Abstract

A recently introduced nonlinear $p$th root delay-and-sum (${\text{NL-}} p {\text{-DAS}}$) beamforming (BF) technique for ultrasound (US) and photoacoustic (PA) imaging, achieving better spatial and contrast resolution compared to a conventional delay and sum (DAS) technique. While the method is advantageous for better resolution, it suffers from grainy speckles and dark areas in the image mainly due to the interference of non-sinusoidal functions. In this Letter, we introduce a modified ${\text{NL-}} p {\text{-DAS}}$ technique called nonlinear $p$th root spectral magnitude scaling (${\text{NL-}} p {\text{-SMS}}$), which performs the $p$th root on the spectral magnitude instead of the temporal amplitude. We evaluated the US and PA images of ${\text{NL-}} p {\text{-SMS}}$ against those of ${\text{NL-}} p {\text{-DAS}}$ by comparing the axial and lateral line profiles, contrasts, and contrast-to-noise ratios (CNRs) in both phantom and in vivo imaging studies with various $p$ values. As a result, we found that the ${\text{NL-}} p {\text{-SMS}}$ has better axial resolution and CNR than the ${\text{NL-}} p {\text{-DAS}}$, and reduces the grainy speckles and dark area artifacts. We believe that, with this enhanced performance, our proposed approach could be an advancement compared to the existing nonlinear BF algorithms.

© 2020 Optical Society of America

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  1. W. Choi, E.-Y. Park, S. Jeon, and C. Kim, Biomed. Eng. Lett. 8, 139 (2018).
    [Crossref]
  2. J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
    [Crossref]
  3. J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
    [Crossref]
  4. G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, IEEE Trans. Med. Imaging 34, 940 (2015).
    [Crossref]
  5. M. Mozaffarzadeh, Y. Yan, M. Mehrmohammadi, and B. Makkiabadi, J. Biomed. Opt. 23, 026005 (2018).
    [Crossref]
  6. S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
    [Crossref]
  7. J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
    [Crossref]
  8. M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, IEEE Trans. Biomed. Eng. 65, 31 (2017).
    [Crossref]
  9. M. Polichetti, F. Varray, J.-C. Béra, C. Cachard, and B. Nicolas, Appl. Sci. 8, 599 (2018).
    [Crossref]
  10. M. Mozaffarzadeh, V. Periyasamy, M. Pramanik, and B. Makkiabadi, J. Biomed. Opt. 23, 121604 (2018).
    [Crossref]
  11. C.-C. Shen and P.-Y. Hsieh, Ultrasonics 96, 165 (2019).
    [Crossref]
  12. F. Prieur, O. M. H. Rindal, and A. Austeng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1133 (2018).
    [Crossref]
  13. J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
    [Crossref]
  14. J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
    [Crossref]
  15. C. Kim, C. Favazza, and L. V. Wang, Chem. Rev. 110, 2756 (2010).
    [Crossref]
  16. E. Merčep, X. L. Deán-Ben, and D. Razansky, IEEE Trans. Med. Imaging 36, 2129 (2017).
    [Crossref]
  17. E. Merčep, J. L. Herraiz, X. L. Deán-Ben, and D. Razansky, Light Sci. Appl. 8, 1 (2019).
    [Crossref]

2020 (1)

J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
[Crossref]

2019 (5)

C.-C. Shen and P.-Y. Hsieh, Ultrasonics 96, 165 (2019).
[Crossref]

E. Merčep, J. L. Herraiz, X. L. Deán-Ben, and D. Razansky, Light Sci. Appl. 8, 1 (2019).
[Crossref]

J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
[Crossref]

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
[Crossref]

2018 (5)

