Multiplexing Kernelized Expectation Maximization Reconstruction for PET-MR

Since the kernel method was first proposed in positron emission tomography (PET), it has been successfully used for different applications. PET-MR scanners allow the acquisition of multiple MR sequences, in parallel to PET, for the same subject, to improve PET image reconstruction and lesion detectability. In this work we propose and investigate a version of the kernel method which exploits the information contained in multiple MR images and potentially CT or PET images. To do so, we modify the non-hybrid and hybrid kernel methods (KEM and HKEM respectively) such that the kernel matrix is obtained using additional Gaussian terms carrying the features from multiple MR images. We call these new methods multiplexing-HKEM (MHKEM) when the PET iterative information is included and "multiplexing-KEM" (MKEM) when only static images are included. We hypothesized a case where two MR images are beneficial using a simulated torso dataset. The technique was implemented in the open source Software for Tomographic Image Reconstruction (STIR) library. The proposed algorithm uses images from two different MR sequences, called MR₁ and MR₂, and PET update images to create multiple feature vectors for each voxel in the image which contains the information about the local neighborhood. The simulated dataset is reconstructed with 10 iterations and 23 subsets using HKEM, KEM, MHKEM and MKEM in three possible cases:1)HKEM, KEM with MR₁;2)HKEM, KEM with MR₂;3)MHKEM, MKEM with MR₁ and MR₂.The results show that HKEM is more reliable than KEM due to its ability to exploit functional and anatomical information together. Although the standard HKEM can work well when we focus on a specific region, it can over-smooth other regions which might also be of interest. The MHKEM can provide good quantification, resolution and noise suppression for different areas where the disease might appear compared to the standard HKEM and KEM where the improvement is restricted to a local area. Whenever the two MR images contain information that complement each other, the MHKEM improved results for the two areas of interest. This techniques can potentially become very useful in oncology, as the detection of primary and metastatic lesions of different type and soft-tissue environment in PET images might benefit from the utilization of multiple MR sequences.