Abstract

A high-resolution large-area terahertz (THz) scanning imaging system is demonstrated based on a 124×124 pyroelectric array camera and a CO2 pumped continuous-wave THz laser. By applying a scanning mechanism to the real-time imaging setup, images of large-area targets were accomplished. Self-made resolution charts were employed to test the resolution. In order to improve the image quality, the noise in the images was studied and modeled, and then the performance of several denoising methods was compared with real-time THz original images. The experimental results show that, with the help of anisotropic diffusion, noise can be effectively suppressed, and the results are visually pleasant even when there is great attenuation. Those results greatly confirm application potentials of THz imaging using pyroelectric cameras in the field of concealed object detection.

© 2010 Optical Society of America

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Q. Song, Y. Zhao, A. Redo-Sanchez, C. Zhang, and X. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

R. Yao, Q. Li, and Q. Wang, “1.63-THz transmission imaging experiment by use of a pyroelectric camera array,” Proc. SPIE 7277, 72770D (2009).

R. Yao, Q. Li, S. Ding, and Q. Wang, “Investigation on 2.45-THz array transmission imaging,” Proc. SPIE 7385, 73850P (2009).
[CrossRef]

Q. Li, R. Yao, Q. Yin, J. Shan, and Q. Wang, “2.52-THz scanning reflection imaging and image preprocessing,” Proc. SPIE 7277, 72770J (2009).

2008 (6)

X. Shen, C. R. Dietlein, E. Grossman, Z. Popović, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17, 2465–2475 (2008).
[CrossRef] [PubMed]

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

B. N. Behnken and G. Karunasiri, “Real-time terahertz imaging of nonmetallic objects for security screening and anti-counterfeiting applications,” Proc. SPIE 7117, 711705 (2008).
[CrossRef]

J. Yang, S. Ruan, and M. Zhang, “Real-time, continuous-wave terahertz imaging by a pyroelectric camera,” Chin. Opt. Lett. 6, 29–31 (2008).
[CrossRef]

A. Redo-Sanchez and X.-C. Zhang, “Terahertz science and technology trends,” IEEE J. Sel. Top. Quantum Electron. 14, 260–269 (2008).
[CrossRef]

V. P. Wallace, E. MacPherson, J. A. Zeitler, and C. Reid, “Three-dimensional imaging of optically opaque materials using nonionizing terahertz radiation,” J. Opt. Soc. Am. A 25, 3120–3133 (2008).
[CrossRef]

2006 (3)

E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39, R301–R310 (2006).
[CrossRef]

A. W. M. Lee, B. S. Williams, and S. Kumar, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320 240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18, 1415–1417 (2006).
[CrossRef]

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, and Q. Hu, “Real-time terahertz imaging over a standoff distance(>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

2005 (3)

R. M. Woodward, “Terahertz technology in global homeland security,” Proc. SPIE 5781, 22–31 (2005).
[CrossRef]

A. W. M. Lee and Q. Hu, “Real-time, continuous-wave terahertz imaging by use of a microbolometer focal-plane array,” Opt. Lett. 30, 2563–2565 (2005).
[CrossRef] [PubMed]

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

2003 (1)

1996 (1)

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

1995 (1)

1994 (1)

M. Lindenbaum, M. Fischer, and A. M. Bruchstein, “On Gabor contribution to image enhancement,” Pattern Recogn. 27, 1–8 (1994).
[CrossRef]

1990 (1)

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

Behnken, B. N.

B. N. Behnken and G. Karunasiri, “Real-time terahertz imaging of nonmetallic objects for security screening and anti-counterfeiting applications,” Proc. SPIE 7117, 711705 (2008).
[CrossRef]

Bruchstein, A. M.

M. Lindenbaum, M. Fischer, and A. M. Bruchstein, “On Gabor contribution to image enhancement,” Pattern Recogn. 27, 1–8 (1994).
[CrossRef]

Dem’yanenko, M. A.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Dietlein, C. R.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popović, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17, 2465–2475 (2008).
[CrossRef] [PubMed]

Ding, S.

