A Kernel Method for PET Image Reconstruction with Graph Laplacian Regularization

SHENG Yu-xia; SUN Kun; CHAI Li

doi:10.12263/DZXB.20221161

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A Kernel Method for PET Image Reconstruction with Graph Laplacian Regularization

PAPERS | 更新时间：2026-04-10

- A Kernel Method for PET Image Reconstruction with Graph Laplacian Regularization
- ACTA ELECTRONICA SINICA Vol. 52, Issue 1, Pages: 118-128(2024)
- 作者机构：
  
  1.武汉科技大学信息科学与工程学院，湖北武汉 430081
  2.浙江大学控制科学与工程学院，浙江杭州 310027
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(62173259);Natural Science Foundation of Hubei Province(2022CFB110)
- DOI：10.12263/DZXB.20221161
  CLC： TN911.7;
- Received：14 October 2022，
  
  Revised：2023-01-19，
  
  Published：25 January 2024
- 稿件说明：
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盛玉霞,孙坤,柴利.基于图拉普拉斯正则化的PET图像核重建方法[J].电子学报,2024,52(01):118-128.

SHENG Yu-xia,SUN Kun,CHAI Li.A Kernel Method for PET Image Reconstruction with Graph Laplacian Regularization[J].ACTA ELECTRONICA SINICA,2024,52(01):118-128.
盛玉霞,孙坤,柴利.基于图拉普拉斯正则化的PET图像核重建方法[J].电子学报,2024,52(01):118-128. DOI： 10.12263/DZXB.20221161.

SHENG Yu-xia,SUN Kun,CHAI Li.A Kernel Method for PET Image Reconstruction with Graph Laplacian Regularization[J].ACTA ELECTRONICA SINICA,2024,52(01):118-128. DOI： 10.12263/DZXB.20221161.

摘要

正电子发射断层成像（Positron Emission Tomography，PET）在很多疾病的早期诊断中有重要的作用，PET图像重建的难点之一是如何在保持重建图像中病灶边缘特性的同时具有良好的去噪性能.针对此问题，本文提出了一种结合图拉普拉斯正则化和深度图像先验的PET图像核重建方法.设计了改进的U-net神经网络，将PET前向投影模型中的核系数表示为神经网络的输出；通过先验图像构建图拉普拉斯矩阵，重建问题被建模为基于神经网络的带图拉普拉斯正则化项的最大似然函数优化问题.利用优化转移方法导出了收敛的迭代重建算法，每一次迭代包括由核重建方法更新图像和利用神经网络更新核系数两个步骤.仿真和临床实验结果表明，本文提出的方法在不同的指标下都有更好的重建效果，优于已有核重建方法以及最新的基于深度系数先验的重建方法.

Abstract

Positron emission tomography (PET) plays an important role in the early diagnosis of many diseases

and one of the difficult problems in PET image reconstruction is how to maintain the edge characteristics of the lesion in the reconstructed image while having good denoising performance. To this problem

a kernel method for PET image reconstruction is proposed

which combines deep image prior and the graph Laplacian regularization. An improved U-net neural network is designed to represent the kernel coefficients in the PET forward model. The graph Laplacian matrix is constructed by the prior information. The reconstruction model is formulated as a maximum likelihood neural network-based constrained optimization problem with graph Laplacian regularization. By applying the optimization transfer algorithm

we derive a convergent iterative algorithm.Each iteration includes a KEM step for updating image and a kernel coefficient update step using neural network. The results from simulations and in-vivo data demonstrate that the proposed method has better reconstruction performance under different criteria

and outperforms the kernelized expectation maximization (KEM) and the state of the art neural KEM methods.

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