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The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…

Optimization and Control · Mathematics 2025-06-24 Clemens Kirisits , Bochra Mejri , Sergei Pereverzev , Otmar Scherzer , Cong Shi

We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…

Computer Vision and Pattern Recognition · Computer Science 2018-12-07 Sidharth Gupta , Konik Kothari , Maarten V. de Hoop , Ivan Dokmanić

The task of extracting intrinsic components, such as reflectance and shading, from neural radiance fields is of growing interest. However, current methods largely focus on synthetic scenes and isolated objects, overlooking the complexities…

Computer Vision and Pattern Recognition · Computer Science 2024-06-18 Yixiong Yang , Shilin Hu , Haoyu Wu , Ramon Baldrich , Dimitris Samaras , Maria Vanrell

The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods…

Optimization and Control · Mathematics 2016-06-21 Yair Censor , Aviv Gibali , Frank Lenzen , Christoph Schnorr

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…

Machine Learning · Statistics 2026-02-13 Jean-François Giovannelli

The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…

Numerical Analysis · Mathematics 2019-10-15 Neil K. Chada , Claudia Schillings , Simon Weissmann

The acquisition of objects outside the Line-of-Sight of cameras is a very intriguing but also extremely challenging research topic. Recent works showed the feasibility of this idea exploiting transient imaging data produced by custom direct…

Computer Vision and Pattern Recognition · Computer Science 2024-09-23 Matteo Caligiuri , Adriano Simonetto , Pietro Zanuttigh

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…

Numerical Analysis · Mathematics 2020-04-02 Alexander Barnett , Charles L. Epstein , Leslie Greengard , Jeremy Magland

In this work, we propose an extension of conventional image data by an additional channel in which the associated projection properties are encoded. This addresses the issue of sensor-dependent object representation in projection-based…

Computer Vision and Pattern Recognition · Computer Science 2023-05-02 Hannes Reichert , Manuel Hetzel , Steven Schreck , Konrad Doll , Bernhard Sick

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

Numerical Analysis · Mathematics 2016-01-20 Matthias Morzfeld , Xuemin Tu , Jon Wilkening , Alexandre J. Chorin

Existing methods for relightable view synthesis -- using a set of images of an object under unknown lighting to recover a 3D representation that can be rendered from novel viewpoints under a target illumination -- are based on inverse…

Computer Vision and Pattern Recognition · Computer Science 2024-11-05 Xiaoming Zhao , Pratul P. Srinivasan , Dor Verbin , Keunhong Park , Ricardo Martin Brualla , Philipp Henzler

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

Optimization and Control · Mathematics 2021-12-07 Rishabh Gupta , Qi Zhang

The captured images under low light conditions often suffer insufficient brightness and notorious noise. Hence, low-light image enhancement is a key challenging task in computer vision. A variety of methods have been proposed for this task,…

Image and Video Processing · Electrical Eng. & Systems 2020-05-22 Cheng Zhang , Qingsen Yan , Yu zhu , Xianjun Li , Jinqiu Sun , Yanning Zhang

Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear…

Signal Processing · Electrical Eng. & Systems 2023-05-19 Jihui Jin , Etienne Ollivier , Richard Touret , Matthew McKinley , Karim G. Sabra , Justin K. Romberg

This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…

Machine Learning · Statistics 2020-11-09 Juho Piironen , Markus Paasiniemi , Aki Vehtari

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

Methodology · Statistics 2023-02-09 Xiao Liu , Kyongmin Yeo

In this work, we present and investigate the novel blind inverse problem of position-blind ptychography, i.e., ptychographic phase retrieval without any knowledge of scan positions, which then must be recovered jointly with the image. The…

Image and Video Processing · Electrical Eng. & Systems 2026-03-18 Simon Welker , Lorenz Kuger , Tim Roith , Berthy Feng , Martin Burger , Timo Gerkmann , Henry Chapman

We present a scheme for fast environment light estimation from the RGBD appearance of individual objects and their local image areas. Conventional inverse rendering is too computationally demanding for real-time applications, and the…

Computer Vision and Pattern Recognition · Computer Science 2020-08-07 Xin Wei , Guojun Chen , Yue Dong , Stephen Lin , Xin Tong

Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably…

Machine Learning · Computer Science 2024-12-05 Congxi Zhang , Yongchun Xie

The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…

Numerical Analysis · Mathematics 2026-02-12 Daniela Calvetti , Erkki Somersalo