A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods.
As a solution to iterative CT image reconstruction, first-order methods are prominent for the large-scale capability and the fast convergence rate [Formula: see text]. In practice, the CT system matrix with a large condition number may lead to slow convergence speed despite the theoretically promising upper bound. The aim of this study is to develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods applied to CT image reconstruction. Instead of working in the projection domain, we transform the projection data and construct a data fidelity model in Fourier space. Inspired by the filtered backprojection formalism, the data are appropriately weighted in Fourier space. We formulate an optimization problem based on weighted least-squares in the Fourier space and total-variation (TV) regularization in image space for parallel-beam, fan-beam and cone-beam CT geometry. To achieve the maximum computational speed, the optimization problem is solved using a fast iterative shrinkage-thresholding algorithm with backtracking line search and GPU implementation of projection/backprojection. The performance of the proposed algorithm is demonstrated through a series of digital simulation and experimental phantom studies. The results are compared with the existing TV regularized techniques based on statistics-based weighted least-squares as well as basic algebraic reconstruction technique. The proposed Fourier-based compressed sensing (CS) method significantly improves both the image quality and the convergence rate compared to the existing CS techniques.
Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA. Department of Radiation Oncology, Stanford University, Stanford, CA 94305, USA. Medical System Laboratory, Samsung Advanced Institute of Technology (SAIT), Suwon, Gyeonggi, 443-803, Korea.
Kihwan
K
Choi
Ruijiang
R
Li
Haewon
H
Nam
Lei
L
Xing
D000465:Algorithms; D054893:Cone-Beam Computed Tomography / Q000379:methods*; D005583:Fourier Analysis; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D013997:Time Factors