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基于最大后验估计的编码孔图像重建算法

秦玉瑞 朱巴邻 王忠海 周荣 杨朝文

秦玉瑞, 朱巴邻, 王忠海, 等. 基于最大后验估计的编码孔图像重建算法[J]. 强激光与粒子束. doi: 10.11884/HPLPB202436.240152
引用本文: 秦玉瑞, 朱巴邻, 王忠海, 等. 基于最大后验估计的编码孔图像重建算法[J]. 强激光与粒子束. doi: 10.11884/HPLPB202436.240152
Qin Yurui, Zhu Balin, Wang Zhonghai, et al. Coded-aperture image reconstruction algorithm based on Maximum a Posteriori estimation[J]. High Power Laser and Particle Beams. doi: 10.11884/HPLPB202436.240152
Citation: Qin Yurui, Zhu Balin, Wang Zhonghai, et al. Coded-aperture image reconstruction algorithm based on Maximum a Posteriori estimation[J]. High Power Laser and Particle Beams. doi: 10.11884/HPLPB202436.240152

基于最大后验估计的编码孔图像重建算法

doi: 10.11884/HPLPB202436.240152
详细信息
    作者简介:

    秦玉瑞,yr.qin@foxmail.com

    通讯作者:

    王忠海,zhonghaiwang@scu.edu.cn

  • 中图分类号: TL812+.1

Coded-aperture image reconstruction algorithm based on Maximum a Posteriori estimation

  • 摘要: 图像重建算法对编码孔伽马相机的成像性能有重要的影响,然而广泛使用的最大似然期望最大化(MLEM)算法无法在较强干扰背景下有效抑制图像中的噪声,当超过一定迭代次数后,图像信噪比会逐渐降低。本文针对MLEM算法的这一“病态性”问题开展了研究。首先将最大后验估计(MAP)算法应用于编码孔图像重建,接着分析了算法中Gibbs先验函数的邻域大小和权值系数等关键参数的选取方法。然后使用编码孔相机开展了成像实验,对比了MLEM算法与MAP算法对22Na点源的图像重建结果。结果表明,在300至1200次迭代下,MLEM重建图像中出现了明显的噪点,且随着迭代深入图像质量逐渐变差;而MAP重建图像没有出现明显噪点,重建图像的平均梯度相较于MLEM降低了26.45%至49.16%,对比度噪声比(CNR)提升了42.32%至351.07%。另外,对比了3×3和5×5邻域大小时的多点源图像重建结果,结果显示,邻域过小会导致重建图像的热点亮度降低,与理论分析结果一致。最后,分别对比了MLEM与MAP算法在较远距离和较强干扰两种场景下的成像结果,MAP算法均表现出更良好的信噪比性能。
  • 图  1  编码孔成像原理示意图

    Figure  1.  Schematic diagram of coding-aperture imaging

    图  2  3倍采样数时的点扩散函数和势函数的邻域权值系数

    Figure  2.  Point spread function and neighbourhood weight coefficients of the potential function at 3 times the samples

    图  3  邻域范围过小会导致热点值降低

    Figure  3.  Too small a neighbourhood range results in lower hotspot values

    图  4  惩罚系数计算方法示意图

    Figure  4.  Schematic diagram of the penalty coefficient calculation method

    图  5  编码孔伽马相机示意图和实物图

    Figure  5.  Schematic and physical diagram of the coded-aperture gamma camera

    图  6  蒙特卡洛模拟示意图

    Figure  6.  Diagram of Monte Carlo simulation

    图  7  系统响应矩阵(484×961)

    Figure  7.  System response matrix (484×961)

    图  8  伽马源精确成像实验平台

    Figure  8.  Experimental platform for precision imaging of γ sources

    图  9  22Na点源在逐渐递增迭代次数下的MLEM和MAP重建图像

    Figure  9.  The MLEM and MAP reconstruction images of 22Na point source with increasing iterations

    图  10  22Na点源在逐渐递增迭代次数下的MLEM与MAP重建图像二维切片

    Figure  10.  2D slices of MLEM and MAP reconstructed images for a 22Na point source with increasing iterations

    图  11  在300、500、800和1200迭代次数下,MLEM和MAP算法重建图像的平均梯度值与CNR值对比

    Figure  11.  Comparison of the mean gradient values and CNRs of reconstructed images using MLEM and MAP algorithms at 300, 500, 800, and 1200 iterations

    图  12  相同参数(δ=0.003,β=0.03,迭代500次)下,使用MLEM、3×3邻域MAP和5×5邻域MAP算法的多点22Na源重建结果对比

    Figure  12.  Comparison of the reconstruction results of multipoint 22Na sources using MLEM, 3×3 neighbourhood MAP and 5×5 neighbourhood MAP algorithms with the same parameters (δ = 0.003, β = 0.03, 500 iterations)

    图  13  对同一个辐射源,MLEM重建图像和分别使用L1、L2、Huber势函数时的MAP重建图像二维切片

    Figure  13.  2D slices of the MLEM reconstructed image and the MAP reconstructed image when using the L1, L2, and Huber potential functions, respectively, for the same radiation source

    图  14  远距离实景成像时,MLEM与MAP算法的成像效果对比

    Figure  14.  Comparison of the effectiveness between the MLEM and the MAP algorithms when imaging at long distances

    图  15  在有干扰源的狭窄环境中,MLEM与MAP算法的成像效果对比

    Figure  15.  Comparison of the effectiveness between the MLEM and MAP algorithms in a confined environment with disturbance sources

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  • 收稿日期:  2024-05-08
  • 修回日期:  2024-05-09
  • 录用日期:  2024-06-13
  • 网络出版日期:  2024-07-09

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