大规模贝叶斯半盲去卷积

Bayesian estimation of regularization and PSF parameters for Wiener-Hunt deconvolution

This paper tackles the problem of image deconvolution with joint estimation of PSF parameters and hyperparameters. Within a Bayesian framework, the solution is inferred via a global a posteriori law for unknown parameters and object. The estimate is chosen as the posterior mean, numerically calculated by means of a Monte-Carlo Markov chain algorithm. The estimates are efficiently computed in the Fourier domain and the effectiveness of the method is shown on simulated examples. Results show precise estimates for PSF parameters and hyperparameters as well as precise image estimates including res…

Unsupervised bayesian convex deconvolution based on a field with an explicit partition function

This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function. To the best of our knowledge, this is an original contribution. Moreover, the explicit expression of the partition function enables the development of an unsupervised edge-preserving convex deconvolution method. The method is fully Bayesian, and produces an estimate in the sense of the posterior mean, numerically calculated by means of a Monte-Carlo Markov Chain technique. The approach is particularly effective and the computational practicability of the method is shown on a simple simulated…

将贝叶斯频谱反卷积与专家科学推理相结合以实现稳健的峰估计

Integrating Bayesian Spectral Deconvolution and Expert Scientific Reasoning for Robust Peak Estimation

本文提出一种结合频谱反卷积与专家科学推理的贝叶斯框架，用于在存在高强度噪声或未知背景时稳健地估计峰结构，通过将物理性质回归层与贝叶斯频谱反卷积结合，提升峰识别的准确性。

准贝叶斯序列反卷积

Quasi-Bayesian sequential deconvolution

针对流式数据密度反卷积的计算瓶颈，提出基于牛顿递归算法的准贝叶斯非参数序列反卷积方法，兼具精度与计算优势，可扩展至大规模数据。

Adaptive Posterior Convergence Rates in Bayesian Density Deconvolution with Supersmooth Errors

Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty quantification and generalizability to more sophisticated models. This article is the first substantive effort to theoretically quantify the behavior of the posterior in this recent line of research. In particular, assuming a known supersmooth error density, a Dirichlet process mixture of Normals on the true density leads to a posterior convergence rate same as the …

Bayesian Spectral Deconvolution of X-Ray Absorption Near Edge Structure Discriminating High- and Low-Energy Domains

In this paper, we propose a Bayesian spectral deconvolution considering the properties of peaks in different energy domains. Bayesian spectral deconvolution regresses spectral data into the sum of multiple basis functions. Conventional methods use a model that treats all peaks equally. However, in X-ray absorption near edge structure (XANES) spectra, the properties of the peaks differ depending on the energy domain, and the specific energy domain of XANES is essential in condensed matter physics. We propose a model that discriminates between the low- and high-energy domains. We also propose a …

Bayesian Semiparametric Multivariate Density Deconvolution via Stochastic Rotation of Replicates

We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually straightforward yet fundamentally novel and highly robust approach to multivariate density deconvolution by stochastically rotating the replicates toward the corresponding true latent values. We also address the additionally significantly challenging problem of accommodating conditionally heteroscedastic measurement errors in this newly introduced framework. We …

Nonparametric Bayesian Deconvolution of a Symmetric Unimodal Density

We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where the observed data are estimated effect sizes from regressions on multiple factors, where the target is the distribution of the true effect sizes. We exploit the fact that any symmetric and unimodal density can be expressed as a mixture of symmetric uniform densities, and model the mixing density in a new way using a Dirichlet process location-mixture of Gamm…

Fast Bayesian Deconvolution using Simple Reversible Jump Moves

We propose a Markov chain Monte Carlo-based deconvolution method designed to estimate the number of peaks in spectral data, along with the optimal parameters of each radial basis function. Assuming cases where the number of peaks is unknown, and a sweep simulation on all candidate models is computationally unrealistic, the proposed method efficiently searches over the probable candidates via trans-dimensional moves assisted by annealing effects from replica exchange Monte Carlo moves. Through simulation using synthetic data, the proposed method demonstrates its advantages over conventional swe…

Bayesian Spectral Deconvolution Based on Poisson Distribution: Bayesian Measurement and Virtual Measurement Analytics (VMA)

In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework for considering not only the target physical model but also the measurement model as a probabilistic model, and enables us to estimate the parameter of a physical model with its confidence interval through a Bayesian posterior distribution given a measurement data set. The measurement with Poisson noise is one of the most effective system to apply our propose…