Optical diffraction tomography within a variational Bayesian framework

References

• Arridge, SR, 1999. Optical tomography in medical imaging, Inverse Probl. 15 (1999), pp. R41–R93.
   Web of Science ®Google Scholar
• Schatzberg, A, and Devaney, AJ, 1992. Super-resolution in diffraction tomography, Inverse Probl. 8 (1992), pp. 149–164.
   Web of Science ®Google Scholar
• Debailleul, M, Simon, B, Georges, V, Haeberlé, O, and Lauer, V, 2008. Holographic microscopy and diffractive microtomography of transparent samples, Meas. Sci. Technol. 19 (2008), Article ID: 074009. Available at http://iopscience.iop.org/0957-0233/19/7/074009/.
   Web of Science ®Google Scholar
• Simon, B, Debailleul, M, Georges, V, Lauer, V, and Haeberlé, O, 2008. Tomographic diffractive microscopy of transparent samples, Eur. Phys. J. Appl. Phys. 44 (2008), pp. 29–35.
   Web of Science ®Google Scholar
• Azimi, M, and Kak, A, , Distorsion in diffraction tomography caused by multiple scattering, IEEE Trans. Med. Imaging MI-2 (1983), pp. 176–195.
   Google Scholar
• Slaney, M, Kak, A, and Larsen, L, , Limitations of imaging with first-order diffraction tomography, IEEE Trans. Microwave Theory Tech. MTT-32 (1984), pp. 860–874.
   Google Scholar
• Belkebir, K, and Sentenac, A, 2003. High-resolution optical diffraction microscopy, J. Opt. Soc. Am. A 20 (2003), pp. 1223–1229.
   Google Scholar
• Lauer, V, 2002. New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope, J. Microsc. 205 (2002), pp. 165–176.
   PubMed Web of Science ®Google Scholar
• Idier, J, 2001. Approche Bayésienne pour les Problèmes Inverses. Paris: Hermès; 2001.
   Google Scholar
• Tierney, L, 1994. Markov chain for exploring posterior distribution, Ann. Stat. 22 (1994), pp. 1701–1762.
   Web of Science ®Google Scholar
• Pieczynski, W, 2003. Modèles de Markov en traitement d'images, Traitement du Signal 20 (2003), pp. 255–278.
   Google Scholar
• Féron, O, and Mohammad-Djafari, A, 2002. Image fusion and joint segmentation using an MCMC algorithm, J. Electron. Imaging 14 (2002), pp. 1–12, ID: 023014.
   Google Scholar
• Féron, O, Duchêne, B, and Mohammad-Djafari, A, 2005. Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data, Inverse Probl. 21 (2005), pp. S95–S115.
   Web of Science ®Google Scholar
• Ayasso, H, Duchêne, B, and Mohammad-Djafari, A, 2010. Bayesian inversion for optical diffraction tomography, J. Modern Opt. (special issue on Digital Optical Microscopy) 57 (2010), pp. 765–776.
   Google Scholar
• Geman, S, and Geman, D, , Stochastic relaxation, Gibbs distribution and the Bayesian restoration of image, IEEE Trans. Pattern Anal. Mach. Int. PAMI-6 (1984), pp. 721–41.
   Google Scholar
• Tierney, L, and Kadane, JB, 1986. Accurate approximations for posterior moments and marginal densities, J. Am. Stat. Ass. 81 (1986), pp. 82–86.
   Web of Science ®Google Scholar
• Robert, C, and Casella, G, 2004. Monte Carlo Statistical Methods. New York: Springer Verlag; 2004.
   Google Scholar
• Smídl, V, and Quinn, A, 2006. The Variational Bayes Method in Signal Processing. Berlin: Springer Verlag; 2006.
   Google Scholar
• Hinton, GE, and Camp, D van, 1993. Keeping the neural networks simple by minimizing the description length of the weights. ACM, Santa Cruz, CA, USA: in Proceedings of the 6th Conference on Computational Learning Theory; 1993. pp. 5–13.
