Methods Of PET Image Denoising And Reconstruction Based On Graph Signal Processing

Positron emission tomography(PET)is an imaging technique in nuclear medicine.PET images can detect the metabolism activity of specific organs or tissues in the body,which is widely used to assess the physiological and pathological conditions of organs such as brain and heart.The limitations of various physical factors and restriction of radiotracer dose lead the observed data(sinogram data)with lower signal-to-noise ratio and count level.It results in massive noise,blurry structure and lesion in PET images.PET images with lower signal-to-noise ratio affect the accuracy of the doctor’s diagnosis.Therefore,improving the quality of PET images is the main purpose of this thesis.Graph signal processing has capacity to reveal the intrinsic structure of complex data.In order to improve the signal-to-noise ratio and better recover structural information in PET images,this thesis applies graph signal processing for PET data denoising and PET image reconstruction in the three stages,including pre-processing,reconstruction and post-processing.The main contribution of this thesis are as follows:(1)In the pre-processing stage,a dynamic PET sinograms denoising algorithm based on kernel graph filtering(KGF)is proposed to reduce the noise in sinograms data.Firstly,the kernel principal components of the noisy sinogram are used to construct a kernel graph filter.The kernel graph filter obtained is then used to filter the original sinogram to obtain the denoised sinograms for PET image reconstruction.Extensive tests and comparisons on the simulated and real life in-vivo dynamic PET datasets show that the proposed algorithm outperforms the existing algorithms in sinogram denoising,especially in low count sinograms.(2)In order to preserve the contrast of lesion while reducing noise in PET image,the graph filtering(Graph F)algorithm is proposed.Firstly,graph signal processing is used to extract the intrinsic structural information of noisy PET images.Secondly,graph filters are designed to reduce noise in graph spectral domain.Finally,the denoised graph spectral signal is projected to image domain to obtain the denoised PET images.The simulation and clinical results show that the denoised PET images have higher contrast and signal-to-noise ratio compared with other PET image denoising algorithms.(3)To reconstruct PET image with high-quality,a novel reconstruction algorithm based on kernel and kernel space composite regularizer is proposed.According to manifold assumption,the smoothness connection between kernel space data and image space data is firstly established.Then kernel space composite regularizer is constructed from PET image data for improving the detectability of lesion.Using this kernel space composite regularizer,a globally convergent iterative algorithm is derived for reconstruction.Tests on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm,and demonstrate that the proposed algorithm can preserve grey matter’s structural information and the lesion’s contrast while reducing noise in PET images.(4)In order to further improve the performance of the reconstruction algorithm,graph spectral theory is used to construct the graph filter-based PET image representation model,which can extract the intrinsic structural information of PET images.Incorporating the proposed representation model into maximum likelihood expectation maximization,the graph filter-based expectation maximization is proposed to reconstruct PET images.Extensive tests and comparisons show that the proposed representation model can better represent the intrinsic structural information of PET images,and the graph filter-based expectation maximization can reconstruct PET images with clearer grey matter structure and lesion.