Related papers: Equivariant Deep Equilibrium Models for Imaging In…

One key ingredient of image restoration is to define a realistic prior on clean images to complete the missing information in the observation. State-of-the-art restoration methods rely on a neural network to encode this prior. Moreover,…

Deep Equilibrium (DEQ) Models, an emerging class of implicit models that maps inputs to fixed points of neural networks, are of growing interest in the deep learning community. However, training and applying DEQ models is currently done in…

Large scale deep learning model, such as modern language models and diffusion architectures, have revolutionized applications ranging from natural language processing to computer vision. However, their deployment in distributed or…

Uncertainty quantification in inverse medical imaging tasks with deep learning has received little attention. However, deep models trained on large data sets tend to hallucinate and create artifacts in the reconstructed output that are not…

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…

Backpropagation algorithm is indispensable for the training of feedforward neural networks. It requires propagating error gradients sequentially from the output layer all the way back to the input layer. The backward locking in…

This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and…

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component…

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…

Diffusion model-based image restoration (IR) aims to use diffusion models to recover high-quality (HQ) images from degraded images, achieving promising performance. Due to the inherent property of diffusion models, most existing methods…

In recent years, deep learning methods have been extensively developed for inverse imaging problems (IIPs), encompassing supervised, self-supervised, and generative approaches. Most of these methods require large amounts of labeled or…

Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…

Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present…

Deep neural networks for medical image reconstruction are traditionally trained using high-quality ground-truth images as training targets. Recent work on Noise2Noise (N2N) has shown the potential of using multiple noisy measurements of the…

Ultrasound reflection tomography is widely used to image large complex specimens that are only accessible from a single side, such as well systems and nuclear power plant containment walls. Typical methods for inverting the measurement rely…

Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework…

Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…

This paper introduces Physics-Informed Deep Equilibrium Models (PIDEQs) for solving initial value problems (IVPs) of ordinary differential equations (ODEs). Leveraging recent advancements in deep equilibrium models (DEQs) and…

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the…

Implicit-depth models such as Deep Equilibrium Networks have recently been shown to match or exceed the performance of traditional deep networks while being much more memory efficient. However, these models suffer from unstable convergence…