Dynamic PET images denoising using spectral graph wavelet transform

Positron emission tomography (PET) is a non-invasive molecular imaging method for quantitative observation of physiological and biochemical changes in living organisms. The quality of the reconstructed PET image is limited by many different physical degradation factors. Various denoising methods including Gaussian filtering (GF) and non-local mean (NLM) filtering have been proposed to improve the image quality. However, image denoising usually blurs edges, of which high frequency components are filtered as noises. On the other hand, it is well-known that edges in a PET image are important to detection and recognition of a lesion. Denoising while preserving the edges of PET images remains an important yet challenging problem in PET image processing. In this paper, we propose a novel denoising method with good edge-preserving performance based on spectral graph wavelet transform (SGWT) for dynamic PET images denoising. We firstly generate a composite image from the entire time series, then perform SGWT on the PET images, and finally reconstruct the low graph frequency content to get the denoised dynamic PET images. Experimental results on simulation and in vivo data show that the proposed approach significantly outperforms the GF, NLM and graph filtering methods. Compared with deep learning-based method, the proposed method has the similar denoising performance, but it does not need lots of training data and has low computational complexity.