Related papers: Generalized Denoising Auto-Encoders as Generative …

Denoising autoencoders (DAE) are trained to reconstruct their clean inputs with noise injected at the input level, while variational autoencoders (VAE) are trained with noise injected in their stochastic hidden layer, with a regularizer…

Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…

Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a…

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…

Image denoising is an important pre-processing step in medical image analysis. Different algorithms have been proposed in past three decades with varying denoising performances. More recently, having outperformed all conventional methods,…

Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies…

Variations of deep neural networks such as convolutional neural network (CNN) have been successfully applied to image denoising. The goal is to automatically learn a mapping from a noisy image to a clean image given training data consisting…

With the inexorable digitalisation of the modern world, every subset in the field of technology goes through major advancements constantly. One such subset is digital images which are ever so popular. Images can not always be as visually…

A rekindled the interest in auto-encoder algorithms has been spurred by recent work on deep learning. Current efforts have been directed towards effective training of auto-encoder architectures with a large number of coding units. Here, we…

Image denoising methods must effectively model, implicitly or explicitly, the vast diversity of patterns and textures that occur in natural images. This is challenging, even for modern methods that leverage deep neural networks trained to…

The recovery of approximately sparse or compressible coefficients in a Polynomial Chaos Expansion is a common goal in modern parametric uncertainty quantification (UQ). However, relatively little effort in UQ has been directed toward…

We introduce a generative modeling framework for thermodynamic computing, in which structured data is synthesized from noise by the natural time evolution of a physical system governed by Langevin dynamics. While conventional diffusion…

Can neural networks systematically capture discrete, compositional task structure despite their continuous, distributed nature? The impressive capabilities of large-scale neural networks suggest that the answer to this question is yes.…

The amount of information lost in sub-Nyquist sampling of a continuous-time Gaussian stationary process is quantified. We consider a combined source coding and sub-Nyquist reconstruction problem in which the input to the encoder is a noisy…

Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind…

Learned image reconstruction techniques using deep neural networks have recently gained popularity, and have delivered promising empirical results. However, most approaches focus on one single recovery for each observation, and thus neglect…

Discovering latent representations of the observed world has become increasingly more relevant in data analysis. Much of the effort concentrates on building latent variables which can be used in prediction problems, such as classification…

Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…

In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…

Discriminative features extracted from the sparse coding model have been shown to perform well for classification. Recent deep learning architectures have further improved reconstruction in inverse problems by considering new dense priors…