Evaluation of Adjoint Methods in Photoacoustic Tomography with Under-Sampled Sensors

  • Hongxiang LinEmail author
  • Takashi Azuma
  • Mehmet Burcin Unlu
  • Shu Takagi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11070)


Photo-Acoustic Tomography (PAT) can reconstruct a distribution of optical absorbers acting as instantaneous sound sources in subcutaneous microvasculature of a human breast. Adjoint methods for PAT, typically Time-Reversal (TR) and Back-Projection (BP), are ways to refocus time-reversed acoustic signals on sources by wave propagation from the position of sensors. TR and BP have different treatments for received signals, but they are equivalent under continuously sampling on a closed circular sensor array in two dimensions. Here, we analyze image quality with discrete under-sampled sensors in the sense of the Shannon sampling theorem. We investigate resolution and contrast of TR and BP, respectively in one source-sensor pair configuration and the frequency domain. With Hankel’s asymptotic expansion to the integrands of imaging functions, our main contribution is to demonstrate that TR and BP have better performance on contrast and resolution, respectively. We also show that the integrand of TR includes additional side lobes which degrade axial resolution whereas that of BP conversely has relatively small amplitudes. Moreover, omnidirectional resolution is improved if more sensors are employed to collect the received signals. Nevertheless, for the under-sampled sensors, we propose the Truncated Back-Projection (TBP) method to enhance the contrast of BP using removing higher frequency components in the received signals. We conduct numerical experiments on the two-dimensional projected phantom model extracted from OA-Breast Database. The experiments verify our theories and show that the proposed TBP possesses better omnidirectional resolution as well as contrast compared with TR and BP with under-sampled sensors.


Photoacoustic tomography Adjoint method Time-reversal Back-projection Hankel asymptotic expansion Resolution Contrast 

Supplementary material

473972_1_En_9_MOESM1_ESM.pdf (392 kb)
Supplementary material 1 (pdf 391 KB)


  1. 1.
    Antholzer, S., Haltmeier, M., Schwab, J.: Deep learning for photoacoustic tomography from sparse data. arXiv:1704.04587 (2017)
  2. 2.
    Ammari, H., Bretin, E., Garnier, J., Wahab, A.: Time reversal in attenuating acoustic media. Contemp. Math. 548, 151–163 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Arridge, S.R., Betcke, M.M., Cox, B.T., Lucka, F., Treeby, B.E.: On the adjoint operator in photoacoustic tomography. Inverse Prob. 32(11), 115012 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Haltmeier, M.: Sampling conditions for the circular radon transform. IEEE Trans. Image Process. 25(6), 2910–2919 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, New York (1965)zbMATHGoogle Scholar
  6. 6.
    Treeby, B.E., Cox, B.T.: k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields. J. Biomed. Opt. 15(2), 021314 (2010)CrossRefGoogle Scholar
  7. 7.
    Lou, Y., Zhou, W., Matthews, T.P., Appleton, C.M., Anastasio, M.A.: Generation of anatomically realistic numerical phantoms for photoacoustic and ultrasonic breast imaging. J. Biomed. Opt. 22(4), 041015 (2017)CrossRefGoogle Scholar
  8. 8.
    Borcea, L., Papanicolaou, G., Tsogka, C.: Theory and applications of time reversal and interferometric imaging. Inverse Prob. 19(6), S139 (2003)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Hongxiang Lin
    • 1
    Email author
  • Takashi Azuma
    • 2
  • Mehmet Burcin Unlu
    • 3
    • 4
    • 5
  • Shu Takagi
    • 1
  1. 1.Department of Mechanical EngineeringThe University of TokyoTokyoJapan
  2. 2.Center for Disease Biology and Integrative MedicineThe University of TokyoTokyoJapan
  3. 3.Department of PhysicsBogazici UniversityIstanbulTurkey
  4. 4.Global Station for Quantum Medical Science and Engineering, Global Institution for Collaborative Research and EducationHokkaido UniversitySapporoJapan
  5. 5.Department of Radiation OncologyStanford University School of MedicineStanfordUSA

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