R. Yao, Q. Li, S. Ding, and Q. Wang, “Investigation on 2.45-THz array transmission imaging,” Proc. SPIE 7385, 73850P (2009).
[CrossRef]

Esaev, D. G.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Fischer, M.

M. Lindenbaum, M. Fischer, and A. M. Bruchstein, “On Gabor contribution to image enhancement,” Pattern Recogn. 27, 1–8 (1994).
[CrossRef]

Grossman, E.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popović, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17, 2465–2475 (2008).
[CrossRef] [PubMed]

Hewitt, T. D.

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

Hu, B. B.

Hu, Q.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, and Q. Hu, “Real-time terahertz imaging over a standoff distance(>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

A. W. M. Lee and Q. Hu, “Real-time, continuous-wave terahertz imaging by use of a microbolometer focal-plane array,” Opt. Lett. 30, 2563–2565 (2005).
[CrossRef] [PubMed]

Hwang, J. -S.

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

Inoue, H.

Karpowicz, N.

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

Karunasiri, G.

B. N. Behnken and G. Karunasiri, “Real-time terahertz imaging of nonmetallic objects for security screening and anti-counterfeiting applications,” Proc. SPIE 7117, 711705 (2008).
[CrossRef]

Kawase, K.

Knyazev, B. A.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Kulipanov, G. N.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Kumar, S.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, and Q. Hu, “Real-time terahertz imaging over a standoff distance(>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

A. W. M. Lee, B. S. Williams, and S. Kumar, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320 240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18, 1415–1417 (2006).
[CrossRef]

Lee, A. W. M.

A. W. M. Lee, B. S. Williams, and S. Kumar, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320 240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18, 1415–1417 (2006).
[CrossRef]

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, and Q. Hu, “Real-time terahertz imaging over a standoff distance(>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

A. W. M. Lee and Q. Hu, “Real-time, continuous-wave terahertz imaging by use of a microbolometer focal-plane array,” Opt. Lett. 30, 2563–2565 (2005).
[CrossRef] [PubMed]

Li, Q.

R. Yao, Q. Li, and Q. Wang, “1.63-THz transmission imaging experiment by use of a pyroelectric camera array,” Proc. SPIE 7277, 72770D (2009).

R. Yao, Q. Li, S. Ding, and Q. Wang, “Investigation on 2.45-THz array transmission imaging,” Proc. SPIE 7385, 73850P (2009).
[CrossRef]

Q. Li, R. Yao, Q. Yin, J. Shan, and Q. Wang, “2.52-THz scanning reflection imaging and image preprocessing,” Proc. SPIE 7277, 72770J (2009).

Lin, K. -I.

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

Lindenbaum, M.

M. Lindenbaum, M. Fischer, and A. M. Bruchstein, “On Gabor contribution to image enhancement,” Pattern Recogn. 27, 1–8 (1994).
[CrossRef]

Liu, X.

Q. Song, Y. Zhao, A. Redo-Sanchez, C. Zhang, and X. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

MacPherson, E.

Malik, J.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

Meyer, F. G.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popović, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17, 2465–2475 (2008).
[CrossRef] [PubMed]

Nuss, M. C.

Ogawa, Y.

Perona, P.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

Pickwell, E.

E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39, R301–R310 (2006).
[CrossRef]

Popovic, Z.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popović, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17, 2465–2475 (2008).
[CrossRef] [PubMed]

Qin, Q.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, and Q. Hu, “Real-time terahertz imaging over a standoff distance(>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

Redo-Sanchez, A.

Q. Song, Y. Zhao, A. Redo-Sanchez, C. Zhang, and X. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

A. Redo-Sanchez and X.-C. Zhang, “Terahertz science and technology trends,” IEEE J. Sel. Top. Quantum Electron. 14, 260–269 (2008).
[CrossRef]

Reid, C.

Ruan, S.

Shan, J.

Q. Li, R. Yao, Q. Yin, J. Shan, and Q. Wang, “2.52-THz scanning reflection imaging and image preprocessing,” Proc. SPIE 7277, 72770J (2009).

Shen, X.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popović, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17, 2465–2475 (2008).
[CrossRef] [PubMed]

Song, Q.

