Related papers: Learned convex regularizers for inverse problems

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…

Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is…

We introduce inverse transport networks as a learning architecture for inverse rendering problems where, given input image measurements, we seek to infer physical scene parameters such as shape, material, and illumination. During training,…

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…

Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is…

Batch Normalization (BN) is a commonly used technique to accelerate and stabilize training of deep neural networks. Despite its empirical success, a full theoretical understanding of BN is yet to be developed. In this work, we analyze BN…

These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…

Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking…

Recovering a high-quality image from noisy indirect measurements is an important problem with many applications. For such inverse problems, supervised deep convolutional neural network (CNN)-based denoising methods have shown strong…

Regularization in convolutional neural networks (CNNs) is usually addressed with dropout layers. However, dropout is sometimes detrimental in the convolutional part of a CNN as it simply sets to zero a percentage of pixels in the feature…

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank…

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…

The Deep neural networks (DNNs) have achieved great success on a variety of computer vision tasks, however, they are highly vulnerable to adversarial attacks. To address this problem, we propose to improve the local smoothness of the…

In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…

Non-uniqueness and instability are characteristic features of image reconstruction processes. As a result, it is necessary to develop regularization methods that can be used to compute reliable approximate solutions. A regularization method…

In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly…

This paper focuses on regularizing the training of the convolutional neural network (CNN). We propose a new regularization approach named ``PatchShuffle`` that can be adopted in any classification-oriented CNN models. It is easy to…

Most existing methods usually formulate the non-blind deconvolution problem into a maximum-a-posteriori framework and address it by manually designing kinds of regularization terms and data terms of the latent clear images. However,…