Abstract

In most photoacoustic tomography (PAT) reconstruction approaches, it is assumed that the receiving transducers have omnidirectional response and can fully surround the region of interest. These assumptions are not satisfied in practice. To deal with these limitations, we present a novel deconvolution based photoacoustic reconstruction with sparsity regularization (DPARS) technique. The DPARS algorithm is a semi-analytical reconstruction approach in which the projections of the absorber distribution derived from a deconvolution-based method are computed and used to generate a large linear system of equations. In these projections, computed over limited viewing angles, the directivity effect of the transducer is taken into account. The distribution of absorbers is computed using a sparse representation of absorber coefficients obtained from the discrete cosine transform. This sparse representation helps improve the numerical conditioning of the system of equations and reduces the computation time of the deconvolution-based approach by one order of magnitude relative to Tikhonov regularization. The algorithm has been tested in simulations, and using two-dimensional and three-dimensional experimental data obtained with a conventional ultrasound transducer. The results show that DPARS, when evaluated using contrast-to-noise ratio and root-mean-square errors, outperforms the conventional delay-and-sum (DAS) reconstruction method.

© 2017 Optical Society of America

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References

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2016 (2)

2015 (5)

C. Sim, H. Kim, H. Moon, H. Lee, J. H. Chang, and H. Kim, “Photoacoustic-based nanomedicine for cancer diagnosis and therapy,” J. Control. Release 203, 118–125 (2015).
[Crossref] [PubMed]

M. A. Lediju Bell, X. Guo, D. Y. Song, and E. M. Boctor, “Transurethral light delivery for prostate photoacoustic imaging,” J. Biomed. Opt. 20(3), 036002 (2015).
[Crossref] [PubMed]

Q. Sheng, K. Wang, T. P. Matthews, J. Xia, L. Zhu, L. V. Wang, and M. A. Anastasio, “A constrained variable projection reconstruction method for photoacoustic computed tomography without accurate knowledge of transducer responses,” IEEE Trans. Med. Imaging 34(12), 2443–2458 (2015).
[Crossref] [PubMed]

H. Gao, J. Feng, and L. Song, “Limited-view multi-source quantitative photoacoustic tomography,” Inverse Probl. 31(6), 065004 (2015).
[Crossref]

M. Cao, J. Yuan, S. Du, G. Xu, X. Wang, P. L. Carson, and X. Liu, “Full-view photoacoustic tomography using asymmetric distributed sensors optimized with compressed sensing method,” Biomed. Signal Process. Control 21, 19–25 (2015).
[Crossref]

2014 (4)

K. Mitsuhashi, K. Wang, and M. A. Anastasio, “Investigation of the far-field approximation for modeling a transducer’s spatial impulse response in photoacoustic computed tomography,” Photoacoustics 2(1), 21–32 (2014).
[Crossref] [PubMed]

S. Tzoumas, A. Rosenthal, C. Lutzweiler, D. Razansky, and V. Ntziachristos, “Spatiospectral denoising framework for multispectral optoacoustic imaging based on sparse signal representation,” Med. Phys. 41(11), 113301 (2014).
[Crossref] [PubMed]

J. Xia and L. V. Wang, “Small-Animal Whole-Body Photoacoustic Tomography: A Review,” IEEE Trans. Biomed. Eng. 61(5), 1380–1389 (2014).
[Crossref] [PubMed]

J. Prakash, A. S. Raju, C. B. Shaw, M. Pramanik, and P. K. Yalavarthy, “Basis pursuit deconvolution for improving model-based reconstructed images in photoacoustic tomography,” Biomed. Opt. Express 5(5), 1363–1377 (2014).
[Crossref] [PubMed]

2013 (4)

J. Kang, E. K. Kim, G. R. Kim, C. Yoon, T. K. Song, and J. H. Chang, “Photoacoustic imaging of breast microcalcifications: A validation study with 3-dimensional ex vivo data and spectrophotometric measurement,” J. Biophotonics 8(1-2), 71–80 (2013).
[PubMed]

N. A. Rejesh, H. Pullagurla, and M. Pramanik, “Deconvolution-based deblurring of reconstructed images in photoacoustic/thermoacoustic tomography,” J. Opt. Soc. Am. A 30(10), 1994–2001 (2013).
[Crossref] [PubMed]

