Abstract

In this paper, a new fast terahertz reflection tomography is proposed using block-based compressed sensing. Since measuring the time-domain signal on two-dimensional grid requires excessive time, reducing measurement time is highly demanding in terahertz tomography. The proposed technique directly reduces the number of sampling points in the spatial domain without modulation or transformation of the signal. Compressed sensing in spatial domain suggests a block-based reconstruction, which substantially reduces computational time without degrading the image quality. An overlap-average method is proposed to remove the block artifact in the block-based compressed sensing. Fast terahertz reflection tomography using the block-based compressed sensing is demonstrated with an integrated circuit and parched anchovy as examples.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. J.-H. Son, “Terahertz electromagnetic interactions with biological matter and their applications,” J. Appl. Phys. 105(10), 102033 (2009).
    [CrossRef]
  4. A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. J. Xu and X. C. Zhang, “Terahertz wave reciprocal imaging,” Appl. Phys. Lett. 88(15), 151107 (2006).
    [CrossRef]
  11. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2011 (1)

2010 (1)

2009 (4)

S. J. Oh, J. Kang, I. Maeng, J.-S. Suh, Y.-M. Huh, S. Haam, and J.-H. Son, “Nanoparticle-enabled terahertz imaging for cancer diagnosis,” Opt. Express 17(5), 3469–3475 (2009).
[CrossRef] [PubMed]

K. H. Jin, Y. Kim, D. S. Yee, O. K. Lee, and J. C. Ye, “Compressed sensing pulse-echo mode terahertz reflectance tomography,” Opt. Lett. 34(24), 3863–3865 (2009).
[CrossRef] [PubMed]

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

J.-H. Son, “Terahertz electromagnetic interactions with biological matter and their applications,” J. Appl. Phys. 105(10), 102033 (2009).
[CrossRef]

2008 (1)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

2007 (1)

H. Jung, J. C. Ye, and E. Y. Kim, “Improved k-t BLAST and k-t SENSE using FOCUSS,” Phys. Med. Biol. 52(11), 3201–3226 (2007).
[CrossRef] [PubMed]

2006 (3)

J. Xu and X. C. Zhang, “Terahertz wave reciprocal imaging,” Appl. Phys. Lett. 88(15), 151107 (2006).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

2004 (1)

S. Wang and X.-C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37(4), R1–R36 (2004).
[CrossRef]

1999 (2)

Z. Jiang and X. C. Zhang, “Terahertz imaging via electrooptic effect,” IEEE Trans. Microw. Theory Tech. 47(12), 2644–2650 (1999).
[CrossRef]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[CrossRef]

1997 (1)

1995 (2)

B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20(16), 1716–1718 (1995).
[CrossRef] [PubMed]

I. F. Gorodnitsky, J. S. George, and B. D. Rao, “Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm,” Electroencephalogr. Clin. Neurophysiol. 95(4), 231–251 (1995).
[CrossRef] [PubMed]

Arnone, D. D.

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[CrossRef]

Bobrow, L.

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

Boivin, L.

Burnett, A.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Choi, J.

Cunningham, J. E.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Davies, A. G.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Ding, S.-H.

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

Fitzgerald, A. J.

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

Gan, L.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

George, J. S.

I. F. Gorodnitsky, J. S. George, and B. D. Rao, “Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm,” Electroencephalogr. Clin. Neurophysiol. 95(4), 231–251 (1995).
[CrossRef] [PubMed]

Gladden, L. F.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Gorodnitsky, I. F.

I. F. Gorodnitsky, J. S. George, and B. D. Rao, “Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm,” Electroencephalogr. Clin. Neurophysiol. 95(4), 231–251 (1995).
[CrossRef] [PubMed]

Gupta, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[CrossRef]

Haam, S.

Hu, B. B.

Huh, Y.-M.

Hunsche, S.

Jiang, Z.

Z. Jiang and X. C. Zhang, “Terahertz imaging via electrooptic effect,” IEEE Trans. Microw. Theory Tech. 47(12), 2644–2650 (1999).
[CrossRef]

Jimenez-Linan, M.

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

Jin, K. H.

Jung, H.

H. Jung, J. C. Ye, and E. Y. Kim, “Improved k-t BLAST and k-t SENSE using FOCUSS,” Phys. Med. Biol. 52(11), 3201–3226 (2007).
[CrossRef] [PubMed]

Kang, J.

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Kim, E. Y.

H. Jung, J. C. Ye, and E. Y. Kim, “Improved k-t BLAST and k-t SENSE using FOCUSS,” Phys. Med. Biol. 52(11), 3201–3226 (2007).
[CrossRef] [PubMed]

Kim, Y.

Koch, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[CrossRef]

Lee, K.

Lee, O. K.

Li, Q.

Linfield, E. H.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Maeng, I.

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[CrossRef]

D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22(12), 904–906 (1997).
[CrossRef] [PubMed]

Neelamani, R.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[CrossRef]

Nuss, M. C.

Oh, S. J.

Park, J. Y.

Parrott, E. P. J.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Purushotham, A. D.

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

Pye, R. J.

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

Rao, B. D.

I. F. Gorodnitsky, J. S. George, and B. D. Rao, “Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm,” Electroencephalogr. Clin. Neurophysiol. 95(4), 231–251 (1995).
[CrossRef] [PubMed]

Rudd, J. V.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[CrossRef]

Shen, H.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Shen, Y. C.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Son, J.-H.

