Dual energy CT has the ability to give more information about the test object by reconstructing the attenuation factors under different energies. These images under different energies share identical structures but different attenuation factors. By referring to the fully sampled low-energy image, we show that it is possible to greatly reduce the sampling rate of the high-energy image in order to lower dose. To compensate the attenuation factor difference between the two modalities, we use piecewise polynomial fitting to fit the low-energy image to the high-energy image. During the reconstruction, the result is constrained by its distance to the fitted image, and the structural information thus can be preserved. An ASD-POCS-based optimization schedule is proposed to solve the problem, and numerical simulations are taken to verify the algorithm. 1. Introduction Computed tomography has become an important nondestructive detection method in medicine, industry, and security. Typically CT scans the object by a single energy to reconstruct the attenuation factors in order to evaluate the density distributions inside the test object. However, some materials’ attenuation factors are close and hard to distinguish, which brings trouble for diagnosis. Since the attenuation factors are different under different X-ray energies, DECT [1] has been brought about to enhance the material distinguishing ability in CT. Furthermore, atomic numbers, electron densities, or specific material equivalent densities can also be reconstructed from DECT for better visualization. In DECT, the test object is scanned under different energies while keeping the object fixed. Thus, two different images, the low-energy image and the high-energy image can be reconstructed independently from the two sets of projections, the low-energy projections and the high-energy projections . Although there are various techniques for DECT reconstruction, for example, prereconstruction [2], postreconstruction [3], and iterative reconstruction [4], we concentrate on reconstructing and in this paper to demonstrate the mathematics of our method. Dose has been concerned more and more recently with the increasing public awareness of the possible risks brought about by the radiation of CT scans. One of the most efficient ways to reduce dose is to reduce the sampling number. According to the concept of compressed sensing (CS) [5, 6], when the sampling numbers are reduced beneath the conventional required sampling rate, one can still accurately recover the signal by incorporating prior knowledge to the
References
[1]
P. Engler and W. D. Friedman, “Review of dual-energy computed tomography techniques,” Materials Evaluation, vol. 48, no. 5, pp. 623–629, 1990.
[2]
R. E. Alvarez and A. Macovski, “Energy-selective reconstructions in X-ray computerised tomography,” Physics in Medicine and Biology, vol. 21, no. 5, pp. 733–744, 1976.
[3]
J. C. M. Steenbeek, C. van Kuijk, J. L. Grashuis, and R. B. van Panthaleon van Eck, “Selection of fat-equivalent materials in postprocessing dual-energy quantitative CT,” Medical Physics, vol. 19, no. 4, pp. 1051–1056, 1992.
[4]
J. A. Fessler, I. Elbakri, P. Sukovic, and N. H. Clinthorne, “Maximum-likelihood dual-energy tomographic image reconstruction,” in Medical Imaging 2002: Image Processing, vol. 4684 of Proceedings of SPIE, pp. 38–49, San Diego, Calif, USA, May 2002.
[5]
E. J. Candès and J. K. Romberg, “Signal recovery from random projections,” in Computational Imaging III, vol. 5674 of Proceedings of SPIE, pp. 76–86, San Jose, Calif, USA, March 2005.
[6]
E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Communications on Pure and Applied Mathematics, vol. 59, no. 8, pp. 1207–1223, 2006.
[7]
A. Bousse, S. Pedemonte, D. Kazantsev, S. Ourselin, S. Arridge, and B. F. Hutton, “Weighted MRI-Based bowsher priors for SPECT brain image reconstruction,” in Proceedings of the IEEE Nuclear Science Symposium Conference Record (NSS/MIC '10), pp. 3519–3522, Knoxville, Tenn, USA, November 2010.
[8]
D. Kazantsev, A. Bousse, S. Pedemonte, S. R. Arridge, B. F. Hutton, and S. Ourselin, “Edge preserving bowsher prior with nonlocal weighting for 3D spect reconstruction,” in Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI '11), pp. 1158–1161, Chicago, Ill, USA, April 2011.
[9]
Y. Liu, Z. Chen, L. Zhang, Y. Xing, J. Cheng, and Z. Wang, “Dual energy CT reconstruction method with reduced data,” in Proceedings of the 10th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, pp. 280–283, Beijing, China, September 2009.
[10]
G.-H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Medical Physics, vol. 35, no. 2, pp. 660–663, 2008.
[11]
T. P. Szczykutowicz and G.-H. Chen, “Dual energy CT using slow kVp switching acquisition and prior image constrained compressed sensing,” Physics in Medicine and Biology, vol. 55, no. 21, pp. 6411–6429, 2010.
[12]
Y. Xing and P. Zheng, “A restoration method for incomplete data in DECT,” in Proceedings of the IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC '11), pp. 4306–4310, Valencia, Spain, October 2011.
[13]
E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Physics in Medicine and Biology, vol. 53, no. 17, pp. 4777–4807, 2008.
[14]
D. Wu, L. Li, and L. Zhang, “Feature constrained compressed sensing CT image reconstruction from incomplete data via robust principal component analysis of the database,” Physics in Medicine and Biology, vol. 58, pp. 4047–4070, 2013.
[15]
I. Gohberg, T. Kailath, and I. Koltracht, “Efficient solution of linear systems of equations with recursive structure,” Linear Algebra and Its Applications, vol. 80, pp. 81–113, 1986.
