Low-Dose CT image denoising using image decomposition and sparse representation

tation 85
N. T. Trung et al.: Low-Dose CT Image Denoising using Image Decomposition and Sparse Representation 85
 (a) Low-dose CT image (b) Normal-dose CT image
 (a) Low-dose CT image (b) Normal-dose CT image
 (c) TGV [28] (d) NLM [8] (e) KSVD [12]
 (c) TGV [28] (d) NLM [8] (e) KSVD [12]
 (f)(f) MRFD MRFD [26] (g) FD-SC1(g) FD-SC1 [27] [27] (h) FD-SC2(h) FD-SC2
 FigureFigure 6. Denoising6. Denoising result result on aon real a real low-dose low-dose lung lung CT image CT image including including one nodule one nodule at position at position (X=190, (X=190, Y=394). Y=394).
 Table III
 Table III test images given in Figure 4 with three noise levels
RunningRunning-time-time comparison comparison of ofMRFD,MRFD, FD-SC1 FD-SC1andandFD-SC2FD-SC2whenwhen and PSNR, are used to analyze the influence of the
 denoising the head image in Figure 4(c)(size 608 481) with σ = 10, 20, and 30.
 denoising the head image in Figure 4(c)(size 608× 481) with parameters. Experiments were conducted on the three
 noisenoise levels levelsσ =σ 10,= 10, 20 20andand3030 (running (running-time-time is is given given× in in seconds)
 seconds). test images given in Figure 4 with three noise levels
 σ = 10, 20, and 30.
 γ
 Noise level MRFD [26] FD-SC1 [27] FD-SC2 To seeTo the see effect the effect of , of weγ performed, we performed experiments experiments with with
 γ = 0.01, 0.02, . . . , 1.0, and the patch size is fixed at 11
 σ = 10 129.00 46.90 9.63 γ = 0.01, 0.02, . . . , 1.0, and the patch size is fixed at 11
 11. The results, as shown in Figure 7, indicate that the×
 σ = 20 78.13 46.77 4.78 11. The results, as shown in Figure 7, indicate that the×
 optimal value of γ approximately was 0.09 for all three
 optimal value of γ approximately was 0.09 for all three
 σ = 30 86.41 46.90 3.73 noise levels. It means that the optimal value of γ is less
 sensitivenoise to levels. noise. It means that the optimal value of γ is less
 sensitive to noise.
4.4 Empirical Study on Parameters
 4.4 Empirical Study on Parameters Figure 8 shows the effect of the patch size. We
 In this subsection, we present the effect of the thresh- Figureperformed 8 shows experiments the effect with of different the patch patch size. sizes, We from
oldIn parameter this subsection,ε in (25) we and present the patch the effect size of√ then thresh-√n performed5 5 to experiments 20 20 while with keeping differentγ patchin these sizes, experiments from
 × ×
onold the parameter performanceε in of(11) the and proposed the patch method size √× (FD-n √n 5 constant5 to 20 at20 0.09. while Visually, keeping theγ in optimal these experiments patch size in the
 ×
CS2).on the Two performance well-known ofimage the quality proposed metrics, method SSIM (FD- constant× the proposed at× 0.09. Visually, method the (FD-SC2) optimal can patch be size determined in the as
andCS2). PSNR, Two are well-known used to analyze image the quality influence metrics, of the SSIM the11 proposed11. method (FD-SC2) can be determined as
parameters. Experiments were conducted on the three 11 11.×
 ×
86 REV Journal on Electronics and Communications, Vol. 9, No. 3–4, July–December, 2019
 PSNR vs gamma in case sigma of noise is 10 PSNR vs gamma in case sigma of noise is 20 PSNR vs gamma in case sigma of noise is 30
 39 36 33
 Abdomen Abdomen Abdomen
 35
 Head Head 32 Head
 38 Lung Lung Lung
 34
 31
 37 33
 30
 32
 36
 31 29
 PSNR 35 PSNR PSNR
 30
 28
 34 29
 27
 28
 33 26
 27
 32 26 25
 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
 gamma gamma gamma
 (a) σ = 10 (b) σ = 20 (c) σ = 30
 SSIM vs gamma in case sigma of noise is 10 SSIM vs gamma in case sigma of noise is 20 SSIM vs gamma in case sigma of noise is 30
 1 0.95 0.95
 Abdomen Abdomen Abdomen
 0.9
 Head 0.9 Head Head
 Lung Lung Lung
 0.95 0.85
 0.85
 0.8
 0.8
 0.9 0.75
 0.75 0.7
 SSIM SSIM SSIM
 0.85 0.65
 0.7
 0.6
 0.65
 0.8 0.55
 0.6
 0.5
 0.75 0.55 0.45
 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
 gamma gamma gamma
 (d) σ = 10 (e) σ = 20 (f) σ = 30
Figure 7. The effects of parameter γ in (11) on the PSNR and SSIM measures. Experiments were performed on images in Figure 4 with noise
levels σ = 10, 20, 30.
