Related papers: Regularization Theory of the Analytic Deep Prior A…

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

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…

Recovering clear images from blurry ones with an unknown blur kernel is a challenging problem. Deep image prior (DIP) proposes to use the deep network as a regularizer for a single image rather than as a supervised model, which achieves…

We mainly analyze and solve the overfitting problem of deep image prior (DIP). Deep image prior can solve inverse problems such as super-resolution, inpainting and denoising. The main advantage of DIP over other deep learning approaches is…

Solving inverse problems requires appropriate regularization techniques to ensure well-posedness and stability. In recent years, denoiser-driven methods have emerged as effective regularization strategies, achieving state-of-the-art…

Data interpolation is a fundamental step in any seismic processing workflow. Among machine learning techniques recently proposed to solve data interpolation as an inverse problem, Deep Prior paradigm aims at employing a convolutional neural…

The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the…

Classical approaches for approximate inference depend on cleverly designed variational distributions and bounds. Modern approaches employ amortized variational inference, which uses a neural network to approximate any posterior without…

A significant number of researchers have applied deep learning methods to image fusion. However, most works require a large amount of training data or depend on pre-trained models or frameworks to capture features from source images. This…

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…

In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…

In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…

Effective regularization techniques are highly desired in deep learning for alleviating overfitting and improving generalization. This work proposes a new regularization scheme, based on the understanding that the flat local minima of the…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

Recent work has shown that the structure of convolutional neural networks (CNNs) induces a strong prior that favors natural images. This prior, known as a deep image prior (DIP), is an effective regularizer in inverse problems such as image…

We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms. Our result relies on a new and efficient algorithm to solve a restricted case of higher-order…

We present a data-assisted iterative regularization method for solving ill-posed inverse problems. The proposed approach, termed \texttt{IRMGL+\(\Psi\)}, integrates classical iterative techniques with a data-driven regularization term…

Classical adaptive control proves total-system stability for control of linear plants, but only for plants meeting very restrictive assumptions. Approximate Dynamic Programming (ADP) has the potential, in principle, to ensure stability…

The deep neural networks are known to be vulnerable to well-designed adversarial attacks. The most successful defense technique based on adversarial training (AT) can achieve optimal robustness against particular attacks but cannot…

Single image inverse problem is a notoriously challenging ill-posed problem that aims to restore the original image from one of its corrupted versions. Recently, this field has been immensely influenced by the emergence of deep-learning…