Low-count PET image restoration using sparse representation

In the field of positron emission tomography (PET), reconstructed images are often blurry and contain noise. These problems are primarily caused by the low resolution of projection data. Solving this problem by improving hardware is an expensive solution, and therefore, we attempted to develop a solution based on optimizing several related algorithms in both the reconstruction and image post-processing domains. As sparse technology is widely used, sparse prediction is increasingly applied to solve this problem. In this paper, we propose a new sparse method to process low-resolution PET images. Two dictionaries ($D_1$ for low-resolution PET images and $D_2$ for high-resolution PET images) are learned from a group real PET image data sets. Among these two dictionaries, $D_1$ is used to obtain a sparse representation for each patch of the input PET image. Then, a high-resolution PET image is generated from this sparse representation using $D_2$. Experimental results indicate that the proposed method exhibits a stable and superior ability to enhance image resolution and recover image details. Quantitatively, this method achieves better performance than traditional methods. This proposed strategy is a new and efficient approach for improving the quality of PET images.