M. Polichetti, F. Varray, J.-C. Béra, C. Cachard, and B. Nicolas, Appl. Sci. 8, 599 (2018).
[Crossref]

M. Mozaffarzadeh, V. Periyasamy, M. Pramanik, and B. Makkiabadi, J. Biomed. Opt. 23, 121604 (2018).
[Crossref]

W. Choi, E.-Y. Park, S. Jeon, and C. Kim, Biomed. Eng. Lett. 8, 139 (2018).
[Crossref]

M. Mozaffarzadeh, Y. Yan, M. Mehrmohammadi, and B. Makkiabadi, J. Biomed. Opt. 23, 026005 (2018).
[Crossref]

F. Prieur, O. M. H. Rindal, and A. Austeng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1133 (2018).
[Crossref]

2017 (2)

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, IEEE Trans. Biomed. Eng. 65, 31 (2017).
[Crossref]

E. Merčep, X. L. Deán-Ben, and D. Razansky, IEEE Trans. Med. Imaging 36, 2129 (2017).
[Crossref]

2016 (2)

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
[Crossref]

2015 (1)

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, IEEE Trans. Med. Imaging 34, 940 (2015).
[Crossref]

2010 (1)

C. Kim, C. Favazza, and L. V. Wang, Chem. Rev. 110, 2756 (2010).
[Crossref]

Adabi, S.

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, IEEE Trans. Biomed. Eng. 65, 31 (2017).
[Crossref]

Austeng, A.

F. Prieur, O. M. H. Rindal, and A. Austeng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1133 (2018).
[Crossref]

Baik, J. W.

J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
[Crossref]

Béra, J.-C.

M. Polichetti, F. Varray, J.-C. Béra, C. Cachard, and B. Nicolas, Appl. Sci. 8, 599 (2018).
[Crossref]

Cachard, C.

M. Polichetti, F. Varray, J.-C. Béra, C. Cachard, and B. Nicolas, Appl. Sci. 8, 599 (2018).
[Crossref]

Caliano, G.

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, IEEE Trans. Med. Imaging 34, 940 (2015).
[Crossref]

Chang, S.

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

Cho, S. H.

J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
[Crossref]

Choi, W.

J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
[Crossref]

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
[Crossref]

W. Choi, E.-Y. Park, S. Jeon, and C. Kim, Biomed. Eng. Lett. 8, 139 (2018).
[Crossref]

Deán-Ben, X. L.

E. Merčep, J. L. Herraiz, X. L. Deán-Ben, and D. Razansky, Light Sci. Appl. 8, 1 (2019).
[Crossref]

E. Merčep, X. L. Deán-Ben, and D. Razansky, IEEE Trans. Med. Imaging 36, 2129 (2017).
[Crossref]

Favazza, C.

C. Kim, C. Favazza, and L. V. Wang, Chem. Rev. 110, 2756 (2010).
[Crossref]

Herraiz, J. L.

E. Merčep, J. L. Herraiz, X. L. Deán-Ben, and D. Razansky, Light Sci. Appl. 8, 1 (2019).
[Crossref]

Hsieh, P.-Y.

C.-C. Shen and P.-Y. Hsieh, Ultrasonics 96, 165 (2019).
[Crossref]

Jeon, S.

S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
[Crossref]

J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
[Crossref]

W. Choi, E.-Y. Park, S. Jeon, and C. Kim, Biomed. Eng. Lett. 8, 139 (2018).
[Crossref]

J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
[Crossref]

Jung, Y.

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

Kang, Y.

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

Kim, C.

J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
[Crossref]

J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
[Crossref]

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
[Crossref]

W. Choi, E.-Y. Park, S. Jeon, and C. Kim, Biomed. Eng. Lett. 8, 139 (2018).
[Crossref]

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
[Crossref]

C. Kim, C. Favazza, and L. V. Wang, Chem. Rev. 110, 2756 (2010).
[Crossref]

Kim, H. H.

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

Kim, J.

J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
[Crossref]

J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
[Crossref]

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

Kim, J. Y.

J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
[Crossref]

Kim, W. J.

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

Lee, J. S.

J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
[Crossref]

Lee, K. J.

J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
[Crossref]

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
[Crossref]

Lovell, J. F.

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

Magenes, G.

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, IEEE Trans. Med. Imaging 34, 940 (2015).
[Crossref]

Mahloojifar, A.

