Abstract
Reducing number of projection angles and lowering current intensity of X-ray tube are two common ways for reducing CT dose. Though reduced radiation dose of CT scan can lower damage to human bodies, Few number of projection angles will result in incomplete projection data while lowering tube current intensity a declined signal to noise ratio of projection data. In this paper, two statistical methods based on sparsity constraint in shearlet domain for low-dose CT image were proposed to solve the above problems. For the limited angle scanned reconstruction, sparse representation of intermediate images in shearlet domain is added into the objective function as a regularization item by means of Augmented Lagrangian method so as to narrow down solution space. For the low X-ray tube scanned reconstruction, a penalized weighted least-squares (PWLS) approach based on discrete shearlet was introduced to improve the performance of resisting noise in sinogram. And then reconstruct CT images by Filtered Back-Projection method. According to experimental data, both of the two approaches can get high-quality images when projection data is far from meeting conditions of completeness or the signal to noise ratio of projection data declines sharply. The proposed algorithms can be used for attaining reconstructed images that clearly keep structural details when the radiation dose is decreased to 10% or even lower degrees.
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References
Brenner DJ, Elliston CD, Hall EJ, Berdon WE (2001) Estimated risks of radiation-induced fatal cancer from pediatric CT. Am J Roentgenol 176(2):289–296
Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509
Chang M, Li L, Chen Z, Zhang L, Wang G (2013) A few-view reweighted sparsity hunting (FRESH) method for CT image reconstruction. Journal of X-ray Science and Technology 21(2):161–176
Dong B, Li J, Shen Z (2013) X-ray CT image reconstruction via wavelet frame based regularization and radon domain inpainting. J Sci Comput 54(2–3):333–349
Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306
Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736–3745
Frikel J (2013) Sparse regularization in limited angle tomography. Appl Comput Harmon Anal 34(1):117–141
Garduño E, Herman GT, Davidi R (2011a) Reconstruction from a few projections by ℓ1-minimization of the Haar transform. Inverse problems 27(5):055006
Garduño E, Herman GT, Davidi R (2011b) Reconstruction from a few projections by ℓ1-minimization of the Haar transform. Inverse Problems 27(5):055006
Guo K, Labate D (2007) Optimally sparse multidimensional representation using shearlets. SIAM J Math Anal 39(1):298–318
Hamalainen K, Kallonen A, Kolehmainen V, Lassas M, Niinimaki K, Siltanen S (2013) Sparse tomography. SIAM J Sci Comput 35(3):B644–B665
Hara AK, Paden RG, Silva AC, Kujak JL, Lawder HJ, Pavlicek W (2009) Iterative reconstruction technique for reducing body radiation dose at CT: feasibility study. Am J Roentgenol 193(3):764–771
Hestenes MR (1969) Multiplier and gradient methods. J Optim Theory Appl 4(5):303–320
Leipsic J, LaBounty TM, Heilbron B, Min JK, Mancini GJ, Lin FY, Earls JP (2010) Adaptive statistical iterative reconstruction: assessment of image noise and image quality in coronary CT angiography. American Journal of Roentgenology 195(3):649–654
Li T, Li X, Wang J, Wen J, Lu H, Hsieh J, Liang Z (2004) Nonlinear sinogram smoothing for low-dose X-ray CT. IEEE Trans Nucl Sci 51(5):2505–2513
Liao HY, Sapiro G (2008) Sparse representations for limited data tomography. IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 5th, 2008
Lim WQ (2010) The discrete shearlet transform: a new directional transform and compactly supported shearlet frames. IEEE Trans Image Process 19(5):1166–1180
