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In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant…

Optimization and Control · Mathematics 2022-02-15 Junqi Tang

The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However, even nowadays it is still a challenging task to devise a method that combines the…

Numerical Analysis · Computer Science 2016-10-20 Martin Bähr , Michael Breuß , Yvain Quéau , Ali Sharifi Boroujerdi , Jean-Denis Durou

This paper presents a novel method for the reconstruction of high-resolution temporal images in dynamic tomographic imaging, particularly for discrete objects with smooth boundaries that vary over time. Addressing the challenge of limited…

Image and Video Processing · Electrical Eng. & Systems 2023-11-10 Ajinkya Kadu , Felix Lucka , Kees Joost Batenburg

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

Methodology · Statistics 2020-08-17 Ana F. Vidal , Valentin De Bortoli , Marcelo Pereyra , Alain Durmus

We consider the estimation of the regularization parameter for the simultaneous deblurring of multiple noisy images via Tikhonov regularization. We approach the problem in three ways. We first reduce the problem to a single-image deblurring…

Astrophysics · Physics 2009-11-10 R. Vio , P. Ma , W. Zhong , J. Nagy , L. Tenorio , W. Wamsteker

This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First,…

Multimedia · Computer Science 2014-05-14 Jian Zhang , Debin Zhao , Ruiqin Xiong , Siwei Ma , Wen Gao

In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…

Functional Analysis · Mathematics 2023-04-26 Kristian Bredies , Silvio Fanzon

The estimation of optical flow and 6-DoF ego-motion, two fundamental tasks in 3D vision, has typically been addressed independently. For neuromorphic vision (e.g., event cameras), however, the lack of robust data association makes solving…

Computer Vision and Pattern Recognition · Computer Science 2025-10-27 Wenpu Li , Bangyan Liao , Yi Zhou , Qi Xu , Pian Wan , Peidong Liu

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Numerical Analysis · Mathematics 2025-05-12 Abinash Nayak

Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…

Numerical Analysis · Mathematics 2024-06-26 Andrea Ebner , Matthias Schwab , Markus Haltmeier

Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…

Optimization and Control · Mathematics 2011-10-25 Nelly Pustelnik , Caroline Chaux , Jean-Christophe Pesquet

In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…

Image and Video Processing · Electrical Eng. & Systems 2024-01-30 Berk Iskender , Marc L. Klasky , Yoram Bresler

Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…

Computer Vision and Pattern Recognition · Computer Science 2015-03-18 Dai-Qiang Chen , Li-Zhi Cheng

Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight, which uses photon time-of-flight information encoded in light after multiple diffuse reflections. The…

Computer Vision and Pattern Recognition · Computer Science 2024-03-07 Rui Ding , Juntian Ye , Qifeng Gao , Feihu Xu , Yuping Duan

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…

Image and Video Processing · Electrical Eng. & Systems 2020-08-26 Andreas Kofler , Markus Haltmeier , Tobias Schaeffter , Marc Kachelrieß , Marc Dewey , Christian Wald , Christoph Kolbitsch

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…

Statistics Theory · Mathematics 2007-06-13 Ana K. Fermin , Carenne Ludena

We propose a new image restoration model based on the minimized surface regularization. The proposed model closely relates to the classical smoothing ROF model \cite{4}. We can reformulate the proposed model as a min-max problem and solve…

Optimization and Control · Mathematics 2016-05-31 Zhi-Feng Pang , Yuping Duan

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…

Proper regularization is crucial in inverse problems to achieve high-quality reconstruction, even with an ill-conditioned measurement system. This is particularly true for three-dimensional photoacoustic tomography, which is computationally…

Optimization and Control · Mathematics 2024-09-26 Chao Wang , Alexandre H. Thiery

The idea of video super resolution is to use different view points of a single scene to enhance the overall resolution and quality. Classical energy minimization approaches first establish a correspondence of the current frame to all its…

Computer Vision and Pattern Recognition · Computer Science 2017-12-05 Jonas Geiping , Hendrik Dirks , Daniel Cremers , Michael Moeller