# Penalized-likelihood PET Image Reconstruction Using 3D Structural Convolutional Sparse Coding

arXiv: https://arxiv.org/abs/1912.07180 · HTML: https://mlsanity.com/paper/1912.07180/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2019.

## Built on by (most cited first, 3 of 3)

- [Neural KEM: A Kernel Method with Deep Coefficient Prior for PET Image Reconstruction](https://mlsanity.com/paper/2201.01443/) (2022)
- [STPDnet: Spatial-temporal convolutional primal dual network for dynamic PET image reconstruction](https://mlsanity.com/paper/2303.04667/) (2023)
- [Efficient Chambolle-Pock based algorithms for Convoltional sparse representation](https://mlsanity.com/paper/2508.02152/) (2025)

## Abstract (arXiv)

Positron emission tomography (PET) is widely used for clinical diagnosis. As PET suffers from low resolution and high noise, numerous efforts try to incorporate anatomical priors into PET image reconstruction, especially with the development of hybrid PET/CT and PET/MRI systems. In this work, we proposed a novel 3D structural convolutional sparse coding (CSC) concept 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. Moreover, we developed the residual-image and order-subset mechanisms to further reduce the computational cost and accelerate the convergence for the proposed 3D PET-CSC method. Experiments based on computer simulations and clinical datasets demonstrate the superiority of 3D PET-CSC compared with other reference methods.