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A Study of Total-Variation Based Noise-Reduction Algorithms For Low-Dose Cone-Beam Computed Tomography
Sovanlal Mukherjee, Jonathan B. Farr, Weiguang Yao
Pages - 188 - 204     |    Revised - 30-09-2016     |    Published - 31-10-2016
Volume - 10   Issue - 4    |    Publication Date - October 2016  Table of Contents
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KEYWORDS
Low-Dose CBCT, Nesterov's First Order Method, Split Bregman Method, Total-Variation Method.
ABSTRACT
In low-dose cone-beam computed tomography, the reconstructed image is contaminated with excessive quantum noise. In this work, we examined the performance of two popular noise-reduction algorithms-total-variation based on the split Bregman (TVSB) and total-variation based on Nesterov's method (TVN)-on noisy imaging data from a computer-simulated Shepp-Logan phantom, a physical CATPHAN phantom and head-and-neck patient. Up to 15% Gaussian noise was added to the Shepp-Logan phantom. The CATPHAN phantom was scanned by a Varian OBI system with scanning parameters 100 kVp, 4 ms, and 20 mA. Images from the head-and-neck patient were generated by the same scanner, but with a 20-ms pulse time. The 4-ms low-dose image of the head-and-neck patient was simulated by adding Poisson noise to the 20-ms image. The performance of these two algorithms was quantitatively compared by computing the peak signal-to-noise ratio (PSNR), contrast-to-noise ratio (CNR) and the total computational time. For CATPHAN, PSNR improved by 2.3 dB and 3.1 dB with respect to the low-dose noisy image for the TVSB and TVN based methods, respectively. The maximum enhancement ratio of CNR for CATPHAN was 4.6 and 4.8 for TVSB and TVN respectively. For data for head-and-neck patient, the PSNR improvement was 2.7 dB and 3.4 dB for TVSB and TVN respectively. Convergence speed for the TVSB-based method was comparatively slower than TVN method. We conclude that TVN algorithm has more desirable properties than TVSB for image denoising.
1 Google Scholar 
2 CiteSeerX 
3 refSeek 
4 Scribd 
5 SlideShare 
6 PdfSR 
A. Chambolle. "An Algorithm for Total Variation Minimization and Applications." J.Math. Imag. Vis., vol. 20, pp. 1-2, 2004.
A.C. Kak and M Slaney. Principles of computerized tomographic imaging. New York: IEEE Press,1988.
D.A. Jaffray, J.S. Siewerdsen, J.W. Wong, A.A. Martinez. "Flatpanel cone-beam computed tomography for image-guided radiation therapy." Int. J. Radiat. Oncol. Biol. Phys., vol. 53, pp.1337-1349, 2002.
D.A. Jaffray. "Emergent technologies for 3-dimensional image-guided radiation delivery." Semin. Radiat. Oncol., vol.15, pp. 208-216, 2005.
D.J. Brenner, E.J. Hall. "Computed tomography-An increasing source of radiation exposure." N. Engl. J. Med., vol. 357, pp. 2277-2284, 2007.
D.L. Donoho, "Compressed sensing." IEEE Trans. Inf. Theory, vol. 52, pp. 1289-1306, 2006.
E.J. Candes, J. Romberg, T. Tao. "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information." IEEE Trans. Inf. Theory, vol. 52, pp. 489- 509, 2006.
E.J. Candes, T. Tao. "Near-optimal signal recovery from random projections: Universal encoding strategies." IEEE Trans. Inf. Theory, vol. 52, pp. 5406-5425, 2006.
E.Y. Sidky, C.M. Kao, X. Pan. "Accurate image reconstruction from few-views and limited angle data in divergent-beam CT." J. X-Ray Sci. Technol., vol. 14, pp. 119-39, 2006.
E.Y. Sidky, X. Pan. "Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization." Phys. Med. Biol., vol. 53, pp. 4777-4807, 2008.
E.Y. Sidky, Y. Duchin, X. Pan, C. Ullberg. "A constrained, total-variation minimization algorithm for low-intensity x-ray CT." Med. Phys., vol. 38, pp. 117-25, 2011.
F. Xu, K. Mueller. "Real-time 3D computed tomographic reconstruction using commodity graphics hardware." Phys. Med. Biol., vol. 52, pp. 3405-3419, 2007.
G. Chen, J. Tang, S. Leng. "Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets." Med. Phys., vol. 35, pp. 660-663, 2008.
G.T. Herman. Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. New York: Academic Press, 1980.
H.H. Bauschke, J.M. Borwein. "On Projection algorithms for solving convex feasibility problems." SIAM Review, vol. 38, pp. 367-426, 1996.
J. A. Fessler. "Penalized weighted least-squares image reconstruction for Positron emission Tomography." IEEE Trans. Med. Imag., vol. 13, pp. 290-300, 1994.
J. Barzilai, J.M. Borwein. "2-Point step size gradient methods." IMA J. Numer. Anal., vol. 8, pp. 141-148, 1988.
J. Dahl, P.C. Hansen, S.H. Jensen, T.L. Jensen. "Algorithms and software for total variation image reconstruction via first-order methods." Numer. Algor., vol. 53, pp. 67-92, 2010.
J. Park, B. Song, J. Kim, S. Park, H. Kim, Z. Liu, T. Suh, W. Song. "Fast compressed sensing-based CBCT reconstruction using Barzilai-Borwein formulation for application to on-line IGRT." Med. Phys., vol. 39, pp. 1207-17, 2012.
J. Tang, B.E. Nett, G. Chen. "Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms." Phys. Med. Biol., vol. 54, pp. 5781-5804, 2009.
