Related papers: The inverse problem for neural networks

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…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…

With the recent success of deep neural networks in computer vision, it is important to understand the internal working of these networks. What does a given neuron represent? The concepts captured by a neuron may be hard to understand or…

Deep learning has received much attention lately due to the impressive empirical performance achieved by training algorithms. Consequently, a need for a better theoretical understanding of these problems has become more evident in recent…

Most methods for neural network verification focus on bounding the image, i.e., set of outputs for a given input set. This can be used to, for example, check the robustness of neural network predictions to bounded perturbations of an input.…

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly…

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…

Image denoisers have been shown to be powerful priors for solving inverse problems in imaging. In this work, we introduce a generalization of these methods that allows any image restoration network to be used as an implicit prior. The…

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…

Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…

Piecewise affine neural networks (PANNs) provide a principled geometric perspective on neural network expressivity by characterizing the input--output map as a continuous piecewise affine (CPA) function whose complexity is governed by the…

Existing Bayesian treatments of neural networks are typically characterized by weak prior and approximate posterior distributions according to which all the weights are drawn independently. Here, we consider a richer prior distribution in…

For every positive integer h, the representation function of order h associated to a subset A of the integers or, more generally, of any group or semigroup X, counts the number of ways an element of X can be written as the sum (or product,…

Neural network verification mainly focuses on local robustness properties, which can be checked by bounding the image (set of outputs) of a given input set. However, often it is important to know whether a given property holds globally for…

Used in the paper is an overcomplete piecewise-polynomial image model incorporating sparsity. The paper shows that using such a model, the edges in the image can be resolved robustly with respect to noise. Two variants of the proposed…

Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the…

Over the year, people have been using deep learning to tackle inversion problems, and we see the framework has been applied to build relationship between recording wavefield and velocity (Yang et al., 2016). Here we will extend the work…

Machine learning methods have found novel application areas in various disciplines as they offer low-computational cost solutions to complex problems. Recently, metasurface design has joined among these applications, and neural networks…

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…