Improving Nonlocal Approach to Super-resolution Reconstruction in PET with the Aid of Local Regularization

Abstract

This paper presents a super resolution method for PET reconstruction where a high resolution underlying source image modeled by a finer grid is reconstructed from a standard projection data acquired for low-resolution image reconstruction. In order to regularize irregular pixels interpolated by backprojection rays, while preserving the edges, a non-local regularizer, which exploits self-similarities of image patches, is implemented within the penalized-likelihood approach. According to our own investigation, the non-local regularizers that exploit self-similarities in a broad neighborhood have a great potential for preserving the coarse-scale edges formed by relatively large flat regions with different intensities. However, the non-local regularizer performed by patch-by-patch comparisons has its limitations in restoring fine-scale edges when there is lack of enough self-similarity in the search window for the patches in the fine-scale edge regions. To overcome this problem, we also consider an edge-preserving local non-quadratic regularizer, which has good preservation for the fine-scale edges. By selectively combining the non-local regularizer with the local non-quadratic regularizer according to the condition of the self-similarities using a space-variant weighting factor, the suboptimal character of each regularizer can be optimized on each pixel location. The simulation results show that our proposed method well preserves the coarse-scale edges as well as fine-scale edges, which leads to a better accuracy in terms of the percentage errors.