Related papers: Noise-Adaptive Diffusion Sampling for Inverse Prob…
Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…
Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions.…
The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…
We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…
Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse…
Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…
We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target…
Deep learning has proven to be important for CT image denoising. However, such models are usually trained under supervision, requiring paired data that may be difficult to obtain in practice. Diffusion models offer unsupervised means of…
Deep learning (DL)-based methods have achieved state-of-the-art performance for many medical image segmentation tasks. Nevertheless, recent studies show that deep neural networks (DNNs) can be miscalibrated and overconfident, leading to…
The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution…
Building upon Lagrangian mechanics on Wess's $q$-commutative spaces, we derive the $q$-deformed Hamiltonian dynamics as formulated by Lavagno et al. (2006). We then develop a computationally tractable scheme and propose a novel Hamiltonian…
In this work, we focus on the inverse medium scattering problem (IMSP), which aims to recover unknown scatterers based on measured scattered data. Motivated by the efficient direct sampling method (DSM) introduced in [23], we propose a…
We introduce a variant of the Hybrid Monte Carlo (HMC) algorithm to address large-deviation statistics in stochastic hydrodynamics. Based on the path-integral approach to stochastic (partial) differential equations, our HMC algorithm…
Diffusion models have demonstrated exceptional ability in modeling complex image distributions, making them versatile plug-and-play priors for solving imaging inverse problems. However, their reliance on large-scale clean datasets for…
Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…
Inverse problems, where the goal is to recover an unknown signal from noisy or incomplete measurements, are central to applications in medical imaging, remote sensing, and computational biology. Diffusion models have recently emerged as…
We explore the use of Hamiltonian Monte Carlo (HMC) sampling as a probabilistic last layer approach for deep neural networks (DNNs). While HMC is widely regarded as a gold standard for uncertainty estimation, the computational demands limit…
This paper concerns the Bayesian approach to inverse acoustic scattering problems of inferring the position and shape of a sound-soft obstacle from phaseless far-field data generated by point source waves. To improve the convergence rate,…