Dynamic PET image denoising using higher-order singular value decomposition

Objectives Kinetic modeling of dynamic positron emission tomography (PET) data leads to estimates of physiological parameters that enable quantitative interpretation of PET images. The high noise levels in dynamic PET images, however, limit the accuracy of parametric fitting. To address this challenge, we have developed an image denoising framework based on higher-order singular value decomposition (HOSVD).

Methods HOSVD is an extension of the 2D matrix SVD technique to higher dimensions. Denoising is performed in three steps: 1. Cluster image voxels based on similarity of spatiotemporal patches. 2. For each cluster, perform HOSVD over the spatiotemporal patches to compute a low-rank approximation of each patch. 3. Aggregate multiple estimates by weighted averaging of neighboring time activity curves belonging to the same cluster. The performance of HOSVD denoising was assessed using both simulation and clinical data. We performed realistic simulations on a dynamic digital phantom based on the Digimouse atlas. 20 noise realizations were generated by reconstructing Poisson deviates of sinograms. The method was then applied to a hepatocellular carcinoma patient study using the [18F]FDG radiotracer. For both studies, images of the Patlak influx constant were computed.

Results We compared HOSVD denoising with traditional Gaussian denoising. In the simulation study, HOSVD denoising led to a 14% reduction in the overall noise standard deviation of Patlak images relative to Gaussian denoising for comparable levels for overall image bias. In the patient study, HOSVD preserved high intensity features (liver lesions) while lowering the variance of colder regions (e.g. the spleen). Comparison with Gaussian denoising revealed a 60% improvement in the contrast-to-noise ratio of lesions in the Patlak image (spleen used as background).

Conclusions HOSVD enables efficient denoising of dynamic PET images by simultaneously exploiting spatial and temporal similarities. Our studies show that it leads to noticeable reduction in noise variance for a given bias level and enhances contrast-to-noise ratio in Patlak images.

Research Support This work was supported by the American Lung Association Senior Research Training Fellowship, the Society of Nuclear Medicine and Molecular Imaging Mitzi and William Blahd, MD, Pilot Research Grant, and NIH grants 1R01EB013293, 1R01CA165221, and 1R01HL110241.