Related papers: On the Sample Complexity of Learning for Blind Inv…

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…

Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However,…

Undersampled inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined linear or non-linear reconstruction problems. There are now a myriad of techniques to design decoders…

Compressed sensing (CS) is a concept that allows to acquire compressible signals with a small number of measurements. As such it is very attractive for hardware implementations. Therefore, correct calibration of the hardware is a central…

Reinforcement learning (RL) offers significant promise for machinery fault detection (MFD). However, most existing RL-based MFD approaches do not fully exploit RL's sequential decision-making strengths, often treating MFD as a simple…

Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar…

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best…

Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…

A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…

The objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem where the degree of ill-posedness of operator $Q$ depends not only on the scale but also on location. In this case, the rates…

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…

It is well-known in practice, that L^1 data fitting leads to improved robustness compared to standard L^2 data fitting. However, it is unclear whether resulting algorithms will perform as well in case of regular data without outliers. In…

In ill-posed imaging inverse problems, uncertainty quantification remains a fundamental challenge, especially in safety-critical applications. Recently, conformal prediction has been used to quantify the uncertainty that the inverse problem…

Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…

This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals…