Using Sparse Coding in Super-resolution Reconstruction for PET

This paper presents a comparative study of effects of using sparse coding (SC) in super-resolution (SR) PET reconstruction. In this work, we focus on a special case of SR reconstruction where the pixel resolution is increased by backprojecting the projection measurements into the high-resolution (HR) image space modeled on a finer grid. While this SR scheme is useful for increasing the pixel resolution, it suffers from the unfortunate effect of generating irregular pixels caused by upscaling the image resolution. To regularize such irregular pixels and preserve fine details, we use a SC-based regularization method whose regularizer takes the form of sparse representation of the underlying image. Although this method better performs for images with complex edge structures than conventional regularization methods using piecewise smoothness constraints, it often treats the irregular pixels as ramp edges and tends to generate artifacts in the reconstructed HR image. To overcome this problem and improve the reconstruction accuracy, we attempt to use the additional side information obtained from the HR anatomical image. Here we propose a novel method of combining SC-based regularization with nonlocal regularization where the weighting factor that controls the balance between the two types of regularizations is determined by the patch differences in the anatomical image as well as those in the PET image. The experimental results demonstrate that our proposed method outperforms not only the conventional penalized-likelihood methods with piecewise smoothness constraints, but also the similar SC-based method with the dictionary trained by the anatomical image.