Y. Zhang, Y. Wang, and C. Zhang, “Efficient discrete cosine transform model-based algorithm for photoacoustic image reconstruction,” J. Biomed. Opt. 18(6), 066008 (2013).
[Crossref] [PubMed]

D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, and V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
[Crossref] [PubMed]

2012 (4)

X. Liu, D. Peng, W. Guo, X. Ma, X. Yang, and J. Tian, “Compressed Sensing Photoacoustic Imaging Based on Fast Alternating Direction Algorithm,” Int. J. Biomed. Imaging 2012, 206214 (2012).
[Crossref] [PubMed]

S. Bu, Z. Liu, T. Shiina, K. Kondo, M. Yamakawa, K. Fukutani, Y. Someda, and Y. Asao, “Model-based reconstruction integrated with fluence compensation for photoacoustic tomography,” IEEE Trans. Biomed. Eng. 59(5), 1354–1363 (2012).
[Crossref] [PubMed]

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 (2012).
[Crossref]

M. Honarvar, R. S. Sahebjavaher, S. E. Salcudean, and R. Rohling, “Sparsity regularization in dynamic elastography,” Phys. Med. Biol. 57(19), 5909–5927 (2012).
[Crossref] [PubMed]

2011 (1)

K. Wang, S. A. Ermilov, R. Su, H.-P. Brecht, A. A. Oraevsky, and M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[Crossref] [PubMed]

2010 (4)

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging. 29, 1275–1285 (2010).

Y.-S. Chen, W. Frey, S. Kim, K. Homan, P. Kruizinga, K. Sokolov, and S. Emelianov, “Enhanced thermal stability of silica-coated gold nanorods for photoacoustic imaging and image-guided therapy,” Opt. Express 18(9), 8867–8878 (2010).
[Crossref] [PubMed]

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15(2), 021311 (2010).
[Crossref] [PubMed]

B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).
[Crossref] [PubMed]

2009 (7)

B. Jafarpour, V. K. Goyal, D. B. McLaughlin, and W. T. Freeman, “Transform-domain sparsity regularization for inverse problems in geosciences,” Geophysics 74(5), R69–R83 (2009).
[Crossref]

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28, 585–594 (2009).

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

D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personal. Med. 2(4), 394 (2009).
[Crossref]

C. Li and L. V. Wang, “Photoacoustic tomography and sensing in biomedicine,” Phys. Med. Biol. 54(19), R59–R97 (2009).
[Crossref] [PubMed]

S. Ma, S. Yang, and H. Guo, “Limited-view photoacoustic imaging based on linear-array detection and filtered mean-backprojection-iterative reconstruction,” J. Appl. Phys. 106(12), 123104 (2009).
[Crossref]

S. Ma, S. Yang, and H. Guo, “Limited-view photoacoustic imaging based on linear-array detection and filtered mean-backprojection-iterative reconstruction,” J. Appl. Phys. 106(12), 123104 (2009).
[Crossref]

2007 (4)

D. W. Yang, D. Xing, S. H. Yang, and L. Z. Xiang, “Fast full-view photoacoustic imaging by combined scanning with a linear transducer array,” Opt. Express 15(23), 15566–15575 (2007).
[Crossref] [PubMed]

A. Agarwal, S. W. Huang, M. O’Donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[Crossref] [PubMed]

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23(3), 969–985 (2007).
[Crossref]

2006 (1)

E. J. Gottlieb, J. M. Cannata, C.-H. Hu, and K. K. Shung, “Development of a high-frequency (> 50 mhz) copolymer annular-array, ultrasound transducer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(5), 1037–1045 (2006).
[Crossref] [PubMed]

2005 (2)

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

D. Yang, D. Xing, H. Gu, Y. Tan, and L. Zeng, “Fast multielement phase-controlled photoacoustic imaging based on limited-field-filtered back-projection algorithm,” Appl. Phys. Lett. 87(19), 194101 (2005).
[Crossref]

2004 (3)

Y. Xu and L. V. Wang, “Time reversal and its application to tomography with diffracting sources,” Phys. Rev. Lett. 92(3), 033902 (2004).
[Crossref] [PubMed]

