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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (1): 1-12.doi: 10.3969/j.issn.1005-3085.2025.01.001

• •    下一篇

基于改进指数全变分的图像重建模型

李  艳1,  郭定辉2   

  1. 1. 公安部第一研究所，北京 100048
    2. 北京航空航天大学数学科学学院，北京 102218
  • 收稿日期:2022-07-18 接受日期:2023-06-29 出版日期:2025-02-15 发布日期:2025-04-15

Image Reconstruction Model Based on Improved Exponential Total Variation

LI Yan1,  GUO Dinghui2   

  1. 1. First Research Institute of the Ministry of Public Security of PRC, Beijing 100048
    2. School of Mathematical Science, Beihang University, Beijing 102218
  • Received:2022-07-18 Accepted:2023-06-29 Online:2025-02-15 Published:2025-04-15

摘要：

将指数全变分引入计算机断层成像重建模型中，建立能够在能量较低时进行灰度变换以适当地抑制阶梯效应且能在能量较高时避免出现过平滑的改进指数全变分重建模型(Modified Exponential Total Variation, METV)，并利用变分方法证明该改进模型对应的最小化问题的解的存在性。通过实验验证了，在添加了不同强度的混合噪声的情况下，相对于TV模型和ETV模型，METV重建模型都能够得到非常接近真实图像的重建图像，且得到的图像边缘结构更加清晰。

关键词: 全变分重建模型, 图像重建, 能量曲线, 变分法, 解的存在性

Abstract:

In this paper, exponential total variational reconstruction model is introduced into computed tomography reconstruction model to establish an improved exponential total variational reconstruction model (METV) which can perform gray transformation at low energy to properly suppress the step effect and avoid over-smoothing at high energy. The existence of the solution of the minimization problem corresponding to the improved model is proved by variational method. It is also verified by experiments that under the condition of adding mixed noise of different intensity, compared with TV and ETV models, the reconstructed image of METV model can be very close to the real image, and the obtained image edge structure is clearer.

Key words: total variation reconstruction model, image reconstruction, energy curve, variational method, existence of a solution

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