基于贝叶斯推断的高斯反卷积信号恢复  

Gaussian Deconvolution Signal Recovery Based on Bayesian Inference

作　　者：吕若曦 曾雪迎 Lv Ruoxi;Zeng Xueying(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2024年第12期162-168,共7页Periodical of Ocean University of China

基　　金：青岛市自然科学基金项目(23-2-1-158-zyyd-jch);中央高校基本科研业务费专项(202064006)资助。

摘　　要：针对高斯卷积和白噪声干扰的降质信号,提出一种基于贝叶斯推断的信号恢复模型和数值算法。在模型中引入模型差异项来描述卷积核估计误差,并用高斯分布来描述其统计特性。基于贝叶斯推断,将后验分布解耦为多个推断问题,对信号、模型误差和卷积核参数分别利用原始对偶混合梯度方法、高斯共轭先验法、随机游走的Metropolis算法进行交替更新,有效恢复信号的同时对卷积核参数进行不确定性量化并避免误差传播。数值实验表明,本方法可以同时估计卷积核和恢复信号,性能优于传统的信号恢复方法。In this paper,we propose a novel signal restoration model and numerical algorithm based on the Bayesian inference to restore the degraded signals caused by Gaussian convolution and white noise interference.A discrepancy term to describe the estimation error of the convolution kernel is introduced in the model,and use Gaussian distribution to describe its statistical properties.Based on Bayesian inference,we then decouple the posterior distribution into multiple inference problems and employ the primal-dual hybrid gradient method,the Gaussian conjugate prior method,the Metropolis algorithm of random walk to update the signal,the model discrepancy term,and the convolution parameter,respectively.This method enables us to achieve effective signal recovery while quantifying the uncertainty associated with the convolution kernel parameter,thereby avoiding error propagation.Numerical experiments show that the proposed method outperforms the compared method by simultaneously recovering the signal and estimating the convolution kernel.

关 键 词：贝叶斯反问题 盲反卷积 信号恢复 原始对偶混合梯度 随机游走的Metropolis算法 

分 类 号：O242[理学—计算数学]