相关论文: Augmented NETT Regularization of Inverse Problems

Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…

An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…

Transfer learning have been frequently used to improve deep neural network training through incorporating weights of pre-trained networks as the starting-point of optimization for regularization. While deep transfer learning can usually…

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.…

Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…

We propose a new method for supervised learning. The hubNet procedure fits a hub-based graphical model to the predictors, to estimate the amount of "connection" that each predictor has with other predictors. This yields a set of predictor…

Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data, demonstrating significant effectiveness in certain scenarios. However, these methods often suffer from limited representation…

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…

Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…

Autoencoders provide a powerful framework for learning compressed representations by encoding all of the information needed to reconstruct a data point in a latent code. In some cases, autoencoders can "interpolate": By decoding the convex…

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and…

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…

Artificial neural networks perform state-of-the-art in an ever-growing number of tasks, and nowadays they are used to solve an incredibly large variety of tasks. There are problems, like the presence of biases in the training data, which…

The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…

This paper is about regularizing deep convolutional networks (CNNs) based on an adaptive framework for transfer learning with limited training data in the target domain. Recent advances of CNN regularization in this context are commonly due…

We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…

We present a novel optimization strategy for training neural networks which we call "BitNet". The parameters of neural networks are usually unconstrained and have a dynamic range dispersed over all real values. Our key idea is to limit the…

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…