Two novel PET image restoration methods guided by PET-MR kernels: Application to brain imaging

Abstract

Purpose: Post-reconstruction positron emission tomography (PET) image restoration methods that take advantage of available anatomical information can play an important role in accurate quantification of PET images. However, when using anatomical information, the resulting PET image may lose resolution in certain regions where the anatomy does not agree with the change in functional activity. In this work, this problem is addressed by using both magnetic resonance (MR) and filtered PET images to guide the denoising process.

Methods: In this work, two novel post-reconstruction methods for restoring PET images using the subject's registered T1-weighted MR image are proposed. The first method is based on a representation of the image using basis functions extracted from T1-weighted MR and filtered PET image. The coefficients for these basis functions are estimated using a sparsity-penalized least squares objective function. The second method is a noniterative fast method that uses guided kernel filtering in combination with twicing to restore the noisy PET image. When applied after conventional PVE correction, these methods can be considered as voxel-based MR-guided partial volume effect (PVE) correction methods.

Results: Using simulation analyses of [ ${}^{18}$ F]FDG PET images of the brain with lesions, the proposed methods are compared to other denoising methods through different figures of merit. The results show promising improvements in image quality as well as reduction in bias and variance of the lesions. We also show the application of the proposed methods on real [ ${}^{18}$ F]FDG data.

Conclusion: Two methods for restoring PET images were proposed. The methods were evaluated on simulation and real brain images. Most MR-guided PVE correction methods are only based on segmented T1-weighted images and their accuracy is very sensitive to segmentation errors, especially in regions of abnormalities and lesions. However, both proposed methods can use the T1-weighted image without segmentation. The simplicity and the very low computational cost of the second method make it suitable for clinical applications and large data studies. The proposed methods can be naturally extended to PVE correction and denoising of other functional modalities using corresponding anatomical information.

Keywords: MR; PET; PVE correction; basis functions; brain imaging; denoising; multicentric studies; post-reconstruction; sparsity; twicing.