Related papers: On Maximum-a-Posteriori estimation with Plug & Pla…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
Existing plug-and-play image restoration methods typically employ off-the-shelf Gaussian denoisers as proximal operators within classical optimization frameworks based on variable splitting. Recently, denoisers induced by generative priors…
Plug-and-Play (PnP) and Regularization-by-Denoising (RED) are recent paradigms for image reconstruction that leverage the power of modern denoisers for image regularization. In particular, they have been shown to deliver state-of-the-art…
Maximum-a-posteriori (MAP) approaches are an effective framework for inverse problems with known forward operators, particularly when combined with expressive priors and careful parameter selection. In blind settings, however, their use…
This paper presents a novel stochastic optimisation methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed…
In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is…
A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems, where the structure of the posterior can be very chaotic…
Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…
In compressed sensing (CS) MRI, model-based methods are pivotal to achieving accurate reconstruction. One of the main challenges in model-based methods is finding an effective prior to describe the statistical distribution of the target…
We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular…
Image denoising can be described as the problem of mapping from a noisy image to a noise-free image. The best currently available denoising methods approximate this mapping with cleverly engineered algorithms. In this work we attempt to…
Ptychography is a coherent diffraction imaging method that uses phase retrieval techniques to reconstruct complex-valued images. It achieves this by sequentially illuminating overlapping regions of a sample with a coherent beam and…
We propose a new approach for large-scale high-dynamic range computational imaging. Deep Neural Networks (DNNs) trained end-to-end can solve linear inverse imaging problems almost instantaneously. While unfolded architectures provide…
Deep model-based architectures (DMBAs) are widely used in imaging inverse problems to integrate physical measurement models and learned image priors. Plug-and-play priors (PnP) and deep equilibrium models (DEQ) are two DMBA frameworks that…
Post-stack seismic inversion is a widely used technique to retrieve high-resolution acoustic impedance models from migrated seismic data. Its modelling operator assumes that a migrated seismic data can be generated from the convolution of a…
This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is…
Hyperspectral images are typically composed of hundreds of narrow and contiguous spectral bands, each containing information regarding the material composition of the imaged scene. However, these images can be affected by various sources of…
Plug & Play methods combine proximal algorithms with denoiser priors to solve inverse problems. These methods rely on the computability of the proximal operator of the data fidelity term. In this paper, we propose a Plug & Play framework…
Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high…
We consider the problem of inferring high-dimensional data $\mathbf{x}$ in a model that consists of a prior $p(\mathbf{x})$ and an auxiliary differentiable constraint $c(\mathbf{x},\mathbf{y})$ on $x$ given some additional information…