相关论文: Quadratic neural networks for solving inverse prob…

Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems,…

This paper presents a study of the effectiveness of Neural Network (NN) techniques for deconvolution inverse problems relevant for applications in Quantum Field Theory, but also in more general contexts. We consider NN's asymptotic limits,…

In this paper we study shallow neural network functions which are linear combinations of compositions of activation and quadratic functions, replacing standard affine linear functions, often called neurons. We show the universality of this…

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…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

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…

Neural networks functions are supposed to be able to encode the desired solution of an inverse problem very efficiently. In this paper, we consider the problem of solving linear inverse problems with neural network coders. First we…

Neural networks with quadratic decision functions have been introduced as alternatives to standard neural networks with affine linear ones. They are advantageous when the objects or classes to be identified are compact and of basic…

We propose a partially learned approach for the solution of ill posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularization theory and recent advances in deep learning to…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

In this survey paper, we review recent uses of convolution neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding…

Recently, deep neural networks (DNNs) have become powerful tools for solving inverse scattering problems. However, the approximation and generalization rates of DNNs for solving these problems remain largely under-explored. In this work, we…

This review provides an introduction to - and overview of - the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…

We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…

Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional,…

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by generative adversarial networks, or GANs). In this work,…