Y. Xu, L. V. Wang, G. Ambartsoumian, and P. Kuchment, “Reconstructions in limited-view thermoacoustic tomography,” Med. Phys. 31(4), 724–733 (2004).
[Crossref] [PubMed]

Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
[Crossref] [PubMed]

2003 (2)

K. P. Köstli and P. C. Beard, “Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response,” Appl. Opt. 42(10), 1899–1908 (2003).
[Crossref] [PubMed]

R. A. Kruger, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Thermoacoustic computed tomography using a conventional linear transducer array,” Med. Phys. 30(5), 856–860 (2003).
[Crossref] [PubMed]

1999 (1)

S.-C. Wooh and Y. Shi, “Optimum beam steering of linear phased arrays,” Wave Motion 29(3), 245–265 (1999).
[Crossref]

1995 (1)

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)--reconstruction tomography,” Med. Phys. 22(10), 1605–1609 (1995).
[Crossref] [PubMed]

1993 (1)

Y. Yang, N. P. Galatsanos, and A. K. Katsaggelos, “Regularized reconstruction to reduce blocking artifacts of block discrete cosine transform compressed images,” IEEE Trans. Circ. Syst. Video Tech. 3(6), 421–432 (1993).
[Crossref]

Agarwal, A.

A. Agarwal, S. W. Huang, M. O’Donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

Ambartsoumian, G.

Y. Xu, L. V. Wang, G. Ambartsoumian, and P. Kuchment, “Reconstructions in limited-view thermoacoustic tomography,” Med. Phys. 31(4), 724–733 (2004).
[Crossref] [PubMed]

Anastasio, M. A.

Q. Sheng, K. Wang, T. P. Matthews, J. Xia, L. Zhu, L. V. Wang, and M. A. Anastasio, “A constrained variable projection reconstruction method for photoacoustic computed tomography without accurate knowledge of transducer responses,” IEEE Trans. Med. Imaging 34(12), 2443–2458 (2015).
[Crossref] [PubMed]

K. Mitsuhashi, K. Wang, and M. A. Anastasio, “Investigation of the far-field approximation for modeling a transducer’s spatial impulse response in photoacoustic computed tomography,” Photoacoustics 2(1), 21–32 (2014).
[Crossref] [PubMed]

K. Wang, S. A. Ermilov, R. Su, H.-P. Brecht, A. A. Oraevsky, and M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
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Appledorn, C. R.

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R. A. Kruger, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Thermoacoustic computed tomography using a conventional linear transducer array,” Med. Phys. 30(5), 856–860 (2003).
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Rohling, R.

M. Honarvar, R. S. Sahebjavaher, S. E. Salcudean, and R. Rohling, “Sparsity regularization in dynamic elastography,” Phys. Med. Biol. 57(19), 5909–5927 (2012).
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E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23(3), 969–985 (2007).
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S. Tzoumas, A. Rosenthal, C. Lutzweiler, D. Razansky, and V. Ntziachristos, “Spatiospectral denoising framework for multispectral optoacoustic imaging based on sparse signal representation,” Med. Phys. 41(11), 113301 (2014).
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A. Rosenthal, D. Razansky, and V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging. 29, 1275–1285 (2010).