J. Wang, T. Li, H. Lu, Z. Liang. "Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography." IEEE Trans. Med. Imag., vol. 25, pp.1272-83, 2006.
J. Wang, T. Li, Z. Liang, L. Xing. "Dose reduction for kilovoltage cone-beam computed tomography in radiation therapy." Phys. Med. Biol., vol. 53, pp. 2897-2909, 2008.
Jia et al. "GPU-based fast low-dose cone beam CT reconstruction via total variation." J. X-Ray Sci. Technol., vol. 19, pp.139-154, 2011.
K. Choi, J. Wang, L. Zhu, T.S. Suh, S. Boyd, L. Xing. "Compressed sensing based cone-beam computed tomography reconstruction with a first-order method." Med. Phys., vol. 37, pp. 5113-5125, 2010.
L. Ritschl, F. Bergner, C. Fleischmann, M. Kachelriess. "Improved total variation-based CT image reconstruction applied to clinical data." Phys. Med. Biol., vol. 56, pp. 1545-61, 2011.
L. Xing, B. Thorndyke, E. Schreibmann, Y. Yang, T.F. Li, G.Y. Kim, G. Luxton, A. Koong. "Overview of image-guided radiation therapy." Med. Dosim., vol. 31, pp. 91-112 , 2006.
L.A. Feldkamp, L.C. Davis, J.W. Kress. "Practical cone-beam algorithm." J. Opt. Soc. Am. A., vol. 1, pp. 612-619, 1984.
L.I. Rudin, S. Osher, E. Fatemi. "Nonlinear total variation based noise removal algorithms." Physica D, vol. 60, pp. 259-268, 1992.
L.M. Bregman. "The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex optimization." USSR Comp. Math. & Math. Phys., vol. 7, pp. 200-217, 1967.
Murphy et al. "The management of imaging dose during image guided radiotherapy: Report of the AAPM Task Group 75." Med. Phys., vol. 34, pp. 4041-4063, 2007.
P. Getreuer. "Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman." Imag. Proc. vol. 2, pp. 74-95, 2012.
P. Sonneveld. "CGS: A fast Lanczos-type solver for nonsymmetric linear systems." SIAM J. Sci. Stat. Comput., vol. 10, pp. 36-52, 1989.
R.D. Timmerman, L. Xing. Image Guided and Adaptive Radiation Therapy, Philadelphia:Lippincott Williams and Wilkins, 2010.
S. Becker, J. Bobin, E.J. Candes. "NESTA: a fast and accurate first-order method for sparse recovery." SIAM J. Imag. Sci., vol. 4, pp. 1-39, 2009.
S. Osher, M. Burger, D. Goldfarb, J.J. Xu, W.T. Yin. "An iterative regularization method for total variation-based image restoration." Multiscale Model. Simul., vol. 4, pp. 460-489, 2005.
S.P. Boyd, L. Vandenberghe. Convex Optimization. Cambridge: Cambridge University Press, 2004.
T. Goldstein, S. Osher. "The Split Bregman Method for L1 Regularized Problems." SIAM J. Imag. Sci.,vol. 2, pp. 323-343, 2009.
T. Niu, L. Zhu. "Accelerated barrier optimization compressed sensing (ABOCS) reconstruction for cone-beam CT: Phantom studies." Med. Phys., vol. 39, pp. 4588-98, 2012.
W. Yao, J.B. Farr. "A multiscale filter for noise reduction of low-dose cone beam projections." Phys. Med. Biol., vol. 60, pp. 6515-6530, 2015.
W. Yin, S. Osher, D. Goldfarb, J. Darbon. "Bregman iterative algorithms for l1-minimization with applications to compressed sensing." SIAM J. Imaging Sci., vol. 1, pp.143-168 2008.
Wen et al. "Dose delivered from Varian's CBCT to patients receiving IMRT for prostate cancer." Phys. Med. Biol., vol. 52, pp. 2267-2276, 2007.
Y. Nesterov. "A method for unconstrained convex minimization problem with the rate of convergence O (1/k2)." Sov. Math. Dokl., vol. 27, pp. 372-376, 1983.
Y. Nesterov. "Gradient methods for minimizing composite objective function. Center for Operations Research and Econometrics (CORE)." Universite Catholique de Louvain, Tech. Rep., 2007.
Y. Yang, E. Schreibmann, T.F. Li, C. Wang, L. Xing. "Evaluation of on-board kV cone beam CT (CBCT)-based dose calculation." Phys. Med. Biol., vol. 52, pp. 685-705, 2007.
Z. Chen, X. Jin, L. Li, G. Wang. "A limited-angle CT reconstruction method based on anisotropic TV minimization." Phys. Med. Biol., vol. 58, pp. 2119-2141, 2013.
Z. Tian, X. Jia, K. Yuan, T. Pan, S.B. Jiang. "Low-dose CT reconstruction via edge-preserving total variation regularization." Phys. Med. Biol., vol. 56, pp. 5949-5967, 2011.
[34] Niu et al. "Accelerated barrier optimization compressed sensing (ABOCS) for CT reconstruction with improved convergence." Phys. Med. Biol., vol. 59, pp. 1801-14, 2014.
Dr. Sovanlal Mukherjee
Department of Radiation Oncology, St. Jude Children’s Research Hospital, 262 Danny Thomas Place, Memphis, TN 38105, USA - United States of America
sovaniitk@gmail.com
Dr. Jonathan B. Farr
Department of Radiation Oncology, St. Jude Children’s Research Hospital - United States of America
Dr. Weiguang Yao
Department of Radiation Oncology, St. Jude Children’s Research Hospital - United States of America