Denoising PET Images Using Singular Value Thresholding and Stein's Unbiased Risk Estimate

Image denoising is an important pre-processing step for accurately quantifying functional morphology and measuring activities of the tissues using PET images. Unlike structural imaging modalities, PET images have two difficulties: (1) the Gaussian noise model does not necessarily fit into PET imaging because the exact nature of noise propagation in PET imaging is not well known, and (2) PET images are low resolution; therefore, it is challenging to denoise them while preserving structural information. To address these two difficulties, we introduce a novel methodology for denoising PET images. The proposed method uses the singular value thresholding concept and Stein's unbiased risk estimate to optimize a soft thresholding rule. Results, obtained from 40 MRI-PET images, demonstrate that the proposed algorithm is able to denoise PET images successfully, while still maintaining the quantitative information.