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, IEEE Trans. Biomed. Eng. 65, 31 (2017).
[Crossref]

Makkiabadi, B.

M. Mozaffarzadeh, V. Periyasamy, M. Pramanik, and B. Makkiabadi, J. Biomed. Opt. 23, 121604 (2018).
[Crossref]

M. Mozaffarzadeh, Y. Yan, M. Mehrmohammadi, and B. Makkiabadi, J. Biomed. Opt. 23, 026005 (2018).
[Crossref]

Managuli, R.

S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
[Crossref]

Matrone, G.

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, IEEE Trans. Med. Imaging 34, 940 (2015).
[Crossref]

Mehrmohammadi, M.

M. Mozaffarzadeh, Y. Yan, M. Mehrmohammadi, and B. Makkiabadi, J. Biomed. Opt. 23, 026005 (2018).
[Crossref]

Meng, J.

J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
[Crossref]

Mercep, E.

E. Merčep, J. L. Herraiz, X. L. Deán-Ben, and D. Razansky, Light Sci. Appl. 8, 1 (2019).
[Crossref]

E. Merčep, X. L. Deán-Ben, and D. Razansky, IEEE Trans. Med. Imaging 36, 2129 (2017).
[Crossref]

Mozaffarzadeh, M.

M. Mozaffarzadeh, V. Periyasamy, M. Pramanik, and B. Makkiabadi, J. Biomed. Opt. 23, 121604 (2018).
[Crossref]

M. Mozaffarzadeh, Y. Yan, M. Mehrmohammadi, and B. Makkiabadi, J. Biomed. Opt. 23, 026005 (2018).
[Crossref]

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, IEEE Trans. Biomed. Eng. 65, 31 (2017).
[Crossref]

Nasiriavanaki, M.

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, IEEE Trans. Biomed. Eng. 65, 31 (2017).
[Crossref]

Nicolas, B.

M. Polichetti, F. Varray, J.-C. Béra, C. Cachard, and B. Nicolas, Appl. Sci. 8, 599 (2018).
[Crossref]

Orooji, M.

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, IEEE Trans. Biomed. Eng. 65, 31 (2017).
[Crossref]

Park, B.

J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
[Crossref]

Park, E.-Y.

J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
[Crossref]

S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
[Crossref]

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

W. Choi, E.-Y. Park, S. Jeon, and C. Kim, Biomed. Eng. Lett. 8, 139 (2018).
[Crossref]

Park, J.

J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
[Crossref]

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

Park, S.

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

Periyasamy, V.

M. Mozaffarzadeh, V. Periyasamy, M. Pramanik, and B. Makkiabadi, J. Biomed. Opt. 23, 121604 (2018).
[Crossref]

Polichetti, M.

M. Polichetti, F. Varray, J.-C. Béra, C. Cachard, and B. Nicolas, Appl. Sci. 8, 599 (2018).
[Crossref]

Pramanik, M.

M. Mozaffarzadeh, V. Periyasamy, M. Pramanik, and B. Makkiabadi, J. Biomed. Opt. 23, 121604 (2018).
[Crossref]

Prieur, F.

F. Prieur, O. M. H. Rindal, and A. Austeng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1133 (2018).
[Crossref]

Razansky, D.

E. Merčep, J. L. Herraiz, X. L. Deán-Ben, and D. Razansky, Light Sci. Appl. 8, 1 (2019).
[Crossref]

E. Merčep, X. L. Deán-Ben, and D. Razansky, IEEE Trans. Med. Imaging 36, 2129 (2017).
[Crossref]

Rindal, O. M. H.

F. Prieur, O. M. H. Rindal, and A. Austeng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1133 (2018).
[Crossref]

Savoia, A. S.

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, IEEE Trans. Med. Imaging 34, 940 (2015).
[Crossref]

Shen, C.-C.

C.-C. Shen and P.-Y. Hsieh, Ultrasonics 96, 165 (2019).
[Crossref]

Song, L.

J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
[Crossref]

Varray, F.

