Related papers: Interpretation of Plug-and-Play (PnP) algorithms f…

Consistency models (CMs) learn a consistent mapping from multiple noise levels to the data endpoint and can therefore perform generative inference in one or a few steps. This property makes them attractive as learned priors for low-latency…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…

In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…

Improving generalization is one of the main challenges for training deep neural networks on classification tasks. In particular, a number of techniques have been proposed, aiming to boost the performance on unseen data: from standard data…

Entropy regularization is an efficient technique for encouraging exploration and preventing a premature convergence of (vanilla) policy gradient methods in reinforcement learning (RL). However, the theoretical understanding of…

During the past few years, inverse problem formulations of ultrasound beamforming have attracted a growing interest. They usually pose beamforming as a minimization problem of a fidelity term resulting from the measurement model plus a…

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…

A new Plug-and-Play (PnP) alternating direction of multipliers (ADMM) scheme is proposed in this paper, by embedding a recently introduced adaptive denoiser using the Schroedinger equation's solutions of quantum physics. The potential of…

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

It is known that the minimum-mean-squared-error (MMSE) denoiser under Gaussian noise can be written as a proximal operator, which suffices for asymptotic convergence of plug-and-play (PnP) methods but does not reveal the structure of the…

In many real-world applications of machine learning such as recommendations, hiring, and lending, deployed models influence the data they are trained on, leading to feedback loops between predictions and data distribution. The performative…

For multi-scale problems, the conventional physics-informed neural networks (PINNs) face some challenges in obtaining available predictions. In this paper, based on PINNs, we propose a practical deep learning framework for multi-scale…

We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…

The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…