title: Accelerated Compressed Sensing Based CT Image Reconstruction.
abstract: In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.
authors.affiliation: Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada M5S 3G9.
authors.forename: SayedMasoud
authors.initials: S
authors.lastname: Hashemi
authors.affiliation: Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON, Canada M5B 2K3.
authors.forename: Soosan
authors.initials: S
authors.lastname: Beheshti
authors.affiliation: Rambus Inc., Sunnyvale, CA 94089, USA.
authors.forename: Patrick R
authors.initials: PR
authors.lastname: Gill
authors.affiliation: Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada M5S 3G9 ; Joint Department of Medical Imaging, Toronto General Hospital, University Health Network, Toronto, ON, Canada M5G 2C4.
authors.forename: Narinder S
authors.initials: NS
authors.lastname: Paul
authors.affiliation: Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada M5S 3G9.
authors.forename: Richard S C
authors.initials: RS
authors.lastname: Cobbold
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D044962:Data Compression; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods; D021621:Imaging, Three-Dimensional; D015233:Models, Statistical; D016011:Normal Distribution; D019047:Phantoms, Imaging; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012984:Software; D014057:Tomography, X-Ray Computed / Q000379:methods*