Related papers: Dimension-reduced KRnet maps for high-dimensional …

Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While…

Dimension reduction (DR) is commonly utilized to capture the intrinsic structure and transform high-dimensional data into low-dimensional space while retaining meaningful properties of the original data. It is used in various applications,…

This paper addresses the challenge of dimension reduction (DR) in Bayesian inference of high-resolution two-or three-dimensional fields, where a priori parametrizations require a large number of terms. The underlying idea is common to…

In this paper, we present a novel approach for training a Variational Autoencoder (VAE) on a highly imbalanced data set. The proposed training of a high-resolution VAE model begins with the training of a low-resolution core model, which can…

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

The manifold assumption for high-dimensional data assumes that the data is generated by varying a set of parameters obtained from a low-dimensional latent space. Deep generative models (DGMs) are widely used to learn data representations in…

High-dimensional datasets often exhibit low-dimensional geometric structures, as suggested by the manifold hypothesis, which implies that data lie on a smooth manifold embedded in a higher-dimensional ambient space. While this insight…

Despite the recent progress in image dehazing, several problems remain largely unsolved such as robustness for varying scenes, the visual quality of reconstructed images, and effectiveness and flexibility for applications. To tackle these…

Identifying the heterogeneous conductivity field and reconstructing the contaminant release history are key aspects of subsurface remediation. Achieving these two goals with limited and noisy hydraulic head and concentration measurements is…

Magnetic Resonance Imaging can produce detailed images of the anatomy and physiology of the human body that can assist doctors in diagnosing and treating pathologies such as tumours. However, MRI suffers from very long acquisition times…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…

Longitudinal datasets measured repeatedly over time from individual subjects, arise in many biomedical, psychological, social, and other studies. A common approach to analyse high-dimensional data that contains missing values is to learn a…

Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…

Variational Autoencoders (VAE) are probabilistic deep generative models underpinned by elegant theory, stable training processes, and meaningful manifold representations. However, they produce blurry images due to a lack of explicit…

The variational autoencoder (VAE) is a powerful generative model that can estimate the probability of a data point by using latent variables. In the VAE, the posterior of the latent variable given the data point is regularized by the prior…

This paper addresses the problem of lossy image compression, a fundamental problem in image processing and information theory that is involved in many real-world applications. We start by reviewing the framework of variational autoencoders…

Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional…

We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator learning models, the proposed approach employs an encoder to…