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Despite its short history, Generative Adversarial Network (GAN) has been extensively studied and used for various tasks, including its original purpose, i.e., synthetic sample generation. However, applying GAN to different data types with…

In phase retrieval and similar inverse problems, the stability of solutions across different noise levels is crucial for applications. One approach to promote it is using signal priors in a form of a generative model as a regularization, at…

Overparameterized autoencoder models often memorize their training data. For image data, memorization is often examined by using the trained autoencoder to recover missing regions in its training images (that were used only in their…

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use…

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…

Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…

Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a…

Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…

Imaging is a standard example of an inverse problem, where the task of reconstructing a ground truth from a noisy measurement is ill-posed. Recent state-of-the-art approaches for imaging use deep learning, spearheaded by unrolled and…

Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous…

Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B${}^{-1}$, an inverse basis-to-basis neural operator framework that…

How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…

In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…

In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…

Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…

In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion…

Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…

Contrastive learning has revolutionized the field of computer vision, learning rich representations from unlabeled data, which generalize well to diverse vision tasks. Consequently, it has become increasingly important to explain these…

Multi-task learning is a framework that enforces different learning tasks to share their knowledge to improve their generalization performance. It is a hot and active domain that strives to handle several core issues; particularly, which…