Using spherical basis functions on a polar grid for iterative image reconstruction in small animal PET

Abstract

Statistical iterative methods have been extensively demonstrated to outperform analytical methods in terms of image quality in nuclear imaging. In the method, the mathematically unknown biodistribution is usually represented by cubic basis functions in 3D. Alternatively, spherical basis functions have demonstrated lower noise produced in the resulting reconstructed images. Additionally, the system response matrix (SRM), a key element required by iterative methods, is usually too large to be stored in random access memory of a regular computer. The SRM can be calculated prior to reconstruction and stored on-disk, and thus be directly accessed during the reconstruction process. But this approach usually makes the process too time consuming. To reduce the number of elements to be computed and stored, a common approach uses the scanner symmetries. In this work we use polar voxels, reducing the number of non-zero elements to be computed by a factor 72, allowing us to speed up the Monte-Carlo simulations in which the computation of the SRM is based. In this work we combine the use blobs, a type of spherical basis function, as basis functions and a polar representation in the SRM. The latter is especially important for blobs, given that due to the overlapping of blobs, the size of the SRM significantly increases. This work will show a quantitative comparison of reconstructed images using Cartesian voxels, polar voxels and blobs. We will show that blobs reduce image noise compared to voxels, producing a lower spatial resolution degradation, compared to polar voxels after Gaussian filtering.