Q. Song, Y. Zhao, A. Redo-Sanchez, C. Zhang, and X. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

Vinokurov, N. A.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Wallace, V. P.

Wang, Q.

R. Yao, Q. Li, S. Ding, and Q. Wang, “Investigation on 2.45-THz array transmission imaging,” Proc. SPIE 7385, 73850P (2009).
[CrossRef]

Q. Li, R. Yao, Q. Yin, J. Shan, and Q. Wang, “2.52-THz scanning reflection imaging and image preprocessing,” Proc. SPIE 7277, 72770J (2009).

R. Yao, Q. Li, and Q. Wang, “1.63-THz transmission imaging experiment by use of a pyroelectric camera array,” Proc. SPIE 7277, 72770D (2009).

Watanabe, Y.

Williams, B. S.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, and Q. Hu, “Real-time terahertz imaging over a standoff distance(>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

A. W. M. Lee, B. S. Williams, and S. Kumar, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320 240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18, 1415–1417 (2006).
[CrossRef]

Woodward, R. M.

R. M. Woodward, “Terahertz technology in global homeland security,” Proc. SPIE 5781, 22–31 (2005).
[CrossRef]

Wu, Q.

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

Xu, J.

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

Yang, J.

Yao, R.

R. Yao, Q. Li, S. Ding, and Q. Wang, “Investigation on 2.45-THz array transmission imaging,” Proc. SPIE 7385, 73850P (2009).
[CrossRef]

Q. Li, R. Yao, Q. Yin, J. Shan, and Q. Wang, “2.52-THz scanning reflection imaging and image preprocessing,” Proc. SPIE 7277, 72770J (2009).

R. Yao, Q. Li, and Q. Wang, “1.63-THz transmission imaging experiment by use of a pyroelectric camera array,” Proc. SPIE 7277, 72770D (2009).

Yin, Q.

Q. Li, R. Yao, Q. Yin, J. Shan, and Q. Wang, “2.52-THz scanning reflection imaging and image preprocessing,” Proc. SPIE 7277, 72770J (2009).

Zeitler, J. A.

Zhang, C.

Q. Song, Y. Zhao, A. Redo-Sanchez, C. Zhang, and X. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

Zhang, M.

Zhang, X. -C.

A. Redo-Sanchez and X.-C. Zhang, “Terahertz science and technology trends,” IEEE J. Sel. Top. Quantum Electron. 14, 260–269 (2008).
[CrossRef]

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

Zhao, Y.

Q. Song, Y. Zhao, A. Redo-Sanchez, C. Zhang, and X. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

Zhong, H.

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

Appl. Phys. Lett. (4)

N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005).
[CrossRef]

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[CrossRef]

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, and Q. Hu, “Real-time terahertz imaging over a standoff distance(>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Chin. Opt. Lett. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

A. Redo-Sanchez and X.-C. Zhang, “Terahertz science and technology trends,” IEEE J. Sel. Top. Quantum Electron. 14, 260–269 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. W. M. Lee, B. S. Williams, and S. Kumar, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320 240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18, 1415–1417 (2006).
[CrossRef]

IEEE Trans. Image Process. (1)

X. Shen, C. R. Dietlein, E. Grossman, Z. Popović, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17, 2465–2475 (2008).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. D: Appl. Phys. (1)

E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39, R301–R310 (2006).
[CrossRef]

Opt. Commun. (1)

Q. Song, Y. Zhao, A. Redo-Sanchez, C. Zhang, and X. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Pattern Recogn. (1)

M. Lindenbaum, M. Fischer, and A. M. Bruchstein, “On Gabor contribution to image enhancement,” Pattern Recogn. 27, 1–8 (1994).
[CrossRef]

Proc. SPIE (5)

Q. Li, R. Yao, Q. Yin, J. Shan, and Q. Wang, “2.52-THz scanning reflection imaging and image preprocessing,” Proc. SPIE 7277, 72770J (2009).

