An immediate after-backprojection filtering method with blob-shaped window functions for voxel-based iterative reconstruction.

Spherically symmetric volume elements (blobs) have better resolution-noise performance than voxels because of the overlapping of their rotational symmetric basis functions; however, using blobs is more computationally expensive than using voxels due to blob overlap. In this paper, we propose an immediate after-backprojection filtering method (ABF) with blob-shaped window functions for a voxel-based reconstruction. We compared this method with the general voxel-based method (without filtering), the blob-based method, the voxel-based method with between-iteration filtering (BIF) and with post-filtering (POF), using computer simulations. Both the quality of the reconstruction and the computational cost were evaluated. The reconstruction quality was measured by the contrast recovery coefficient (CRC) versus the background noise. It is shown that images reconstructed using this method are characterized by less image noise and preserved image contrast in comparison with both the general voxel-based method and the voxel-based method with BIF. The improvement in image quality achieved by this method varies with the parameters chosen for the Kaiser-Bessel (KB) windows. As with blobs, wider KB windows achieve better contrast-noise trade-offs in the reconstructed images, but are more computationally expensive. When using a KB window of a = 2.0, alpha = 10.4 and m = 2, known as the basis function of a 'standard' blob, this new method achieves identical CRC-noise features to the blob-based method with 'standard' blobs. In addition, the ABF method can be combined with the post-filtering method to achieve better noise-resolution performance than the general voxel-based post-filtering method. The computational cost of the ABF method is slightly greater than that of the general voxel-based method, but much less than that of the blob-based method.