Neural KEM: A Kernel Method with Deep Coefficient Prior for PET Image Reconstruction

TL;DR

Neural KEM introduces a deep coefficient prior into kernel-based PET image reconstruction, combining neural networks with the KEM algorithm to improve image quality in low-count PET data.

Contribution

It proposes a novel neural KEM algorithm that integrates deep learning as an implicit regularizer within the kernel method for PET reconstruction.

Findings

Outperforms existing KEM methods in simulations and real data.

Guarantees monotonic increase in data likelihood during optimization.

Effectively incorporates deep prior for improved image quality.

Abstract

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.