Image reconstruction of low-count positron emission tomography (PET) data is challenging. Kernel methods address the challenge by incorporating image prior information in the forward model of iterative PET image reconstruction. The kernelized expectation-maximization (KEM) algorithm has been developed and demonstrated to be effective and easy to implement. A common approach for a further improvement of the kernel method would be adding an explicit regularization, which however leads to a complex optimization problem. In this paper, we propose an implicit regularization for the kernel method by using a deep coefficient prior, which represents the kernel coefficient image in the PET forward model using a convolutional neural-network. To solve the maximum-likelihood neural network-based reconstruction problem, we apply the principle of optimization transfer to derive a neural KEM algorithm. Each iteration of the algorithm consists of two separate steps: a KEM step for image update from the projection data and a deep-learning step in the image domain for updating the kernel coefficient image using the neural network. This optimization algorithm is guaranteed to monotonically increase the data likelihood. The results from computer simulations and real patient data have demonstrated that the neural KEM can outperform existing KEM and deep image prior methods.

翻译：重塑低数正电子排放断层仪( PET) 数据 的图像重建具有挑战性。 Kernel 方法通过将图像先前信息纳入迭代 PET 图像重建的前方模型中来应对挑战。 已经开发并展示了内核期望- 最大化( KEM) 算法, 该算法是有效和容易执行的。 进一步改进内核方法的共同方法将增加一个清晰的正规化, 但是这会导致复杂的优化问题。 在本文中, 我们提议对内核方法进行隐含的规范化, 方法是使用一个深厚系数, 之前的系数代表 PET 前方模型中的内核系数图象, 使用一个神经网络 。 为了解决以最大相似性神经网络为基础的重建问题, 我们应用优化传输原则来生成一个神经的 KEM 算法。 算法的每一次循环包括两个不同的步骤: KEM 图像更新的KEM 步骤, 以及 利用神经网络更新内核系数图像的深层学习步骤。 这种优化算法保证单质地增加数据的可能性。 KEM 以前的计算机模拟和真实的图像方法可以显示现有的 KEM 。