3D Structural Convolutional Sparse Coding for PET Image Reconstruction

Objectives: As PET suffers from low resolution and high noise, numerous efforts try to incorporate anatomical priors into PET image reconstruction. In this work, we proposed a novel 3D structural convolutional sparse coding (CSC) framework for penalized-likelihood PET image reconstruction, named 3D PET-CSC. The proposed 3D PET-CSC takes advantage of the convolutional operation and manages to incorporate anatomical priors without the need of registration or supervised training. As 3D PET-CSC codes the whole 3D PET image, instead of patches, it alleviates the staircase artifacts commonly presented in traditional patch-based sparse coding methods.

Methods: The schematic plot of proposed PET-CSC framework is shown in Fig.1(A). During the training phase, 3D convolutional kernels were iteratively learnt from the 3D MRI image, which incorporates the structural information from a higher resolution. During the coding phase, the PET image was represented by the multiplication of the learned kernels and feature map. The MRI image was based on the Brainweb database. The 18F-FDG brain PET data was acquired from the 5-ring GE Discovery MI PET/CT scanner with an acquisition time of 30 min. T415×1981×272.The reconstructed image size is 128×128×89 and the voxel size is 2×2×2.8 mm³. For bias quantification purposes, we inserted a simulated tumor with diameter of 14 mm near the boundary of the white and gray matter, and down-sampled the 30-min dataset to 1/20 of its original count to generate 10 low-count realizations.

Results: The proposed method can robustly recover PET image with higher contrast and less noise, as presented in Fig.1(B). According to Fig.1(C), in contrast to traditional patch-based dictionary learning method, the convolutional sparse coding was conducted on the whole image, which can alleviate the artifacts from the patches’ aggregation.Conclusion: We have proposed a novel 3D CSC regularization into 3D PET image reconstruction. Based on the clinical datasets, we can see that the proposed 3D PET-CSC can efficiently and robustly incorporate the anatomical prior into PET reconstruction without the need of registration and training. Compared with the traditional dictionary learning method, the proposed method can produce PET images with higher quality.Acknowledgements: This work was supported by NIH grants R01 AG052653.

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