Interior tomography with curvelet-based regularization.
The interior problem, i.e. reconstruction from local truncated projections in computed tomography (CT), is common in practical applications. However, its solution is non-unique in a general unconstrained setting. To solve the interior problem uniquely and stably, in recent years both the prior knowledge- and compressive sensing (CS)-based methods have been developed. Those theoretically exact solutions for the interior problem are called interior tomography. Along this direction, we propose here a new CS-based method for the interior problem based on the curvelet transform. A curvelet is localized in both radial and angular directions in the frequency domain. A two-dimensional (2D) image can be represented in a curvelet frame. We employ the curvelet transform coefficients to regularize the interior problem and obtain a curvelet frame based regularization method (CFRM) for interior tomography. The curvelet coefficients of the reconstructed image are split into two sets according to their visibility from the interior data, and different regularization parameters are used for these two sets. We also presents the results of numerical experiments, which demonstrate the feasibility of the proposed approach.
Division of Nuclear Technology and Applications, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China.|Beijing Engineering Research Center of Radiographic Techniques and Equipment, Beijing, China.
Baodong
B
Liu
Department of Mathematics, University of Central Florida, Orlando, FL, USA.
Alexander
A
Katsevich
Department of Electrical and Computer Engineering, University of Massachusetts Lowell, Lowell, MA, USA.
Hengyong
H
Yu
D000465:Algorithms; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D013909:Thorax / Q000000981:diagnostic imaging; D014057:Tomography, X-Ray Computed / Q000379:methods*
Computed tomography (CT); curvelet transform; interior tomography; local reconstruction; radon transform; regularization method