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Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…
Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…
Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…
Normalization techniques have proved to be a crucial ingredient of successful training in a traditional supervised learning regime. However, in the zero-shot learning (ZSL) world, these ideas have received only marginal attention. This work…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral…
A key challenge in solving the deterministic inverse reinforcement learning (IRL) problem online and in real-time is the existence of multiple solutions. Nonuniqueness necessitates the study of the notion of equivalent solutions, i.e.,…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of…
We introduce the isoperimetric loss as a regularization criterion for learning the map from a visual representation to a semantic embedding, to be used to transfer knowledge to unknown classes in a zero-shot learning setting. We use a…
This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were…
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…
We propose a novel framework for the regularised inversion of deep neural networks. The framework is based on the authors' recent work on training feed-forward neural networks without the differentiation of activation functions. The…
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…
In the past few years, deep learning-based methods have demonstrated enormous success for solving inverse problems in medical imaging. In this work, we address the following question:\textit{Given a set of measurements obtained from real…
Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique…
Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…