Abstract

For photoacoustic computed tomography (PACT), an insufficient number of ultrasound detectors can cause serious streak-type artifacts. These artifacts get overlaid on top of image features, and thus locally jeopardize image quality and resolution. Here, a reconstruction algorithm, termed Contamination-Tracing Back-Projection (CTBP), is proposed for the mitigation of streak-type artifacts. During reconstruction, CTBP adaptively adjusts the back-projection weight, whose value is determined by the likelihood of contamination, to minimize the negative influences of strong absorbers. An iterative solution of the eikonal equation is implemented to accurately trace the time of flight of different pixels. Numerical, phantom and in vivo experiments demonstrate that CTBP can dramatically suppress streak artifacts in PACT and improve image quality.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (3)

2018 (4)

H. N. Y. Nguyen, A. Hussain, and W. Steenbergen, “Reflection artifact identification in photoacoustic imaging using multi-wavelength excitation,” Biomed. Opt. Express 9(10), 4613–4630 (2018).
[Crossref]

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, “Double-stage delay multiply and sum beamforming algorithm: Application to linear-array photoacoustic imaging,” IEEE Trans. Biomed. Eng. 65(1), 31–42 (2018).
[Crossref]

2017 (1)

2015 (2)

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, “The delay multiply and sum beamforming algorithm in ultrasound B-mode medical imaging,” IEEE Trans. Med. Imag. 34(4), 940–949 (2015).
[Crossref]

Y. Han, S. Tzoumas, A. Nunes, and V. Ntziachristos, “Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging,” Med. Phys. 42(9), 5444–5452 (2015).
[Crossref]

2014 (1)

2013 (1)

2012 (4)

Y. Zhang, Y. Wang, and C. Zhang, “Total variation based gradient descent algorithm for sparse-view photoacoustic image reconstruction,” Ultrasonics 52(8), 1046–1055 (2012).
[Crossref]

J. Meng, L. V. Wang, L. Ying, D. Liang, and L. Song, “Compressed-sensing photoacoustic computed tomography in vivo with partially known support,” Opt. Express 20(15), 16510–16523 (2012).
[Crossref]

L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).
[Crossref]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, and D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imag. 31(10), 1922–1928 (2012).
[Crossref]

2011 (1)

M. A. Lediju, G. E. Trahey, B. C. Byram, and J. J. Dahl, “Short-lag spatial coherence of backscattered echoes: Imaging characteristics,” IEEE Trans. Sonics Ultrason. 58(7), 1377–1388 (2011).
[Crossref]

2009 (2)

L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
[Crossref]

G. Paltauf, R. Nuster, and P. Burgholzer, “Weight factors for limited angle photoacoustic tomography,” Phys. Med. Biol. 54(11), 3303–3314 (2009).
[Crossref]

2007 (1)

M. S. Hassouna and A. A. Farag, “Multi-stencils fast marching methods: A highly accurate solution to the eikonal equation on cartesian domains,” IEEE Trans. Pattern Anal. Mach. Intell. 29(9), 1563–1574 (2007).
[Crossref]

2005 (1)

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E 71(1), 016706 (2005).
[Crossref]

2004 (1)

J. F. Barrett and N. Keat, “Artifacts in CT: recognition and avoidance,” RadioGraphics 24(6), 1679–1691 (2004).
[Crossref]

Adabi, S.

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, “Double-stage delay multiply and sum beamforming algorithm: Application to linear-array photoacoustic imaging,” IEEE Trans. Biomed. Eng. 65(1), 31–42 (2018).
[Crossref]

Adler, B.

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Antholzer, S.

S. Antholzer, M. Haltmeier, and J. Schwab, “Deep learning for photoacoustic tomography from sparse data,” Inverse Probl. Sci. Eng. 27(7), 987–1005 (2019).
[Crossref]

Arridge,

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Barrett, J. F.

J. F. Barrett and N. Keat, “Artifacts in CT: recognition and avoidance,” RadioGraphics 24(6), 1679–1691 (2004).
[Crossref]

Beard, S.

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Bell, M. A. L.

Betcke, N.

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Boctor, E. M.

Buehler, A.

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, and D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imag. 31(10), 1922–1928 (2012).
[Crossref]

Burgholzer, P.

G. Paltauf, R. Nuster, and P. Burgholzer, “Weight factors for limited angle photoacoustic tomography,” Phys. Med. Biol. 54(11), 3303–3314 (2009).
[Crossref]

Byram, B. C.

