Efficient inversion of multiple-scattering model for optical diffraction tomography

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their applicability to thin samples with low refractive-index contrasts. More recent works have shown the benefit of adopting nonlinear models. They account for multiple scattering and reflections, improving the quality of reconstruction. To reduce the complexity and memory requirements of these methods, we derive an explicit formula for the Jacobian matrix of the nonlinear Lippmann-Schwinger model which lends itself to an efficient evaluation of the gradient of the data-fidelity term. This allows us to deploy efficient methods to solve the corresponding inverse problem subject to sparsity constraints. © 2017 Optical Society of America OCIS codes: (180.1655) Coherence tomography; (180.3170) Interference microscopy; (100.3010) Image reconstruction techniques. References and links 1. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969). 2. D. Jin, R. Zhou, Z. Yaqoob, and P. T. So, “Tomographic phase microscopy: Principles and applications in bioimaging,” J. Opt. Soc. Am. B 34, B64–B77 (2017). 3. A. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6, 374–376 (1981). 4. E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method,” Inverse Probl. 28, 065007 (2012). 5. U. S. Kamilov, D. Liu, H. Mansour, and P. T. Boufounos, “A recursive Born approach to nonlinear inverse scattering,” IEEE Signal Process. Lett. 23, 1052–1056 (2016). 6. H. -Y. Liu, U. S. Kamilov, D. Liu, H. Mansour, and P. T. Boufounos, “Compressive imaging with iterative forward models,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2017), pp. 6025–6029. 7. H. -Y. Liu, D. Liu, H. Mansour, P. T. Boufounos, L. Waller, and U. S. Kamilov, “SEAGLE: Sparsity-driven image reconstruction under multiple scattering,” arXiv preprint arXiv:1705.04281 (2017). 8. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, vol. 93 (Springer Science & Business Media, 2012). 9. J. A. Schmalz, G. Schmalz, T. E. Gureyev, and K. M. Pavlov, “On the derivation of the Green’s function for the Helmholtz equation using generalized functions,” Am. J. Phys. 78, 181–186 (2010). 10. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001). 11. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717 (2007). 12. B. Chen and J. J. Stamnes, “Validity of diffraction tomography based on the first Born and the first Rytov approximations,” Appl. Opt. 37, 2996–3006 (1998). 13. Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009). 14. Y. Sung and R. R. Dasari, “Deterministic regularization of three-dimensional optical diffraction tomography,” J. Opt. Soc. Am. A 28, 1554–1561 (2011). 15. J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. C. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Opt. Express 23, 16933–16948 (2015). 16. P. C. Chaumet and K. Belkebir, “Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method,” Inverse Probl. 25, 024003 (2009). #302238 https://doi.org/10.1364/OE.25. 021786 Journal © 2017 Received 11 Jul 2017; revised 23 Aug 2017; accepted 23 Aug 2017; published 29 Aug 2017 Vol. 25, No. 18 | 4 Sep 2017 | OPTICS EXPRESS 21786