Example-Based Super-Resolution Image Reconstruction for Positron Emission Tomography Using Sparse Coding

This paper presents example-based methods for super-resolution (SR) reconstruction from a single set of low-resolution projections (or a sinogram) in positron emission tomography (PET). While deep learning-based SR approaches have shown promise across various imaging modalities, their application in medical imaging is often hindered by the challenge of acquiring large and diverse training datasets, which are typically scarce in clinical practice. To address this limitation, we adopt sparse coding (SC)-based SR techniques, which require only a moderate amount of training data to construct dictionaries for reconstructing high-resolution (HR) images from low-quality projections acquired with low-resolution detectors. Initially, we employ SC-based regularization using a single over-complete dictionary to represent learned image features within a single feature space. We then extend this approach to joint sparse coding (JSC)-based regularization, which improves SR reconstruction accuracy by using a joint dictionary trained on a limited set of HR PET and anatomical images, such as X-ray computed tomography (CT) or magnetic resonance (MR) images, from the same patient. These images are assumed to reside in coupled feature spaces. To further improve performance, we propose integrating SC (or JSC) regularization with non-local regularization (NLR), where the balance between these two types of regularization is adaptively determined based on patch differences in the PET and anatomical images. Experimental results indicate that while SC-based methods integrated with NLR offer modest improvements over non-SC-based methods, JSC-based methods achieve significantly superior reconstruction accuracy, outperforming both SC-based and non-SC-based methods, as validated by multiple image quality assessment metrics.