M. A. Lediju, G. E. Trahey, B. C. Byram, and J. J. Dahl, “Short-lag spatial coherence of backscattered echoes: Imaging characteristics,” IEEE Trans. Sonics Ultrason. 58(7), 1377–1388 (2011).
[Crossref]

Cai, C.

Caliano, G.

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, “The delay multiply and sum beamforming algorithm in ultrasound B-mode medical imaging,” IEEE Trans. Med. Imag. 34(4), 940–949 (2015).
[Crossref]

Cox, P.

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Dahl, J. J.

M. A. Lediju, G. E. Trahey, B. C. Byram, and J. J. Dahl, “Short-lag spatial coherence of backscattered echoes: Imaging characteristics,” IEEE Trans. Sonics Ultrason. 58(7), 1377–1388 (2011).
[Crossref]

Deán-Ben, X. L.

Y. Han, L. Ding, X. L. Deán-Ben, D. Razansky, J. Prakash, and V. Ntziachristos, “Three-dimensional optoacoustic reconstruction using fast sparse representation,” Opt. Lett. 42(5), 979–982 (2017).
[Crossref]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, and D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imag. 31(10), 1922–1928 (2012).
[Crossref]

Ding, L.

Farag, A. A.

M. S. Hassouna and A. A. Farag, “Multi-stencils fast marching methods: A highly accurate solution to the eikonal equation on cartesian domains,” IEEE Trans. Pattern Anal. Mach. Intell. 29(9), 1563–1574 (2007).
[Crossref]

Haltmeier, M.

S. Antholzer, M. Haltmeier, and J. Schwab, “Deep learning for photoacoustic tomography from sparse data,” Inverse Probl. Sci. Eng. 27(7), 987–1005 (2019).
[Crossref]

Han, Y.

Y. Han, L. Ding, X. L. Deán-Ben, D. Razansky, J. Prakash, and V. Ntziachristos, “Three-dimensional optoacoustic reconstruction using fast sparse representation,” Opt. Lett. 42(5), 979–982 (2017).
[Crossref]

Y. Han, S. Tzoumas, A. Nunes, and V. Ntziachristos, “Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging,” Med. Phys. 42(9), 5444–5452 (2015).
[Crossref]

Hariri, A.

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

Hassouna, M. S.

M. S. Hassouna and A. A. Farag, “Multi-stencils fast marching methods: A highly accurate solution to the eikonal equation on cartesian domains,” IEEE Trans. Pattern Anal. Mach. Intell. 29(9), 1563–1574 (2007).
[Crossref]

Haung, X.

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

Hauptmann, F.

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Hu, S.

L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).
[Crossref]

Hussain, A.

Huynh, J.

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Keat, N.

J. F. Barrett and N. Keat, “Artifacts in CT: recognition and avoidance,” RadioGraphics 24(6), 1679–1691 (2004).
[Crossref]

Kuo, N.

Lediju, M. A.

M. A. Lediju, G. E. Trahey, B. C. Byram, and J. J. Dahl, “Short-lag spatial coherence of backscattered echoes: Imaging characteristics,” IEEE Trans. Sonics Ultrason. 58(7), 1377–1388 (2011).
[Crossref]

Liang, D.

Lucka, M.

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Luo, J.

Ma, C.

Magenes, G.

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, “The delay multiply and sum beamforming algorithm in ultrasound B-mode medical imaging,” IEEE Trans. Med. Imag. 34(4), 940–949 (2015).
[Crossref]

Mahloojifar, A.

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, “Double-stage delay multiply and sum beamforming algorithm: Application to linear-array photoacoustic imaging,” IEEE Trans. Biomed. Eng. 65(1), 31–42 (2018).
[Crossref]

Matrone, G.

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, “The delay multiply and sum beamforming algorithm in ultrasound B-mode medical imaging,” IEEE Trans. Med. Imag. 34(4), 940–949 (2015).
[Crossref]

Meng, J.

Mozaffarzadeh, M.

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, “Double-stage delay multiply and sum beamforming algorithm: Application to linear-array photoacoustic imaging,” IEEE Trans. Biomed. Eng. 65(1), 31–42 (2018).
[Crossref]

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

Nasiriavanaki, M.

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, “Double-stage delay multiply and sum beamforming algorithm: Application to linear-array photoacoustic imaging,” IEEE Trans. Biomed. Eng. 65(1), 31–42 (2018).
[Crossref]

Nguyen, H. N. Y.

Ntziachristos, V.