   Google Scholar
• MacKay, DJC, , Ensemble learning and evidence maximization (1995). Available at http://www.inference.phy.cam.ac.uk/mackay/nips.pdf [accessed 20 September 2010].
   Google Scholar
• Jordan, MI, Ghahramani, Z, Jaakkola, TS, and Saul, LK, 1999. An introduction to variational methods for graphical models, Machine Learn. 37 (1999), pp. 183–233.
   Web of Science ®Google Scholar
• Jaakkola, TS, and Jordan, MI, 2000. Bayesian parameter estimation via variational methods, Stat. Comput. 10 (2000), pp. 25–37.
   Web of Science ®Google Scholar
• Likas, AC, and Galatsanos, NP, , A variational approach for Bayesian blind image deconvolution, IEEE Trans. Signal Process., SP-52 (2004), pp. 2222–2233.
   Google Scholar
• Ayasso, H, and Mohammad-Djafari, A, , Joint NDT image restoration and segmentation using Gauss Markov Potts prior models and variational Bayesian computation, IEEE Trans. Image Process. IP-19 (2010), pp. 2265–2277.
   Google Scholar
• Choudrey, R, 2002. Variational Methods for Bayesian Independent Component Analysis, Ph.D. thesis. University of Oxford; 2002.
   Google Scholar
• Kullback, S, and Leibler, R, 1951. On information and sufficiency, Ann. Math. Stat. 22 (1951), pp. 79–87.
   Google Scholar
• Maire, G, Girard, J, Drsek, F, Giovannini, H, Talneau, A, Belkebir, K, Chaumet, PC, and Sentenac, A, 2010. Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime, J. Modern Opt. (special issue on Digital Optical Microscopy) 57 (2010), pp. 746–755.
   Google Scholar
• Chew, W, 1995. Waves and Fields in Inhomogeneous Media. New York: IEEE Press; 1995.
   Google Scholar
• Colton, D, and Kress, R, 1992. Inverse Acoustic and Electromagnetic Scattering Theory. New York: Springer; 1992.
   Google Scholar
• Lesselier, D, and Duchêne, B, 1991. "Buried, 2-D penetrable objects illuminated by line-sources: FFT-based iterative computations of the anomalous field". In: Sarkar, TK, ed. Application of Conjugate Gradient Methods to Electromagnetics and Signal Analysis. New York: Elsevier; 1991. pp. 400–438.
   Google Scholar
• Souriau, L, Duchêne, B, Lesselier, D, and Kleinman, RE, 1996. A modified gradient approach to inverse scattering for binary objects in stratified media, Inverse Probl. 12 (1996), pp. 463–481.
   Web of Science ®Google Scholar
• Clemmow, PC, 1966. The Plane Wave Spectrum Representation of Electromagnetic Fields. Oxford: Pergamon Press; 1966.
   Google Scholar
• Gibson, WC, 2007. The Method of Moments in Electromagnetics. Boca Raton, FL: Chapman & Hall/CRC; 2007.
   Google Scholar
• Sarkar, TK, Arvas, E, and Rao, SM, , Conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies, IEEE Trans. Antennas Propag. AP-34 (1986), pp. 635–640.
   Google Scholar
• Richmond, J, , Scattering by a dielectric cylinder of arbitrary cross-section shape, IEEE Trans. Anten-nas Propag. AP-13 (1965), pp. 334–341.
   Google Scholar
• Bernardo, JM, and Smith, AFM, 1994. Bayesian Theory. Chichester: Wiley & Sons; 1994.
   Google Scholar
• van den Berg, PM, and Kleinman, RE, 1997. A contrast source inversion method, Inverse Probl. 13 (1997), pp. 1607–1620.
   Web of Science ®Google Scholar
• Maire, G, Drsek, F, Girard, J, Giovannini, H, Talneau, A, Konan, D, Belkebir, K, Chaumet, PC, and Sentenac, A, , Experimental demonstration of quantitative imaging beyond Abbe's limit with optical diffraction tomography, Phys. Rev. Lett. 102 (2009).
   Google Scholar