Stringer, M.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Suh, J.-S.

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Tych, K.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Wallace, V. P.

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

Wang, Q.

Wang, S.

S. Wang and X.-C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37(4), R1–R36 (2004).
[CrossRef]

Xu, J.

J. Xu and X. C. Zhang, “Terahertz wave reciprocal imaging,” Appl. Phys. Lett. 88(15), 151107 (2006).
[CrossRef]

Yao, R.

Ye, J. C.

Yee, D. S.

Zeitler, J. A.

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

Zhang, X. C.

J. Xu and X. C. Zhang, “Terahertz wave reciprocal imaging,” Appl. Phys. Lett. 88(15), 151107 (2006).
[CrossRef]

Z. Jiang and X. C. Zhang, “Terahertz imaging via electrooptic effect,” IEEE Trans. Microw. Theory Tech. 47(12), 2644–2650 (1999).
[CrossRef]

Zhang, X.-C.

S. Wang and X.-C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37(4), R1–R36 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Y. C. Shen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95(23), 231112 (2009).
[CrossRef]

J. Xu and X. C. Zhang, “Terahertz wave reciprocal imaging,” Appl. Phys. Lett. 88(15), 151107 (2006).
[CrossRef]

Electroencephalogr. Clin. Neurophysiol. (1)

I. F. Gorodnitsky, J. S. George, and B. D. Rao, “Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm,” Electroencephalogr. Clin. Neurophysiol. 95(4), 231–251 (1995).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

Z. Jiang and X. C. Zhang, “Terahertz imaging via electrooptic effect,” IEEE Trans. Microw. Theory Tech. 47(12), 2644–2650 (1999).
[CrossRef]

J. Appl. Phys. (1)

J.-H. Son, “Terahertz electromagnetic interactions with biological matter and their applications,” J. Appl. Phys. 105(10), 102033 (2009).
[CrossRef]

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

S. Wang and X.-C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37(4), R1–R36 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Med. Biol. (1)

H. Jung, J. C. Ye, and E. Y. Kim, “Improved k-t BLAST and k-t SENSE using FOCUSS,” Phys. Med. Biol. 52(11), 3201–3226 (2007).
[CrossRef] [PubMed]

Radiology (1)

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006).
[CrossRef] [PubMed]

Other (5)

L. Gan, “Block compressed sensing of natural images,” in Proc. Int. Conf. Digital Signal Processing, pp.403–406, Cardiff, UK (2007).

S. H. Cho, J.-H. Park, S.-H. Lee, H. Park, J.-H. Son, and C. B. Ahn, “Direct block-based compressed sensing for THz reflection tomography,” in Proc. Int. 2nd THz-Bio Workshop, pp.92–93, Seoul, Korea (2011).

T. Acharya and P.-S. Tsai, JPEG2000 standard for image compression: concepts, algorithms and VLSI architectures (Wiley-Interscience, 2005).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C: the art of scientific computing 2nd ed. (Cambridge University Press, 1992).

S. Qian and D. Chen, Joint time-frequency analysis: methods and applications (Prentice Hall, 1996).

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Figures (7)

Fig. 1
Fig. 1

Nonstationary signal having four different frequencies, 1 KHz, 3 KHz, 2 KHz, and 4 KHz in 4 intervals (a). Four distinct spectra are observed if a segmented Fourier transform is applied to each segmented signal (b). Spectrum of the signal if Fourier transform is applied to the entire signal (c).

Fig. 2
Fig. 2

Reconstructed images by the block-based CS before and after applying the overlap-average method are shown in the first and second rows, respectively. Cubic interpolated images are shown in the third row for comparison. The compression factors are 8, 4, and 2 in the first, second, and third columns, respectively.

Fig. 3
Fig. 3

Terahertz reflection-type time-domain spectroscopy system used for the terahertz tomography.

Fig. 4
Fig. 4

Photograph of an integrated circuit (a), two dimensional terahertz peak image (b), and four tomographic images at the depths of 0.14mm, 2.06mm, 2.44mm, and 3.19mm are shown from 4 different time delays (c-f).

Fig. 5
Fig. 5

Terahertz tomographic images obtained with full scan (a), and by the block-based CS with compression factors of 8 (b), 4 (c), and 2 (d), respectively.

Fig. 6
Fig. 6

Terahertz tomographic images of the parched anchovy. Photograph of the sample and dissection image are shown in (a) and (b), respectively. Terahertz sectional images are shown in (c)-(f) with transverse resolution of 250μm. Slice thickness is 105μm.

Fig. 7
Fig. 7

Terahertz tomographic images obtained by the block-based CS. Reconstructed images are shown by full scan (a, e), by the block-based CS with compression factors of 8 (b, f), 4 (c, g), and 2 (d, h).

Tables (3)

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Table 1 Evaluation of PSNR [dB] for the Images in Fig. 2 for Various Compression Factors by the Block-Based CS and Cubic Interpolation. Figure Numbers are Shown in Parenthesis.

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Table 2 PSNR of the Reconstructed Images by the Cubic Interpolation and Block-Based CS for a Plane Shown in Fig. 5.

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Table 3 Average PSNR of the images by the cubic interpolation and block-based CS.

Equations (1)

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m ( t ) = A μ ( t ) ,

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