M. Polichetti, F. Varray, J.-C. Béra, C. Cachard, and B. Nicolas, Appl. Sci. 8, 599 (2018).
[Crossref]

Wang, L. V.

C. Kim, C. Favazza, and L. V. Wang, Chem. Rev. 110, 2756 (2010).
[Crossref]

Yan, Y.

M. Mozaffarzadeh, Y. Yan, M. Mehrmohammadi, and B. Makkiabadi, J. Biomed. Opt. 23, 026005 (2018).
[Crossref]

Zhang, Y.

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

Appl. Sci. (1)

M. Polichetti, F. Varray, J.-C. Béra, C. Cachard, and B. Nicolas, Appl. Sci. 8, 599 (2018).
[Crossref]

Biomed. Eng. Lett. (1)

W. Choi, E.-Y. Park, S. Jeon, and C. Kim, Biomed. Eng. Lett. 8, 139 (2018).
[Crossref]

Chem. Rev. (1)

C. Kim, C. Favazza, and L. V. Wang, Chem. Rev. 110, 2756 (2010).
[Crossref]

Exp. Biol. Med. (1)

J. Kim, E.-Y. Park, B. Park, W. Choi, K. J. Lee, and C. Kim, Exp. Biol. Med. 245, 321 (2020).
[Crossref]

IEEE Trans. Biomed. Eng. (2)

M. Mozaffarzadeh, A. Mahloojifar, M. Orooji, S. Adabi, and M. Nasiriavanaki, IEEE Trans. Biomed. Eng. 65, 31 (2017).
[Crossref]

J. Kim, W. Choi, E.-Y. Park, Y. Kang, K. J. Lee, H. H. Kim, W. J. Kim, and C. Kim, IEEE Trans. Biomed. Eng. 66, 3330 (2019).
[Crossref]

IEEE Trans. Med. Imaging (2)

G. Matrone, A. S. Savoia, G. Caliano, and G. Magenes, IEEE Trans. Med. Imaging 34, 940 (2015).
[Crossref]

E. Merčep, X. L. Deán-Ben, and D. Razansky, IEEE Trans. Med. Imaging 36, 2129 (2017).
[Crossref]

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

F. Prieur, O. M. H. Rindal, and A. Austeng, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1133 (2018).
[Crossref]

J. Biomed. Opt. (3)

M. Mozaffarzadeh, V. Periyasamy, M. Pramanik, and B. Makkiabadi, J. Biomed. Opt. 23, 121604 (2018).
[Crossref]

M. Mozaffarzadeh, Y. Yan, M. Mehrmohammadi, and B. Makkiabadi, J. Biomed. Opt. 23, 026005 (2018).
[Crossref]

J. Park, S. Jeon, J. Meng, L. Song, J. S. Lee, and C. Kim, J. Biomed. Opt. 21, 036010 (2016).
[Crossref]

Light Sci. Appl. (2)

J. Kim, J. Y. Kim, S. Jeon, J. W. Baik, S. H. Cho, and C. Kim, Light Sci. Appl. 8, 103 (2019).
[Crossref]

E. Merčep, J. L. Herraiz, X. L. Deán-Ben, and D. Razansky, Light Sci. Appl. 8, 1 (2019).
[Crossref]

Photoacoustics (1)

S. Jeon, E.-Y. Park, W. Choi, R. Managuli, K. J. Lee, and C. Kim, Photoacoustics 15, 100136 (2019).
[Crossref]

Sci. Rep. (1)

J. Kim, S. Park, Y. Jung, S. Chang, J. Park, Y. Zhang, J. F. Lovell, and C. Kim, Sci. Rep. 6, 35137 (2016).
[Crossref]

Ultrasonics (1)

C.-C. Shen and P.-Y. Hsieh, Ultrasonics 96, 165 (2019).
[Crossref]

Supplementary Material (6)