Y. Han, L. Ding, X. L. Deán-Ben, D. Razansky, J. Prakash, and V. Ntziachristos, “Three-dimensional optoacoustic reconstruction using fast sparse representation,” Opt. Lett. 42(5), 979–982 (2017).
[Crossref]

Y. Han, S. Tzoumas, A. Nunes, and V. Ntziachristos, “Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging,” Med. Phys. 42(9), 5444–5452 (2015).
[Crossref]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, and D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imag. 31(10), 1922–1928 (2012).
[Crossref]

Nunes, A.

Y. Han, S. Tzoumas, A. Nunes, and V. Ntziachristos, “Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging,” Med. Phys. 42(9), 5444–5452 (2015).
[Crossref]

Nuster, R.

G. Paltauf, R. Nuster, and P. Burgholzer, “Weight factors for limited angle photoacoustic tomography,” Phys. Med. Biol. 54(11), 3303–3314 (2009).
[Crossref]

Omidi, P.

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

Orooji, M.

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, “Double-stage delay multiply and sum beamforming algorithm: Application to linear-array photoacoustic imaging,” IEEE Trans. Biomed. Eng. 65(1), 31–42 (2018).
[Crossref]

Ourselin, S.

F. Hauptmann, M. Lucka, N. Betcke, J. Huynh, B. Adler, P. Cox, S. Beard, S. Ourselin, and Arridge, “Model-based learning for accelerated, limited-view 3-d photoacoustic tomography,” IEEE Trans. Med. Imag. 37(6), 1382–1393 (2018).
[Crossref]

Paltauf, G.

G. Paltauf, R. Nuster, and P. Burgholzer, “Weight factors for limited angle photoacoustic tomography,” Phys. Med. Biol. 54(11), 3303–3314 (2009).
[Crossref]

Prakash, J.

Pramanik, M.

Qian, J.

Razansky, D.

Y. Han, L. Ding, X. L. Deán-Ben, D. Razansky, J. Prakash, and V. Ntziachristos, “Three-dimensional optoacoustic reconstruction using fast sparse representation,” Opt. Lett. 42(5), 979–982 (2017).
[Crossref]

X. L. Deán-Ben, A. Buehler, V. Ntziachristos, and D. Razansky, “Accurate model-based reconstruction algorithm for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imag. 31(10), 1922–1928 (2012).
[Crossref]

Savoia, A. S.

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, “The delay multiply and sum beamforming algorithm in ultrasound B-mode medical imaging,” IEEE Trans. Med. Imag. 34(4), 940–949 (2015).
[Crossref]

Schwab, J.

S. Antholzer, M. Haltmeier, and J. Schwab, “Deep learning for photoacoustic tomography from sparse data,” Inverse Probl. Sci. Eng. 27(7), 987–1005 (2019).
[Crossref]

Si, K.

Song, D. Y.

Song, L.

Steenbergen, W.

Trahey, G. E.

M. A. Lediju, G. E. Trahey, B. C. Byram, and J. J. Dahl, “Short-lag spatial coherence of backscattered echoes: Imaging characteristics,” IEEE Trans. Sonics Ultrason. 58(7), 1377–1388 (2011).
[Crossref]

Tzoumas, S.

Y. Han, S. Tzoumas, A. Nunes, and V. Ntziachristos, “Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging,” Med. Phys. 42(9), 5444–5452 (2015).
[Crossref]

Wang, L. V.

L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).
[Crossref]

J. Meng, L. V. Wang, L. Ying, D. Liang, and L. Song, “Compressed-sensing photoacoustic computed tomography in vivo with partially known support,” Opt. Express 20(15), 16510–16523 (2012).
[Crossref]

L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3(9), 503–509 (2009).
[Crossref]

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E 71(1), 016706 (2005).
[Crossref]

Wang, X.

Wang, Y.

Y. Zhang, Y. Wang, and C. Zhang, “Total variation based gradient descent algorithm for sparse-view photoacoustic image reconstruction,” Ultrasonics 52(8), 1046–1055 (2012).
[Crossref]

Xu, M.

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E 71(1), 016706 (2005).
[Crossref]

Ying, L.

Zafar, M.

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

Zhang, C.

Y. Zhang, Y. Wang, and C. Zhang, “Total variation based gradient descent algorithm for sparse-view photoacoustic image reconstruction,” Ultrasonics 52(8), 1046–1055 (2012).
[Crossref]

Zhang, Y.

