Adaptative regularization parameter for Poisson noise with a bilevel approach: application to spectral computerized tomography

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2020-12-22 DOI:10.1080/17415977.2020.1864348

B. Sixou

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.

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基于双能级法的泊松噪声自适应正则化参数:在光谱计算机断层扫描中的应用

在本文中，我们提出了一种基于双层方法的泊松噪声破坏数据的自适应正则化参数的选择方法。所考虑的前向算子是非线性的。详细研究了光滑低阶问题的存在性和唯一性，约束的可微性，以及用于计算降阶泛函梯度的伴随方法。还研究了泊松噪声下KL函数的方差。将该方法应用于谱CT逆问题。与标量正则化参数相比，所选择的双层方法获得了更好的重建结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

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.