NameDescription
» Visualization 1       (a) Signal histograms of representative US images processed with the NL-p-DAS for various p values. Fixed dynamic ranges, independent of p, were applied in the conventional methods. (b),(c) Representative US (b) and PA (c) signal histograms.
» Visualization 2       Comparison of the PA and US images beamformed with the NL-p-SMS using STFT with various window sizes and FFT.
» Visualization 3       Comparison of computational complexities of NL-p-DAS (a) and NL-p-SMS (b).
» Visualization 4       (a) NL-p-DAS (top) and NL-p-SMS (bottom) US images of a hyperechoic phantom. (b) Line profiles extracted along the white dotted line in (a).
» Visualization 5       Simulated PA images of three targets with a diameter of 4 mm reconstructed with DAS, NL-p-DAS, and NL-p-SMS. The center frequency of the simulated transducer is 8.5 MHz with a fractional bandwidth of 75%.
» Visualization 6       (a) US images of a human thyroid in vivo NL-p-DAS (top) and NL-p-SMS (bottom) for various p values. (b) Enlarged images in the area highlighted with a red dashed box in (a). (c) Axial line profiles extracted from the dashed line in (b).

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Figures (4)

Fig. 1.
Fig. 1. Overall receiving BF processes of (a) DAS, (b) ${\text{NL-}} p {\text{-DAS}}$, and (c) ${\text{NL-}} p {\text{-SMS}}$. A time delay has been applied to perform focusing after receiving the signal. The $p$th root scaling was applied before adding the signals in both ${\text{NL-}} p {\text{-DAS}}$ and ${\text{NL-}} p {\text{-SMS}}$. After synthesizing the received signals, we gave a power of $p$ to compensate for the downscaled signal magnitude. From the left, it shows the RF preprocess, projection process, and reconstructed line profile of each BF method.
Fig. 2.
Fig. 2. (a) ${\text{NL-}} p {\text{-DAS}}$ (top) and ${\text{NL-}} p {\text{-SMS}}$ (bottom) US images of a hypoechoic cyst phantom for the various $p$. (b) Normalized Michelson contrast (left) and CNR (right) in (a).
Fig. 3.
Fig. 3. Comparisons of PA lateral and axial resolutions. (a) B-mode PA images and (b) corresponding line profiles of two nylon threads adjacent to each other laterally. (c) B-mode PA images and (d) corresponding line profiles of two nylon threads adjacent to each other axially.
Fig. 4.
Fig. 4. In vivo (a) US and (b) PA images of a human thyroid and forearm, respectively. The images are reconstructed by DAS, ${\text{NL-}} p {\text{-DAS}}$ ($p = {{3}}$), and ${\text{NL-}} p {\text{-SMS}}$ ($p = {{3}}$). ${{N}}$. STD, the normalized standard deviation, is defined as the standard deviation of the enlarged speckle area divided by that of the speckle area in the DAS image.

Equations (8)

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y D A S = i = 1 N s i ( t t i ) ,
y N L p D A S = ( i = 1 N s N L p D A S , i ( t t i ) ) p ,
s i ( t ) = k = 1 n p i , k [ E n v ( t t i , k ) cos ( ω 0 ( t t i , k ) + ϕ ) ] ,
s N L p D A S , i ( t ) = k = 1 n { p i , k p [ E n v ( t t i , k ) p sign ( ψ i , k ) | ψ i , k | p ] } ,
s N L p S M S , i ( t ) = { F F T 1 ( | F F T ( s i ( t ) ) | p e j F F T ( s i ( t ) ) ) for US BF S T F T 1 ( | S T F T ( s i ( t ) ) | p e j S T F T ( s i ( t ) ) ) for PA BF .
y N L p S M S = ( D ( i = 1 N s N L p S M S , i ( t t i ) ) ) p ,
C = | μ c y s t μ b a c k | / | μ c y s t μ b a c k | ( μ c y s t + μ b a c k ) ( μ c y s t + μ b a c k ) ,
C N R = | μ c y s t μ b a c k | / | μ c y s t μ b a c k | σ c y s t 2 + σ b a c k 2 σ c y s t 2 + σ b a c k 2 .

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