This talk will attempt to address the following two questions:
(Q1) "Better" Imaging: provided with the same CT sinogram, can we develop new reconstruction method to further improve the state-of-art image quality?
(Q2) "Faster" Imaging: under the similar image quality standard, can we fully explore the new method for faster CT imaging, in terms of (1) faster undersampled 3D/4D data acquisition, and (2) faster image reconstruction speed that is clinically usable? A key is (A1) the use of L1-type iterative reconstruction method based on tensor framelet (TF). Another critical component for developing fast clinically-usable reconstruction is (A2) the rapid parallel algorithm for computing X-ray transform and its adjoint (O(1) per parallel thread). Then we will move on to (A3) the super-resolution technique for spiral CT to enhance axial image resolution and reduce axial partial volume artifacts, (A4) fused Analytical and Iterative Reconstruction (AIR) method as a general framework to fuse analytical reconstruction method and iterative method, and (A5) adaptive TF Technique for 4D imaging