Accurate tumor segmentation from PET images is crucial in many radiation oncology applications. Among others, partial volume effect (PVE) is recognized as one of the most important factors degrading imaging quality and segmentation accuracy in PET. Taking into account that image restoration and tumor segmentation are tightly coupled and can promote each other, we proposed a variational method to solve both problems simultaneously in this study. The proposed method integrated total variation (TV) semi-blind de-convolution and Mumford-Shah segmentation with multiple regularizations. Unlike many existing energy minimization methods using either TV or L2 regularization, the proposed method employed TV regularization over tumor edges to preserve edge information, and L2 regularization inside tumor regions to preserve the smooth change of the metabolic uptake in a PET image. The blur kernel was modeled as anisotropic Gaussian to address the resolution difference in transverse and axial directions commonly seen in a clinic PET scanner. The energy functional was rephrased using the Γ-convergence approximation and was iteratively optimized using the alternating minimization (AM) algorithm. The performance of the proposed method was validated on a physical phantom and two clinic datasets with non-Hodgkin's lymphoma and esophageal cancer, respectively. Experimental results demonstrated that the proposed method had high performance for simultaneous image restoration, tumor segmentation and scanner blur kernel estimation. Particularly, the recovery coefficients (RC) of the restored images of the proposed method in the phantom study were close to 1, indicating an efficient recovery of the original blurred images; for segmentation the proposed method achieved average dice similarity indexes (DSIs) of 0.79 and 0.80 for two clinic datasets, respectively; and the relative errors of the estimated blur kernel widths were less than 19% in the transversal direction and 7% in the axial direction.

中文翻译：

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使用多个正则化在PET中同时进行肿瘤分割，图像恢复和模糊核估计。

从PET图像准确分割肿瘤在许多放射肿瘤学应用中至关重要。其中，部分体积效应（PVE）被认为是降低PET成像质量和分割精度的最重要因素之一。考虑到图像恢复和肿瘤分割紧密相关并且可以互相促进，我们提出了一种变分方法来同时解决这两个问题。所提出的方法将总变异（TV）半盲反卷积和Mumford-Shah分割与多个正则化相结合。与许多使用TV或L2正则化的现有能量最小化方法不同，所提出的方法在肿瘤边缘上采用TV正则化来保留边缘信息，并在肿瘤区域内进行L2正则化，以保持PET图像中代谢摄取的平稳变化。将模糊核建模为各向异性高斯模型，以解决在临床PET扫描仪中常见的横向和轴向分辨率差异。能量函数使用Γ收敛近似重新表达，并使用交替最小化（AM）算法进行迭代优化。分别在物理模型和非霍奇金淋巴瘤和食道癌的两个临床数据集上验证了该方法的性能。实验结果表明，该方法在同时图像复原，肿瘤分割和扫描仪模糊核估计方面具有较高的性能。尤其，在幻像研究中，该方法的恢复图像的恢复系数（RC）接近1，表明可以有效恢复原始模糊图像。对于分割，所提出的方法对于两个临床数据集分别达到0.79和0.80的平均骰子相似性指数（DSI）；估计的模糊核宽度的相对误差在横向方向上小于19％，在轴向方向上小于7％。