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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 inherent ill-posed nature of image reconstruction problems, due to limitations in the physical acquisition process, is typically addressed by introducing a regularisation term that incorporates prior knowledge about the underlying…

Image and Video Processing · Electrical Eng. & Systems 2025-03-11 Naïl Khelifa , Ferdia Sherry , Carola-Bibiane Schönlieb

In image denoising problems, one widely-adopted approach is to minimize a regularized data-fit objective function, where the data-fit term is derived from a physical image acquisition model. Typically the regularizer is selected with two…

Optimization and Control · Mathematics 2015-08-13 Albert Oh , Rebecca Willett

The Plug-and-Play (PnP) framework makes it possible to integrate advanced image denoising priors into optimization algorithms, to efficiently solve a variety of image restoration tasks generally formulated as Maximum A Posteriori (MAP)…

Image and Video Processing · Electrical Eng. & Systems 2023-03-07 Rita Fermanian , Mikael Le Pendu , Christine Guillemot

This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It additionally implements a Monte Carlo algorithm specifically tailored for sampling…

Machine Learning · Statistics 2024-02-20 Elhadji C. Faye , Mame Diarra Fall , Nicolas Dobigeon

In recent years, Diffusion Models have become the new state-of-the-art in deep generative modeling, ending the long-time dominance of Generative Adversarial Networks. Inspired by the Regularization by Denoising principle, we introduce an…

Image and Video Processing · Electrical Eng. & Systems 2025-03-31 Pasquale Cascarano , Lorenzo Stacchio , Andrea Sebastiani , Alessandro Benfenati , Ulugbek S. Kamilov , Gustavo Marfia

The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the…

Computer Vision and Pattern Recognition · Computer Science 2021-10-27 Jiaming Liu , M. Salman Asif , Brendt Wohlberg , Ulugbek S. Kamilov

Elasticity image, visualizing the quantitative map of tissue stiffness, can be reconstructed by solving an inverse problem. Classical methods for magnetic resonance elastography (MRE) try to solve a regularized optimization problem…

Image and Video Processing · Electrical Eng. & Systems 2021-05-28 Narges Mohammadi , Marvin M. Doyley , Mujdat Cetin

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

Computer Vision and Pattern Recognition · Computer Science 2019-08-20 Tim Meinhardt , Michael Moeller , Caner Hazirbas , Daniel Cremers

We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…

Machine Learning · Computer Science 2023-09-07 Avrajit Ghosh , Michael T. McCann , Madeline Mitchell , Saiprasad Ravishankar

Event cameras are novel bio-inspired sensors that measure per-pixel brightness differences asynchronously. Recovering brightness from events is appealing since the reconstructed images inherit the high dynamic range (HDR) and high-speed…

Computer Vision and Pattern Recognition · Computer Science 2024-03-05 Zelin Zhang , Anthony Yezzi , Guillermo Gallego

Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…

Image and Video Processing · Electrical Eng. & Systems 2025-04-15 Jianwei Ke

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…

Machine Learning · Computer Science 2023-10-03 Morteza Mardani , Jiaming Song , Jan Kautz , Arash Vahdat

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

Image and Video Processing · Electrical Eng. & Systems 2020-06-23 Jaweria Amjad , Zhaoyan Lyu , Miguel R. D. Rodrigues

Learning-based image reconstruction models, such as those based on the U-Net, require a large set of labeled images if good generalization is to be guaranteed. In some imaging domains, however, labeled data with pixel- or voxel-level label…

Image and Video Processing · Electrical Eng. & Systems 2024-01-08 Sean I. Young , Adrian V. Dalca , Enzo Ferrante , Polina Golland , Christopher A. Metzler , Bruce Fischl , Juan Eugenio Iglesias

Depth sensing devices have created various new applications in scientific and commercial research with the advent of Microsoft Kinect and PMD (Photon Mixing Device) cameras. Most of these applications require the depth cameras to be…

Computer Vision and Pattern Recognition · Computer Science 2017-09-11 Ramanpreet Singh Pahwa , Minh N. Do , Tian Tsong Ng , Binh-Son Hua

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…

Implicit Neural Representation (INR) has emerged as an effective method for unsupervised image denoising. However, INR models are typically overparameterized; consequently, these models are prone to overfitting during learning, resulting in…

Computer Vision and Pattern Recognition · Computer Science 2024-01-04 Zipei Yan , Zhengji Liu , Jizhou Li

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and…

Computer Vision and Pattern Recognition · Computer Science 2023-09-19 Huayu Wang , Chen Luo , Taofeng Xie , Qiyu Jin , Guoqing Chen , Zhuo-Xu Cui , Dong Liang

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