 (a) σ = 10 (b) σ = 20 (c) σ = 30
 (d) σ = 10 (e) σ = 20 (f) σ = 30
Figure 8. The effects of the patch size on the PSNR and SSIM measures. Experiments were performed on images in Figure 4 with noise levels
σ = 10, 20, 30.
N. T. Trung et al.: Low-Dose CT Image Denoising using Image Decomposition and Sparse Representation 87
5 Conclusions ies,” IEEE Transactions on Image processing, vol. 15, no. 12,
 pp. 3736–3745, 2006.
This paper has presented an effective denoising method [13] J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman,
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 Proceedings of the IEEE 12th International Conference on
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assumption that noise mainly lies in the medium [14] W. Dong, L. Zhang, G. Shi, and X. Li, “Nonlocally
and high frequency components. Thus, a noisy image centralized sparse representation for image restoration,”
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subtle image details as well as the nature of image. In matching 3D algorithm,” in Proceedings of the Medical
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88 REV Journal on Electronics and Communications, Vol. 9, No. 3–4, July–December, 2019
[29] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Nguyen Linh Trung obtained his B.Eng. and
 “Image quality assessment: from error visibility to struc- Ph.D. degrees, both in Electrical Engineering,
 tural similarity,” IEEE Transactions on Image Processing, from Queensland University of Technology,
 vol. 13, no. 4, pp. 600–612, 2004. Brisbane, Australia. Since 2006, he has been
 on the faculty of University of Engineering
 and Technology, a member university of Viet-
 nam National University, Hanoi, where he
 is currently an associate professor of elec-
 Nguyen Thanh Trung received his B.Eng. tronic engineering in the Faculty of Electronics
 degree in Electronics and Telecommunications and Telecommunications and director of the
 from the Faculty of Technology, Vietnam Na- Advanced Institute of Engineering and Tech-
 tional University, Hanoi, Vietnam in 2003, M.S. nology. He is interested in signal processing methods, including
 degree in electronics engineering from Uni- time-frequency signal analysis, blind source separation, compressive
 versity of Engineering and Technology, Viet- sampling, tensor-based signal analysis, graph signal processing, and
 nam National University, Hanoi, Vietnam in apply them to wireless communication and networking, biomedical
 2012. He is now a Phd student at VNU-UET engineering, with a current focus on large-scale processing.
 and a lecturer at the Faculty of Electronics
 and Communication, University of Informa-
 tion and Communication Technology, Thain-
guyen University, Vietnam. His research interests include biomedical
signal and image processing,sparse coding, machine learning. Marie Luong received the Engineer Diploma
 degree from the Ecole Nationale Supérieure
 d’Electricité et de Mécanique de Nancy,
 France, and the Ph.D. degree in Auto-
 matic, Diagnosis, Signal processing from the
 Trinh Dinh Hoan received the B.S. degree L’Institut National Polytechnique de Lorraine
 in mathematics education from the Vietnam (Lorraine University), France, in 1991 and
 National University, Hanoi, the M.S. degree 1996, respectively. She is currently an Asso-
 in mathematics from the Hanoi Institute of ciate Professor with the Université Paris 13,
 Mathematics, and the Ph.D. degree in signal Sorbonne Paris Cité, France. Her research in-
 and image processing from the Laboratoire terests include image restoration, superresolu-
 Analyse, Géométrie et Applications, Univer- tion, segmentation, watermarking, and medical imaging.
 sité Paris 13, Sorbonne Paris Cité, France,
 in 2005, 2008, and 2013, respectively. He is
 currently a Researcher with the Signals and
 Systems Laboratory, Université de Lorraine
and CNRS, CRAN UMR 7039, 2 avenue de la Forêt de Haye, 54518
Vandœuvre-Lès-Nancy Cedex, France. His research interests include
image restoration, super resolution, segmentation, sparse coding,
machine learning, optimization, and medical imaging.