Mastora I, Remy-Jardin M, Delannoy V, Duhamel A, Scherf C, Suess C, Remy J (2004) Multi–detector row spiral CT angiography of the thoracic outlet: dose reduction with anatomically adapted online tube current modulation and preset dose savings 1. Radiology 230:116–124
Miao Q, Shi C, Xu P, Yang M, Shi Y (2011) A novel algorithm of image fusion using shearlets. Opt Commun 284(6):1540–1547
Niu S, Gao Y, Bian Z, Huang J, Che W, Chen W, Yu G, Liang Z, Ma J (2014) Sparse-view x-ray CT reconstruction via total generalized variation regularization[J]. Phys Med Biol 59(12):2997
Patel VM, Easley GR, Healy DM (2009) Shearlet-based deconvolution. IEEE Trans Image Process 18(12):2673–2685
Prakash P, Kalra MK, Kambadakone AK, Pien H, Hsieh J, Blake MA, Sahani DV (2010) Reducing abdominal CT radiation dose with adaptive statistical iterative reconstruction technique. Investigative Radiology 45(4):202–210
Ramani S, Fessler JA (2012) A splitting-based iterative algorithm for accelerated statistical X-ray CT reconstruction. IEEE Trans Med Imaging 31(3):677–688
Silva AC, Lawder HJ, Hara A, Kujak J, Pavlicek W (2010) Innovations in CT dose reduction strategy: application of the adaptive statistical iterative reconstruction algorithm. Am J Roentgenol 194(1):191–199
Singh S, Kalra MK, Gilman MD, Hsieh J, Pien HH, Digumarthy SR, Shepard JAO (2011) Adaptive statistical iterative reconstruction technique for radiation dose reduction in chest CT: a pilot study. Radiology 259(2):565–573
Sodickson A, Baeyens PF, Andriole KP, Prevedello LM, Nawfel RD, Hanson R, Khorasani R (2009) Recurrent CT, cumulative radiation exposure, and associated radiation-induced cancer risks from CT of adults 1. Radiology 251(1):175–184
Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612
Wang J, Li T, Lu H, Liang Z (2006) Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography. IEEE Trans Med Imaging 25(10):1272–1283
Wang J, Lu H, Wen J, Liang Z (2008) Multiscale penalized weighted least-squares sinogram restoration for low-dose X-ray computed tomography. IEEE Trans Biomed Eng 55(3):1022–1031
Wang J, Li T, Xing L (2009) Iterative image reconstruction for CBCT using edge-preserving prior. Med Phys 36(1):252–260
Xu Q, Yu H, Mou X, Zhang L, Hsieh J, Wang G (2012) Low-dose X-ray CT reconstruction via dictionary learning. IEEE Trans Med Imaging 31(9):1682–1697
Zhang Y, Zhang J, Lu H (2010) Statistical sinogram smoothing for low-dose CT with segmentation-based adaptive filtering. IEEE Trans Nucl Sci 57(5):2587–2598
Zhang H, Zhang L, Sun Y, Zhang J (2015) Projection domain denoising method based on dictionary learning for low-dose CT image reconstruction. Journal of X-ray science and technology 23(5):567–578
Zhao J, Lü L, Sun H (2010) Multi-threshold image denoising based on shearlet transform. Applied Mechanics and Materials 29:2251–2255
Zhu Z, Wahid K, Babyn P, Cooper D, Pratt I, Carter Y (2013). Improved compressed sensing-based algorithm for sparse-view CT image reconstruction. Computational and mathematical methods in medicine. 185750–185750
Zhu L, Niu T, Petrongolo M (2014) Iterative CT reconstruction via minimizing adaptively reweighted total variation. Journal of X-ray Science and Technology 22(2):227–240
Acknowledgements
This work was supported by National Natural Science Foundation of China (No.61340034), China Postdoctoral Science Foundation (No.2013 M530873), Natural Science Foundation of Tianjin of China (No.16JCYBJC28800) and Tianjin Research Program of Application Foundation and Advanced Technology (No.13JCYBJC15600).
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Zhang, H., Zhang, L., Sun, Y. et al. Low dose CT image statistical reconstruction algorithms based on discrete shearlet. Multimed Tools Appl 76, 15049–15064 (2017). https://doi.org/10.1007/s11042-017-4471-x
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DOI: https://doi.org/10.1007/s11042-017-4471-x