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M. Honarvar, R. S. Sahebjavaher, S. E. Salcudean, and R. Rohling, “Sparsity regularization in dynamic elastography,” Phys. Med. Biol. 57(19), 5909–5927 (2012).
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M. Honarvar, R. S. Sahebjavaher, S. E. Salcudean, and R. Rohling, “Sparsity regularization in dynamic elastography,” Phys. Med. Biol. 57(19), 5909–5927 (2012).
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C. Sim, H. Kim, H. Moon, H. Lee, J. H. Chang, and H. Kim, “Photoacoustic-based nanomedicine for cancer diagnosis and therapy,” J. Control. Release 203, 118–125 (2015).
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M. A. Lediju Bell, X. Guo, D. Y. Song, and E. M. Boctor, “Transurethral light delivery for prostate photoacoustic imaging,” J. Biomed. Opt. 20(3), 036002 (2015).
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H. Gao, J. Feng, and L. Song, “Limited-view multi-source quantitative photoacoustic tomography,” Inverse Probl. 31(6), 065004 (2015).
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S. Tzoumas, A. Rosenthal, C. Lutzweiler, D. Razansky, and V. Ntziachristos, “Spatiospectral denoising framework for multispectral optoacoustic imaging based on sparse signal representation,” Med. Phys. 41(11), 113301 (2014).
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Q. Sheng, K. Wang, T. P. Matthews, J. Xia, L. Zhu, L. V. Wang, and M. A. Anastasio, “A constrained variable projection reconstruction method for photoacoustic computed tomography without accurate knowledge of transducer responses,” IEEE Trans. Med. Imaging 34(12), 2443–2458 (2015).
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K. Mitsuhashi, K. Wang, and M. A. Anastasio, “Investigation of the far-field approximation for modeling a transducer’s spatial impulse response in photoacoustic computed tomography,” Photoacoustics 2(1), 21–32 (2014).
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Q. Sheng, K. Wang, T. P. Matthews, J. Xia, L. Zhu, L. V. Wang, and M. A. Anastasio, “A constrained variable projection reconstruction method for photoacoustic computed tomography without accurate knowledge of transducer responses,” IEEE Trans. Med. Imaging 34(12), 2443–2458 (2015).
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M. Cao, J. Yuan, S. Du, G. Xu, X. Wang, P. L. Carson, and X. Liu, “Full-view photoacoustic tomography using asymmetric distributed sensors optimized with compressed sensing method,” Biomed. Signal Process. Control 21, 19–25 (2015).
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Y. Zhang, Y. Wang, and C. Zhang, “Efficient discrete cosine transform model-based algorithm for photoacoustic image reconstruction,” J. Biomed. Opt. 18(6), 066008 (2013).
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S.-C. Wooh and Y. Shi, “Optimum beam steering of linear phased arrays,” Wave Motion 29(3), 245–265 (1999).
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Q. Sheng, K. Wang, T. P. Matthews, J. Xia, L. Zhu, L. V. Wang, and M. A. Anastasio, “A constrained variable projection reconstruction method for photoacoustic computed tomography without accurate knowledge of transducer responses,” IEEE Trans. Med. Imaging 34(12), 2443–2458 (2015).
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M. Cao, J. Yuan, S. Du, G. Xu, X. Wang, P. L. Carson, and X. Liu, “Full-view photoacoustic tomography using asymmetric distributed sensors optimized with compressed sensing method,” Biomed. Signal Process. Control 21, 19–25 (2015).
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M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016706 (2005).
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Y. Xu, L. V. Wang, G. Ambartsoumian, and P. Kuchment, “Reconstructions in limited-view thermoacoustic tomography,” Med. Phys. 31(4), 724–733 (2004).
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D. Yang, D. Xing, H. Gu, Y. Tan, and L. Zeng, “Fast multielement phase-controlled photoacoustic imaging based on limited-field-filtered back-projection algorithm,” Appl. Phys. Lett. 87(19), 194101 (2005).
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Yang, S.

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S. Ma, S. Yang, and H. Guo, “Limited-view photoacoustic imaging based on linear-array detection and filtered mean-backprojection-iterative reconstruction,” J. Appl. Phys. 106(12), 123104 (2009).
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Yang, X.

X. Liu, D. Peng, W. Guo, X. Ma, X. Yang, and J. Tian, “Compressed Sensing Photoacoustic Imaging Based on Fast Alternating Direction Algorithm,” Int. J. Biomed. Imaging 2012, 206214 (2012).
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Y. Yang, N. P. Galatsanos, and A. K. Katsaggelos, “Regularized reconstruction to reduce blocking artifacts of block discrete cosine transform compressed images,” IEEE Trans. Circ. Syst. Video Tech. 3(6), 421–432 (1993).
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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 (2012).
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D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personal. Med. 2(4), 394 (2009).
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J. Kang, E. K. Kim, G. R. Kim, C. Yoon, T. K. Song, and J. H. Chang, “Photoacoustic imaging of breast microcalcifications: A validation study with 3-dimensional ex vivo data and spectrophotometric measurement,” J. Biophotonics 8(1-2), 71–80 (2013).
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Yuan, J.

