Related papers: Bayesian Signal Separation via Plug-and-Play Diffu…

The present operation of the ground-based network of gravitational-wave laser interferometers in "enhanced" configuration brings the search for gravitational waves into a regime where detection is highly plausible. The development of…

We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…

In graph signal processing (GSP), prior information on the dependencies in the signal is collected in a graph which is then used when processing or analyzing the signal. Blind source separation (BSS) techniques have been developed and…

GNSS localization is an important part of today's autonomous systems, although it suffers from non-Gaussian errors caused by non-line-of-sight effects. Recent methods are able to mitigate these effects by including the corresponding…

In this paper, a Bayesian fusion technique for remotely sensed multi-band images is presented. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g.,…

Most existing graph diffusion models have significant bias problems. We observe that the forward diffusion's maximum perturbation distribution in most models deviates from the standard Gaussian distribution, while reverse sampling…

Bayesian model selection, with precedents in George and McCulloch (1993) and Abramovich et al. (1998), support credibility measures that relate model uncertainty, but computation can be costly when sparse priors are approximate. We design…

Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to…

In recent studies, diffusion models have shown promise as priors for solving audio inverse problems. These models allow us to sample from the posterior distribution of a target signal given an observed signal by manipulating the diffusion…

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…

All 21-cm signal experiments rely on electronic receivers that affect the data via both multiplicative and additive biases through the receiver's gain and noise temperature. While experiments attempt to remove these biases, the residuals of…

Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…

We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem…

Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on…

Diffusion models have emerged as powerful learned priors for Bayesian inverse problems (BIPs). Diffusion-based solvers rely on a presumed likelihood for the observations in BIPs to guide the generation process. Likelihood misspecification…

We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically…

Mixture models are a standard tool in statistical analyses, widely used for density modeling and model-based clustering. In this work, we propose a Bayesian mixture model with repulsion between mixture components. Such repulsion helps…

We explore the connection between Plug-and-Play (PnP) methods and Denoising Diffusion Implicit Models (DDIM) for solving ill-posed inverse problems, with a focus on single-pixel imaging. We begin by identifying key distinctions between PnP…

In this paper, we propose a novel method for separately estimating spectral distributions from images captured by a typical RGB camera. The proposed method allows us to separately estimate a spectral distribution of illumination,…

Diffusion models have been demonstrated as powerful deep learning tools for image generation in CT reconstruction and restoration. Recently, diffusion posterior sampling, where a score-based diffusion prior is combined with a likelihood…