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One of the most significant challenges in statistical signal processing and machine learning is how to obtain a generative model that can produce samples of large-scale data distribution, such as images and speeches. Generative Adversarial…

Gravity inversion allows us to constrain the interior mass distribution of a planetary body using the observed shape, rotation, and gravity. Traditionally, techniques developed for gravity inversion can be divided into Monte Carlo methods,…

The convolutional neural networks (CNNs) are not inherently shift invariant or equivariant. The downsampling operation, used in CNNs, is one of the key reasons which breaks the shift invariant property of a CNN. Conversely, downsampling…

Downward continuation is a critical task in potential field processing, including gravity and magnetic fields, which aims to transfer data from one observation surface to another that is closer to the source of the field. Its effectiveness…

Image inversion is a fundamental task in generative models, aiming to map images back to their latent representations to enable downstream applications such as editing, restoration, and style transfer. This paper provides a comprehensive…

Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator $f$ maps the subsurface velocity structures to seismic signals. The existing computational methods for solving…

Inverse problems consist in reconstructing signals from incomplete sets of measurements and their performance is highly dependent on the quality of the prior knowledge encoded via regularization. While traditional approaches focus on…

Due to the effectiveness of using machine learning in physics, it has been widely received increased attention in the literature. However, the notion of applying physics in machine learning has not been given much awareness to. This work is…

The projected gradient descent (PGD) method has shown to be effective in recovering compressed signals described in a data-driven way by a generative model, i.e., a generator which has learned the data distribution. Further reconstruction…

We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…

Gravitational lensing is the relativistic effect generated by massive bodies, which bend the space-time surrounding them. It is a deeply investigated topic in astrophysics and allows validating theoretical relativistic results and studying…

The use of accurate scanning transmission electron microscopy (STEM) image simulation methods require large computation times that can make their use infeasible for the simulation of many images. Other simulation methods based on linear…

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…

Graph convolutional neural networks (GCNs) generalize tradition convolutional neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to high dimensional irregular graphs (e.g., text documents on word embeddings). Due to…

Generative Adversarial Networks (GANs) are a type of generative model which have received much attention due to their ability to model complex real-world data. Despite their recent successes, the process of training GANs remains…

A Generative Adversarial Network (GAN) with generator $G$ trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. Here, we propose a new method of deploying a…

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…

Deep generative models such as GANs, normalizing flows, and diffusion models are powerful regularizers for inverse problems. They exhibit great potential for helping reduce ill-posedness and attain high-quality results. However, the latent…

Generative Adversarial Networks (GANs) is a novel class of deep generative models which has recently gained significant attention. GANs learns complex and high-dimensional distributions implicitly over images, audio, and data. However,…

Unsupervised learning of generative models has seen tremendous progress over recent years, in particular due to generative adversarial networks (GANs), variational autoencoders, and flow-based models. GANs have dramatically improved sample…