M. Cao, J. Yuan, S. Du, G. Xu, X. Wang, P. L. Carson, and X. Liu, “Full-view photoacoustic tomography using asymmetric distributed sensors optimized with compressed sensing method,” Biomed. Signal Process. Control 21, 19–25 (2015).
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D. Yang, D. Xing, H. Gu, Y. Tan, and L. Zeng, “Fast multielement phase-controlled photoacoustic imaging based on limited-field-filtered back-projection algorithm,” Appl. Phys. Lett. 87(19), 194101 (2005).
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Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
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Y. Zhang, Y. Wang, and C. Zhang, “Efficient discrete cosine transform model-based algorithm for photoacoustic image reconstruction,” J. Biomed. Opt. 18(6), 066008 (2013).
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D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personal. Med. 2(4), 394 (2009).
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Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. Yang, D. Xing, H. Gu, Y. Tan, and L. Zeng, “Fast multielement phase-controlled photoacoustic imaging based on limited-field-filtered back-projection algorithm,” Appl. Phys. Lett. 87(19), 194101 (2005).
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Biomed. Opt. Express (2)

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M. Cao, J. Yuan, S. Du, G. Xu, X. Wang, P. L. Carson, and X. Liu, “Full-view photoacoustic tomography using asymmetric distributed sensors optimized with compressed sensing method,” Biomed. Signal Process. Control 21, 19–25 (2015).
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J. Xia and L. V. Wang, “Small-Animal Whole-Body Photoacoustic Tomography: A Review,” IEEE Trans. Biomed. Eng. 61(5), 1380–1389 (2014).
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IEEE Trans. Circ. Syst. Video Tech. (1)

Y. Yang, N. P. Galatsanos, and A. K. Katsaggelos, “Regularized reconstruction to reduce blocking artifacts of block discrete cosine transform compressed images,” IEEE Trans. Circ. Syst. Video Tech. 3(6), 421–432 (1993).
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K. Wang, S. A. Ermilov, R. Su, H.-P. Brecht, A. A. Oraevsky, and M. A. Anastasio, “An imaging model incorporating ultrasonic transducer properties for three-dimensional optoacoustic tomography,” IEEE Trans. Med. Imaging 30(2), 203–214 (2011).
[Crossref] [PubMed]

Q. Sheng, K. Wang, T. P. Matthews, J. Xia, L. Zhu, L. V. Wang, and M. A. Anastasio, “A constrained variable projection reconstruction method for photoacoustic computed tomography without accurate knowledge of transducer responses,” IEEE Trans. Med. Imaging 34(12), 2443–2458 (2015).
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IEEE Trans. Med. Imaging. (1)

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Fast semi-analytical model-based acoustic inversion for quantitative optoacoustic tomography,” IEEE Trans. Med. Imaging. 29, 1275–1285 (2010).

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

E. J. Gottlieb, J. M. Cannata, C.-H. Hu, and K. K. Shung, “Development of a high-frequency (> 50 mhz) copolymer annular-array, ultrasound transducer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(5), 1037–1045 (2006).
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Int. J. Biomed. Imaging (1)

X. Liu, D. Peng, W. Guo, X. Ma, X. Yang, and J. Tian, “Compressed Sensing Photoacoustic Imaging Based on Fast Alternating Direction Algorithm,” Int. J. Biomed. Imaging 2012, 206214 (2012).
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Int. J. Funct. Inform. Personal. Med. (1)