Y. Zhang, Y. Wang, and C. Zhang, “Total variation based gradient descent algorithm for sparse-view photoacoustic image reconstruction,” Ultrasonics 52(8), 1046–1055 (2012).
[Crossref]

Appl. Sci. (1)

P. Omidi, M. Zafar, M. Mozaffarzadeh, A. Hariri, X. Haung, M. Orooji, and M. Nasiriavanaki, “A novel dictionary-based image reconstruction for photoacoustic computed tomography,” Appl. Sci. 8(9), 1570 (2018).
[Crossref]

Biomed. Opt. Express (4)

IEEE Trans. Biomed. Eng. (1)

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, “Double-stage delay multiply and sum beamforming algorithm: Application to linear-array photoacoustic imaging,” IEEE Trans. Biomed. Eng. 65(1), 31–42 (2018).
[Crossref]

IEEE Trans. Med. Imag. (3)

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Figures (7)

Fig. 1.
Fig. 1. Phantom experiment with sparse sampling. (a) The direct reconstruction result and (b) the result of CTBP, under the condition of sparse sampling density. (c) The TOF calculation. The black curves denote the iso-TOF curves of a specific detector. White points are the contamination sources, which are generated with (a). (d) The weight map used in CTBP. (e) The photograph of phantom. (f) The reconstructed profiles correspond to the dotted lines in (a) and (b) (from the top to bottom). Scale bar: 5 mm.
Fig. 2.
Fig. 2. Phantom experiment with limited view. (a)–(c) and (d)–(f) are the results of 1/3 ring and full ring detection, respectively. (a)(d), (b)(e), and (c)(f) are the results of direct back-projection, back-projection after raw data moving average, and CTBP with data moving average, respectively. Scale bar: 5 mm.
Fig. 3.
Fig. 3. In vivo imaging of the mouse liver cross-section. (a)(b) and (c)(d) are the results of 1/3 ring and full ring acquisitions, respectively. (a)(c) and (b)(d) are the results of direct back-projection and CTBP, respectively. Scale bar: 5 mm.
Fig. 4.
Fig. 4. Imaging of the mouse liver region with external carbon rod. (a) The schematic diagram of experimental setup. OF: optical fiber; UA: ultrasound array; WT: water; CR: carbon rod. (b) The result of direct back-projection. The blue arrow denotes the rod. (c) The result of CTBP. (d) Back-projection result of the corresponding slice without the rod, as gold standard. Scale bar: 5 mm.
Fig. 5.
Fig. 5. Imaging of the mouse liver region (near the lungs) with inserted carbon rod. (a) Photo of the frozen section corresponding to the region imaged by PA. IVC: inferior vena cava; LV: liver; CR: carbon rod; AA: abdominal aorta; L: lung; SC: spinal cord. (b) The result of direct back-projection. The blue arrow denotes the rod. (c) The result of CTBP. (d) Back-projection result of the corresponding slice without the rod, as gold standard. Scale bar: 5 mm.
Fig. 6.
Fig. 6. In vivo mouse brain imaging along the coronal plane. (a) Experimental setup. OF: optical fiber; AF: acoustic focus; UA: ultrasound array; WT: water. (b) The result of direct back-projection. (c) The result of CTBP. The blue arrow denotes the part with strong absorption. Scale bar: 5 mm.
Fig. 7.
Fig. 7. Results of numerical experiments. (a)–(d) and (e)–(h) are the results of direct back-projection and CTBP, respectively. (a)(b)(e)(f) are the results of sparse sampling, where elements are evenly distributed on a full ring array. The total number of elements for (a)(e) and (b)(f) are 128 and 64, respectively. (c)(d)(g)(h) are the results of limited view, where (c)(g) and (d)(h) are the results of 1/2 ring and 1/3 ring, respectively. Red box denotes the part used to perform quantitative evaluation. Scale bar: 5 mm.

Tables (1)

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Table 1. Quantitative evaluation of image gradient (MG)

Equations (5)

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p 0 ( b ) ( r ) = Ω 0 b ( r 0 , t = T O F ( r , r 0 ) ) d Ω 0 / Ω 0 ,
| t ( r ) | = 1 v ( r ) ,
p 0 ( C T ) ( r ) = 1 Ω 0 i w ( C T ) ( r , r i ) b ( r i , t = T O F ( r , r i ) ) Δ Ω 0 ( r , r i ) ,
w ( C T ) ( r , r i ) = ( 1 w min ) e a n ( r , r i ) + w min ,
M G = i | | I i | | 2 ,

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