models, use stochastic interpolants to corrupt…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…

A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples…

High precision polarization measurements open new opportunities for the study of the magnetic field structure as traced by polarimetric measurements of the interstellar dust emission. Polarization parameters suffer from bias in the presence…

This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured…

Accurately measuring the geometry and spatially-varying reflectance of real-world objects is a complex task due to their intricate shapes formed by concave features, hollow engravings and diverse surfaces, resulting in inter-reflection and…

The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…

In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…

Multiplicative noise, also known as speckle or pepper noise, commonly affects images produced by synthetic aperture radar (SAR), lasers, or optical lenses. Unlike additive noise, which typically arises from thermal processes or external…

We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…

Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…

This document contains an educational introduction to the problem of sparsifying parametric models with L0 regularization. We utilize this approach together with dictionary learning to learn sparse polynomial policies for deep reinforcement…

Deep learning-based image denoising techniques often struggle with poor generalization performance to out-of-distribution real-world noise. To tackle this challenge, we propose a novel noise translation framework that performs denoising on…

Inverse reinforcement learning methods aim to retrieve the reward function of a Markov decision process based on a dataset of expert demonstrations. The commonplace scarcity and heterogeneous sources of such demonstrations can lead to the…

We present a method for training a neural network to perform image denoising without access to clean training examples or access to paired noisy training examples. Our method requires only a single noisy realization of each training example…