D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personal. Med. 2(4), 394 (2009).
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H. Gao, J. Feng, and L. Song, “Limited-view multi-source quantitative photoacoustic tomography,” Inverse Probl. 31(6), 065004 (2015).
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S. Ma, S. Yang, and H. Guo, “Limited-view photoacoustic imaging based on linear-array detection and filtered mean-backprojection-iterative reconstruction,” J. Appl. Phys. 106(12), 123104 (2009).
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M. A. Lediju Bell, X. Guo, D. Y. Song, and E. M. Boctor, “Transurethral light delivery for prostate photoacoustic imaging,” J. Biomed. Opt. 20(3), 036002 (2015).
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D. Queirós, X. L. Déan-Ben, A. Buehler, D. Razansky, A. Rosenthal, and V. Ntziachristos, “Modeling the shape of cylindrically focused transducers in three-dimensional optoacoustic tomography,” J. Biomed. Opt. 18(7), 076014 (2013).
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B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010).
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Y. Zhang, Y. Wang, and C. Zhang, “Efficient discrete cosine transform model-based algorithm for photoacoustic image reconstruction,” J. Biomed. Opt. 18(6), 066008 (2013).
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J. Kang, E. K. Kim, G. R. Kim, C. Yoon, T. K. Song, and J. H. Chang, “Photoacoustic imaging of breast microcalcifications: A validation study with 3-dimensional ex vivo data and spectrophotometric measurement,” J. Biophotonics 8(1-2), 71–80 (2013).
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C. Sim, H. Kim, H. Moon, H. Lee, J. H. Chang, and H. Kim, “Photoacoustic-based nanomedicine for cancer diagnosis and therapy,” J. Control. Release 203, 118–125 (2015).
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S. Tzoumas, A. Rosenthal, C. Lutzweiler, D. Razansky, and V. Ntziachristos, “Spatiospectral denoising framework for multispectral optoacoustic imaging based on sparse signal representation,” Med. Phys. 41(11), 113301 (2014).
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Opt. Express (3)

Photoacoustics (1)

K. Mitsuhashi, K. Wang, and M. A. Anastasio, “Investigation of the far-field approximation for modeling a transducer’s spatial impulse response in photoacoustic computed tomography,” Photoacoustics 2(1), 21–32 (2014).
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C. Li and L. V. Wang, “Photoacoustic tomography and sensing in biomedicine,” Phys. Med. Biol. 54(19), R59–R97 (2009).
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M. Honarvar, R. S. Sahebjavaher, S. E. Salcudean, and R. Rohling, “Sparsity regularization in dynamic elastography,” Phys. Med. Biol. 57(19), 5909–5927 (2012).
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Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1), 016706 (2005).
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Phys. Rev. Lett. (1)

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Figures (13)

Fig. 1
Fig. 1 Equation (2) enables us to compute the pressure at the transducer location.
Fig. 2
Fig. 2 Element i receives the signal from a considerable region of the medium but with different directivity effect. Sampled points are shown with red cross signs. They are equally distanced. Also one sampled point with the surrounding nodes can be seen.
Fig. 3
Fig. 3 (a) Experimental set up for PAT, a close-up of the probe and the rotary stage was shown at the upper left corner (b) The structure of the DPARS algorithm.
Fig. 4
Fig. 4 Weighting function used for FDPARS in 1-D case.
Fig. 5
Fig. 5 (a) The experimental setup for transducer calibration. A point source was located at different positions in the elevational (y) and axial (x) directions. The maximum intensity detected by the transducer with respect to the location of the point source along the elevation and lateral directions are shown in (b) and (d); (c) and (e) show the calibration results in which the intensities were normalized with the maximum intensities recorded in the same depth
Fig. 6
Fig. 6 The US transducer receives a signal when the object is located outside of its imaging (center) plane. As mentioned in Fig. 5(a), y represents the deviation of the point source from the main plane of the US transducer. The DAS method was used for reconstruction the recorded data when the point source was at (a) the depth 33 mm and 14 mm out of plane (b) the depth 37 mm and 6 mm out of plane (c) the depth 78 mm and 14 mm out of plane.
Fig. 7
Fig. 7 Simulation results for 2-D PAT. (a) shows the absorber and the scanning geometry. The red arrows show the main directions of the sensors as shown clearly in the close-up photo at the upper right corner. PA data were collected at three positions in 60° increments. (b) Measured transducer element sensitivity with respect to the angle of the incident acoustic wave. (c) Actual absorber distribution, and reconstructions with (d) DPARS, (e) FDPARS, and (f) DAS.
Fig. 8
Fig. 8 Simulation for circular 2-D PAT. (a) Absorber and scanning geometry. The red arrows show the main directions of the sensors that are perpendicular to the detection surface as shown at the lower right corner in the close-up photo. The PA data were collected through 60° in steps of 1°. (b) Sensitivity of the sensor with respect to angle of PA point source. (c) Initial distribution of the absorber and the actual image that should be reconstructed. Results for PAT reconstruction: (d) DPARS, in case the sensors have omni-directional response, (e) DPARS, (f) FDPARS, (g) Tikhonov regularization, and (h) DAS.
Fig. 9
Fig. 9 White Gaussian noise was added to data. (a) DPARS, (b) FDPARS, (c) Tikhonov regularization, and (d) DAS reconstruction results with noisy data
Fig. 10
Fig. 10 RMS error and CNR versus regularization parameters for the DPARS method for noisy, and noiseless data. (a) and (b) show the sparsity regularization results and, (c) and (d) show those of Tikhonov regularization.
Fig. 11
Fig. 11 Results for 2-D PAT. (a) PA data were collected at 3 positions around the sample, (b) the sample which was printed on paper, and kept in the US plane of the transducer. Reconstructed images with: (c) DPARS, (d) FDPARS, (e) without any regularization, and (f) DAS.
Fig. 12
Fig. 12 Experimental set-up and results for 3-D PAT. (a) shows the absorber. The PA data were collected through 140° with a step size of 2°. (b) shows the sample with respect to the transducer. DPARS (c) and DAS (d) were used for the image reconstructions. The Z direction is parallel to the rotation axis and the lateral direction of the transducer.
Fig. 13
Fig. 13 Cross-sections of 3-D DPARS, FDPARS, and DAS images in different vales of Z. Z axis is parallel to the rotational axis

