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Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters,…

Optimization and Control · Mathematics 2020-01-23 Carla Bertocchi , Emilie Chouzenoux , Marie-Caroline Corbineau , Jean-Christophe Pesquet , Marco Prato

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…

Computer Vision and Pattern Recognition · Computer Science 2018-09-11 Kyong Hwan Jin , Michael T. McCann , Emmanuel Froustey , Michael Unser

Many application domains, spanning from computational photography to medical imaging, require recovery of high-fidelity images from noisy, incomplete or partial/compressed measurements. State of the art methods for solving these inverse…

Image and Video Processing · Electrical Eng. & Systems 2022-07-13 Xinyi Wei , Hans van Gorp , Lizeth Gonzalez Carabarin , Daniel Freedman , Yonina C. Eldar , Ruud J. G. van Sloun

An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…

Machine Learning · Computer Science 2023-11-06 Zakhar Shumaylov , Jeremy Budd , Subhadip Mukherjee , Carola-Bibiane Schönlieb

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

Numerical Analysis · Mathematics 2021-04-15 Babak Maboudi Afkham , Julianne Chung , Matthias Chung

Deep unrolling, or unfolding, is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. However, the convergence guarantees and generalizability of the unrolled…

Machine Learning · Computer Science 2024-12-02 Samar Hadou , Navid NaderiAlizadeh , Alejandro Ribeiro

Deep neural networks (DNN) have achieved great success in image restoration. However, most DNN methods are designed as a black box, lacking transparency and interpretability. Although some methods are proposed to combine traditional…

Computer Vision and Pattern Recognition · Computer Science 2022-04-29 Chong Mou , Qian Wang , Jian Zhang

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

Numerical Analysis · Mathematics 2020-06-09 Markus Haltmeier , Linh V. Nguyen

The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…

Image and Video Processing · Electrical Eng. & Systems 2021-06-01 Marija Vella , João F. C. Mota

Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…

Machine Learning · Computer Science 2023-09-06 Ali Mohammad-Djafari , Ning Chu , Li Wang , Liang Yu

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Numerical Analysis · Mathematics 2020-02-26 Kailai Xu , Eric Darve

Regularization methods are often employed in deep learning neural networks (DNNs) to prevent overfitting. For penalty based DNN regularization methods, convex penalties are typically considered because of their optimization guarantees.…

Machine Learning · Statistics 2022-04-07 Sujit Vettam , Majnu John

Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…

Signal Processing · Electrical Eng. & Systems 2026-03-12 Dvir Avrahami , Amit Milstein , Caroline Chaux , Tirza Routtenberg , Nir Shlezinger

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

Image and Video Processing · Electrical Eng. & Systems 2020-07-20 Dongdong Chen , Mike E. Davies

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

Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…

Machine Learning · Computer Science 2020-03-19 Huynh Van Luong , Boris Joukovsky , Nikos Deligiannis

Deformable image registration is a fundamental task in medical image analysis, aiming to establish a dense and non-linear correspondence between a pair of images. Previous deep-learning studies usually employ supervised neural networks to…

Computer Vision and Pattern Recognition · Computer Science 2018-09-11 Jun Zhang

Deep unfolding networks have recently gained popularity in the context of solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with…

Image and Video Processing · Electrical Eng. & Systems 2021-06-04 Jiaming Liu , Yu Sun , Weijie Gan , Xiaojian Xu , Brendt Wohlberg , Ulugbek S. Kamilov

We propose a new approach for large-scale high-dynamic range computational imaging. Deep Neural Networks (DNNs) trained end-to-end can solve linear inverse imaging problems almost instantaneously. While unfolded architectures provide…

Instrumentation and Methods for Astrophysics · Physics 2023-09-28 Amir Aghabiglou , Matthieu Terris , Adrian Jackson , Yves Wiaux
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