1. Wenkun Zhang, Hanming Zhang, Lei Li, Jinlai Ye, Bin Yan, Linyuan Wang
Limited Angle CT Reconstruction by Simultaneous Spatial and Radon Domain Total Variation Minimization
Wenkun Zhang, Hanming Zhang, Lei Li, Jinlai Ye, Bin Yan, Linyuan Wang
Information System Engineering College, Information Engineering University
Abstract
Reconstructing image from limited angle projection is difficult due to the deficiency of continuous angle data. Sparse optimization method that utilizes the additional sparse prior of image was one of the important techniques. Total variation (TV) regularization model, which is based on the sparsity of the discrete gradient magnitude, has been tested and efficiently applied in CT reconstruction. This paper proposed a simultaneous spatial and radon domain TV minimization model to recover the CT image from limited angle data. A new added TV regularization term, which minimizes the sparse representation of sinogram, is utilized to reduce the unwanted artifacts in radon domain. Alternating direction method of multiplier (ADMM) was used to solve the optimization problem. The numerical simulation experiments indicated that the proposed algorithm show better performance in artifacts depression and sinogram inpainting than the algorithms with only spatial domain TV regularization term.
Results
Shepp-Logan phantom is used in the simulation experiments. We compare the results of FBP, TV regularization model based iterative algorithm and the proposed algorithm. The scanning angle was set at 140, 120, and 90, and the angle step is 1. Poisson noise corresponding to 5×105 photon counts was added to the simulated projection data. The maximum iteration reached by the two iterative algorithms was
Method
In this study, we attempt to design an efficient algorithm with simultaneous spatial and radon domain TV regularization. The simultaneous spatial and radon domain regularization optimization model is defined as
We apply the augmented Lagrange function to convert the above model to an unconstrained form. ADMM is used to optimize the convergence of the model by splitting of four variables and optimizing the four sub-problems. The four variables and its corresponding multiplier can be updated as follow
Figure 1 Simulation reconstruction results.
Figure 2 Simulation reconstruction results.
Angle
FBP TV
TV-TV
150
0.2761
0.0199
0.0033
120
0.3247
0.0298
0.0188
90
0.3762
0.0432
0.0310
Figure 3 The RMSE of the results reconstructed with the different algorithms from different scanning angles.