Tables (2)

Tables Icon

Table 1 CNR and RMS error of the results of DAS, DPARS and FDPARS methods for simulated 2-D PAT

Tables Icon

Table 2 CNR and RMS errors of DAS, DPARS and FDPARS methods for experimental 2-D and 3-D PAT

Equations (28)

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( 2 1 c 2 2 t 2 )p( r, t )=  p 0 ( r ) dI(t) dt
p( r i , t )= p i ( t )= β 4π C p dr | r r i |  A( r ) dI( t ' ) d t '
p i ( t )= βk 4π C p  ( 1 t   | r r i |=ct A( r )dS )* p p 0 (t)
p d i ( t )= βk 4π C p  ( 1 t   | r r i |=ct A( r )dS )* p d0 ( t )
| r r i |=ct A( r )dS= 4π C p t βk  IFT( p d i` ( ω ) w(ω) p ` d0 (ω)   )
R i ( t )= | r r i |=ct A( r )dS
R i ( t )= | r r i |=ct A( r )  D i ( r ) dS
R i ( t m )= γ S i (c t m ) A γ   D γ i  ΔS, m=1, 2, , M  i  =1, 2, , N 
A γ = j N s (γ) a j   A ^ γ j
a 1 =1 δ l 1  δ l 2 + δ l 1  δ l 2
a 2 =δ l 2  δ l 1  δ l 2
a 3 = δ l 1  δ l 1  δ l 2
a 4 =δ l 1  δ l 2
R i ( t m )=  γ S i (c t m ) j N s (γ) Δ S  D γ i   a j   A ^ γ j  
{ R } NM×1 = [ F ] NM× N p   { A } N p ×1
f ˜ (u)= n d =0 N d 1 f( n d )cos[ π N d ( n d + 1 2 )u ] u=0, ,  N d 1
{ A ˜ } N p ×1 = [ T 1 ] N p × N p   { A ^ } N p ×1
{ A } N p ×1 = [T] N p × N p   { A ˜ } N p ×1
{ A } N p ×1 [ T tr ] N p × N p' { A ˜ tr } N p' ×1
{ R } NM×1 =  [ F ] NM× N p   [ T tr ] N p × N p' { A ˜ tr } N p' ×1
{ A } N p ×1 [ T tr ] N p × N p' [W] N p' × N p' { A ˜ tr } N p' ×1
{ R } NM×1 =  [ F ] NM× N p   [ T tr ] N p × N p' [W] N p' × N p' { A ˜ tr } N p' ×1
[ F T ] N p ×NM { R } NM×1 =( [ F T ] N p ×NM [ F ] NM× N p +λ [ I ] N p × N p )  { A ^ } N p ×1
e r = αA  A 0 2
d e r dα = 0
α=  A T A 0 A T A
RMS= ( i=1 N p ( A i   A i 0 ) 2 / N p ) 0.5
CNR= (2 ( m i m b ) 2 /( σ i 2 +  σ b 2 )) 0.5

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