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Sparsity-constrained PET image reconstruction with learned dictionaries

机译：具有学习词典的稀疏约束PET图像重建

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摘要

PET imaging plays an important role in scientific and clinical measurement of biochemical and physiological processes. Model-based PET image reconstruction such as the iterative expectation maximization algorithm seeking the maximum likelihood solution leads to increased noise. The maximum a posteriori (MAP) estimate removes divergence at higher iterations. However, a conventional smoothing prior or a total-variation (TV) prior in a MAP reconstruction algorithm causes over smoothing or blocky artifacts in the reconstructed images. We propose to use dictionary learning (DL) based sparse signal representation in the formation of the prior for MAP PET image reconstruction. The dictionary to sparsify the PET images in the reconstruction process is learned from various training images including the corresponding MR structural image and a self-created hollow sphere. Using simulated and patient brain PET data with corresponding MR images, we study the performance of the DL-MAP algorithm and compare it quantitatively with a conventional MAP algorithm, a TV-MAP algorithm, and a patch-based algorithm. The DL-MAP algorithm achieves improved bias and contrast (or regional mean values) at comparable noise to what the other MAP algorithms acquire. The dictionary learned from the hollow sphere leads to similar results as the dictionary learned from the corresponding MR image. Achieving robust performance in various noise-level simulation and patient studies, the DL-MAP algorithm with a general dictionary demonstrates its potential in quantitative PET imaging.
机译：PET成像在生化和生理过程的科学和临床测量中起着重要作用。基于模型的PET图像重建（例如寻求最大似然解的迭代期望最大化算法）会导致噪声增加。最大后验（MAP）估计消除了较高迭代次数的发散。但是，MAP重建算法中的常规平滑先验或总变化（TV）先验会导致重建图像中出现过度平滑或块状伪影。我们建议在MAP PET图像重建先验的形成中使用基于字典学习（DL）的稀疏信号表示。从各种训练图像（包括相应的MR结构图像和自创建的空心球）中学习了在重建过程中稀疏PET图像的字典。使用模拟和患者的大脑PET数据以及相应的MR图像，我们研究了DL-MAP算法的性能，并将其与常规MAP算法，TV-MAP算法和基于补丁的算法进行了定量比较。 DL-MAP算法可在与其他MAP算法获得的噪声相当的噪声下实现改进的偏差和对比度（或区域平均值）。从空心球学到的字典得到与从相应的MR图像学到的字典相似的结果。 DL-MAP算法在各种噪声级模拟和患者研究中均具有出色的性能，带有通用词典的DL-MAP算法证明了其在定量PET成像中的潜力。

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