Abstract
We address the problem of dynamic CT reconstruction from parsimoniously sampled sinograms. In this paper we propose a novel approach to solve the aforesaid problem by modeling the dynamic CT sequence as a lowrank matrix. This dynamic CT matrix is formed by stacking each frame as a column of the matrix. As these images are temporally correlated, the dynamic CT matrix would therefore be of low-rank as its columns are not independent. We exploit the low-rank information to reconstruct the CT matrix from its parsimoniously sampled sinograms. Mathematically this is a low-rank matrix recovery problem, and we propose a novel algorithm to solve it. Our proposed method reduces the reconstruction error by 50% or more when compared to previous recovery techniques.
An Erratum for this chapter can be found at http://dx.doi.org/10.1007/978-3-642-40760-4_82
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References
Song, J., Liu, Q.H., Johnson, G.A., Badea, C.T.: Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-ct. Medical Physics 34, 4476–4482 (2007)
Yu, H., Wang, G.: Compressed sensing based interior tomography. Physics in Medicine & Biology 54, 2791–2805 (2009)
Lee, H., Xing, L., Davidi, R., Li, R., Qian, J., Lee, R.: Improved compressed sensing-based cone-beam CT reconstruction using adaptive prior image constraints. Physics in Medicine & Biology 57, 2287 (2012)
Chen, G.H., Tang, J., Leng, S.: Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets. Med. Phys. 35(2), 660–663 (2008)
Ramirez-Giraldo, J.C., Trzasko, J., Leng, S., Yu, L., Manduca, A., McCollough, C.H.: Nonconvex prior image constrained compressed sensing (NCPICCS): Theory and simulations on perfusion CT. Med. Phys. 38(4), 2157–2167 (2011)
Gamper, U., Boesiger, P., Kozerke, S.: Compressed sensing in dynamic MRI. Magnetic Resonance in Medicine 59(2), 365–373 (2008)
Jung, H., Park, J., Yoo, J., Ye, J.C.: k-t FOCUSS: A General Compressed Sensing Framework for High Resolution Dynamic MRI. Magnetic Resonance in Medicine 61, 103–116 (2009)
Zhao, B., Haldar, J.P., Brinegar, C., Liang, Z.-P.: Low Rank Matrix Recovery for Real-Time Cardiac MRI. In: IEEE International Symposium on Biomedical Imaging, pp. 996–999 (2010)
Recht, B., Fazel, M., Parrilo, P.A.: Guaranteed Minimum Rank Solutions to Linear Matrix Equations via Nuclear Norm Minimization. SIAM Review 52(3), 471–501 (2010)
Majumdar, A., Ward, R.K.: Some Empirical Advances in Matrix Completion. Signal Processing 91(5), 1334–1338 (2011)
Mohimani, H., Babaie-Zadeh, M., Jutten, C.: A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed ℓ (0) Norm. IEEE Trans. on Signal Processing 57(1), 289–301 (2008)
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Majumdar, A., Ward, R.K. (2013). Dynamic CT Reconstruction by Smoothed Rank Minimization. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2013. MICCAI 2013. Lecture Notes in Computer Science, vol 8151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40760-4_17
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DOI: https://doi.org/10.1007/978-3-642-40760-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40759-8
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