A novel alternative algorithm for limited angle tomography

This paper studies incomplete data problems of circular cone-beam computed tomography, which occur frequently in medical imaging and industrial imaging. The incomplete data problems in which projection data are only available in an angular range can be attributed to the limited angle tomography. Limited angle tomography is a severely ill-posed inverse problem. In recent years, image reconstruction based on total variation (TV) was employed to reduce the problem and gave better performance on edge-preserving reconstruction. However, the artificial parameter can only be determined through considerable experimentation. In this paper, an alternating minimization method based on TV is proposed to reduce the data insufficiency in tomographic imaging. This novel alternating minimization method provides a robust and effective reconstruction without any artificial parameter in the iterative processes, by using the TV as a multiplicative constraint. The results demonstrate that this new reconstruction method brings satisfactory performance.

[1]  Yi Sun,et al.  Image reconstruction by an alternating minimisation , 2011, Neurocomputing.

[2]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[3]  E Somersalo,et al.  Statistical inversion for medical x-ray tomography with few radiographs: I. General theory. , 2003, Physics in medicine and biology.

[4]  Frank Natterer,et al.  Mathematical methods in image reconstruction , 2001, SIAM monographs on mathematical modeling and computation.

[5]  Stephen J. Wright,et al.  Sparse Reconstruction by Separable Approximation , 2008, IEEE Transactions on Signal Processing.

[6]  Yi Sun,et al.  Adaptive wavelet-Galerkin methods for limited angle tomography , 2010, Image Vis. Comput..

[7]  Alin Achim,et al.  18th IEEE International Conference on Image Processing, ICIP 2011, Brussels, Belgium, September 11-14, 2011 , 2011, ICIP.

[8]  Peyman Milanfar,et al.  A moment-based variational approach to tomographic reconstruction , 1996, IEEE Trans. Image Process..

[9]  Rafal Zdunek,et al.  Kaczmarz extended algorithm for tomographic image reconstruction from limited-data , 2004, Math. Comput. Simul..

[10]  Ville Kolehmainen,et al.  Limited Data X-Ray Tomography Using Nonlinear Evolution Equations , 2008, SIAM J. Sci. Comput..

[11]  J S Kole.  Statistical image reconstruction for transmission tomography using relaxed ordered subset algorithms. , 2005, Physics in medicine and biology.

[12]  E. Sidky,et al.  Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization , 2008, Physics in medicine and biology.

[13]  Matti Lassas,et al.  Wavelet-based reconstruction for limited-angle X-ray tomography , 2006, IEEE Transactions on Medical Imaging.

[14]  Gonglin Yuan,et al.  Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems , 2009, Optim. Lett..