Related papers: Bayesian Inversion for Nonlinear Imaging Models us…

Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point…

Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through…

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…

Variational method and deep learning method are two mainstream powerful approaches to solve inverse problems in computer vision. To take advantages of advanced optimization algorithms and powerful representation ability of deep neural…

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…

Image denoisers have been shown to be powerful priors for solving inverse problems in imaging. In this work, we introduce a generalization of these methods that allows any image restoration network to be used as an implicit prior. The…

In this paper, we consider the highly ill-posed problem of jointly recovering two real-valued signals from the phaseless measurements of their circular convolution. The problem arises in various imaging modalities such as Fourier…

Generative models, such as GANs, learn an explicit low-dimensional representation of a particular class of images, and so they may be used as natural image priors for solving inverse problems such as image restoration and compressive…

Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…

Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as…

Due to the cross-domain distribution shift aroused from diverse medical imaging systems, many deep learning segmentation methods fail to perform well on unseen data, which limits their real-world applicability. Recent works have shown the…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…

Existing image restoration methods mostly leverage the posterior distribution of natural images. However, they often assume known degradation and also require supervised training, which restricts their adaptation to complex real…

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Recent advances in deep learning have led to a paradigm shift in the field of reversible steganography. A fundamental pillar of reversible steganography is predictive modelling which can be realised via deep neural networks. However,…

Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…

We propose a sampling algorithm to perform system identification from a set of input-output graph signal pairs. The dynamics of the systems we study are given by a partially known adjacency matrix and a generic parametric graph filter of…