{"title":"Bayesian Inference","authors":"F. Ronquist, P. Beerli","doi":"10.4135/9780857020123.n32","DOIUrl":null,"url":null,"abstract":"The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. Subband decomposi-tions of natural images have significantly non-Gaussian higher-order point statistics; these statistics capture image properties that elude Fourier-based techniques. We develop a Bayesian estimator that is a natural exten-sion of the Wiener solution, and that exploits these higher-order statistics. The resulting nonlinear estimator performs a “coring” operation. We provide a simple model for the subband statistics, and use it to develop a semi-blind noise-removal algorithm based on a steerable wavelet pyramid. common","PeriodicalId":430973,"journal":{"name":"Computer Age Statistical Inference, Student Edition","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Age Statistical Inference, Student Edition","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4135/9780857020123.n32","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. Subband decomposi-tions of natural images have significantly non-Gaussian higher-order point statistics; these statistics capture image properties that elude Fourier-based techniques. We develop a Bayesian estimator that is a natural exten-sion of the Wiener solution, and that exploits these higher-order statistics. The resulting nonlinear estimator performs a “coring” operation. We provide a simple model for the subband statistics, and use it to develop a semi-blind noise-removal algorithm based on a steerable wavelet pyramid. common