{"title":"Adaptative regularization parameter for Poisson noise with a bilevel approach: application to spectral computerized tomography","authors":"B. Sixou","doi":"10.1080/17415977.2020.1864348","DOIUrl":null,"url":null,"abstract":"In this paper, we present a method of choice of an adaptative regularization parameter for data corrupted by Poisson noise based on a bilevel approach. The forward operator considered is nonlinear. The existence and unicity of the smoothed lower level problem, the differentiability properties of the constraint, and the adjoint method used to calculate the gradient of the reduced functional are studied in detail. The variance of the KL functional for Poisson noise is also investigated. The method is applied to the spectral CT inverse problem. Better reconstruction results are obtained with the bilevel method of choice than with a scalar regularization parameter.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1519 - 1536"},"PeriodicalIF":1.1000,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1864348","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems in Science and Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/17415977.2020.1864348","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we present a method of choice of an adaptative regularization parameter for data corrupted by Poisson noise based on a bilevel approach. The forward operator considered is nonlinear. The existence and unicity of the smoothed lower level problem, the differentiability properties of the constraint, and the adjoint method used to calculate the gradient of the reduced functional are studied in detail. The variance of the KL functional for Poisson noise is also investigated. The method is applied to the spectral CT inverse problem. Better reconstruction results are obtained with the bilevel method of choice than with a scalar regularization parameter.
期刊介绍：
Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome.
Topics include:
-Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks).
-Material properties: determination of physical properties of media.
-Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.).
-Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.).
-Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