R. M. Woodward, “Terahertz technology in global homeland security,” Proc. SPIE 5781, 22–31 (2005).
[CrossRef]

B. N. Behnken and G. Karunasiri, “Real-time terahertz imaging of nonmetallic objects for security screening and anti-counterfeiting applications,” Proc. SPIE 7117, 711705 (2008).
[CrossRef]

R. Yao, Q. Li, and Q. Wang, “1.63-THz transmission imaging experiment by use of a pyroelectric camera array,” Proc. SPIE 7277, 72770D (2009).

R. Yao, Q. Li, S. Ding, and Q. Wang, “Investigation on 2.45-THz array transmission imaging,” Proc. SPIE 7385, 73850P (2009).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Experimental setup: l 1 = 6   cm , l 2 = 7   cm , l 3 = 27   cm .

Fig. 2
Fig. 2

Imaging beam spot (2D and three-dimensional contour views).

Fig. 3
Fig. 3

Photo of the resolution chart and imaging results: (a) Photo; (b) single-frame image of 0.8 mm strips; (c) single-frame image of 0.6 mm strips; (d) single-frame image of 0.4 mm strips; (e) two-frame averaging result of 0.8 mm strips; (f) two-frame averaging result of 0.6 mm strips; (g) five-frame averaging result of 0.4 mm strips.

Fig. 4
Fig. 4

Scanning imaging result of a razor blade: (a) photo of the razor blade; (b) image mosaic result based on five-frame averaging; (c) image mosaic result after applying overlap processing.

Fig. 5
Fig. 5

Imaging results with different sub-image sizes. (a) Image size: 180 × 360 , sub-image size: 60 × 60 ; (b) image size: 160 × 320 , sub-image size 40 × 40 .

Fig. 6
Fig. 6

Scanning imaging result of a metal sheet: (a) photo of metal sheet; (b) five-frame averaging result; (c) result of background removing.

Fig. 7
Fig. 7

Histograms computed using small strips (shown as inserts): (a) single-frame image; (b) five-frame averaging result.

Fig. 8
Fig. 8

Results of different denoising methods: (a) anisotropic diffusion applied to five-frame averaging result ( k = 8 , and five iterative times); (b) 5 × 5 Gaussian filtering ( σ = 1.5 ) ; (c) 5 × 5 median filtering; (d) anisotropic diffusion applied to Fig. 3c ( k = 15 , and five iterative times).

Fig. 9
Fig. 9

Imaging result of a hexagon nut and denoised images: (a) single-frame image; (b) five-frame averaging result; (c) anisotropic diffusion applied to five-frame averaging result ( k = 8 , and five iterative times); (d) 5 × 5 Gaussian filtering applied to (a) ( σ = 2.5 ) ; (c) 5 × 5 median filtering applied to (a); (d) anisotropic diffusion applied to (a) ( k = 15 , and five iterative times).

Fig. 10
Fig. 10

Imaging result of a horseshoe gasket and denoised images: (a) single-frame image; (b) five-frame averaging result; (c) anisotropic diffusion applied to five-frame averaging result ( k = 8 , and five iterative times); (d) 5 × 5 Gaussian filtering applied to (a) ( σ = 2.5 ) ; (c) 5 × 5 median filtering applied to (a); (d) anisotropic diffusion applied to (a) ( k = 15 , and five iterative times).

Fig. 11
Fig. 11

Imaging result of a concealed horseshoe gasket: (a) through a PE envelope; (b) anisotropic diffusion ( k = 8 , and five iterative times); (c) through one piece of paper; (d) anisotropic diffusion ( k = 20 , and 5 iterative times).

Tables (1)

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Table 1 Comparison of Different Denoised Results

Equations (6)

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f ( x , y ) = t ( x , y ) i ( x , y ) .
f ( x , y , t ) t = div ( g ( | f ( x , y , t ) | ) f ( x , y , t ) ) ,
f ( x , y , t ) t = 0 = f ( x , y , 0 ) ,
g ( | f | ) = 1 / ( 1 + f / k ) 2 ,
RMSE = ( ( [ f ̂ ( x , y ) f 0 ( x , y ) ] 2 / M N ) 1 / 2 ) ,
PSNR = 20 log 10 ( 255 / RMSE ) ,

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