Transmission matrix inference via pseudolikelihood decimation. (English) Zbl 1510.78055
Summary: Recently, significant efforts in medical imaging are towards the exploitation of disordered media as optics tools. Among several approaches, the transmission matrix description is promising for characterizing complex structures and, currently, has enabled imaging and focusing through disorder. In the present work, we report a statistical mechanics description of the transmission problem. We convert a linear input-output transmission recovery into the statistical inference of an effective interaction matrix. We do this by relying on a pseudolikelihood maximization process based on random intensity observations. Our aim is to bridge results from spin-glass theory to the field of disordered photonics, uncovering insights from the scattering problem and encouraging the development of novel imaging techniques for better medical investigations.
MSC:
78A70 | Biological applications of optics and electromagnetic theory |
78A45 | Diffraction, scattering |
82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
92C55 | Biomedical imaging and signal processing |
62P30 | Applications of statistics in engineering and industry; control charts |
62F15 | Bayesian inference |
62C10 | Bayesian problems; characterization of Bayes procedures |
65K10 | Numerical optimization and variational techniques |
Software:
minFuncReferences:
[1] | Robert, C., Machine Learning: A Probabilistic Perspective (2014), London: Taylor and Francis, London |
[2] | Friedman, J.; Hastie, T.; Tibshirani, R., The Elements of Statistical Learning (Springer Series in Statistics vol 1) (2001), New York: Springer, New York · Zbl 0973.62007 |
[3] | Peckner, R.; Myers, S. A.; Jacome, A. S V.; Egertson, J. D.; Abelin, J. G.; MacCoss, M. J.; Carr, S. A.; Jaffe, J. D., Nat. Methods, 15, 371 (2018) · doi:10.1038/nmeth.4643 |
[4] | Altay, E.; Satman, M. H., J. Financ. Manag. Anal., 18, 18 (2005) |
[5] | Popoff, S. M.; Lerosey, G.; Fink, M.; Boccara, A. C.; Gigan, S., New J. Phys., 13 (2011) · doi:10.1088/1367-2630/13/12/123021 |
[6] | Bertolotti, J.; van Putten, E. G.; Blum, C.; Lagendijk, A.; Vos, W. L.; Mosk, A. P., Nature, 491, 232 (2012) · doi:10.1038/nature11578 |
[7] | Vellekoop, I. M.; Lagendijk, A.; Mosk, A. P., Nat. Photon., 4, 320 (2010) · doi:10.1038/nphoton.2010.3 |
[8] | Sebbah, P., Waves and Imaging Through Complex Media (2001), Berlin: Springer, Berlin |
[9] | Yoon, J.; Lee, K.; Park, J.; Park, Y., Opt. Express, 23, 10158-10167 (2015) · doi:10.1364/oe.23.010158 |
[10] | Carpenter, J.; Eggleton, B. J.; Schröder, J., Opt. Express, 22, 96 (2014) · doi:10.1364/oe.22.000096 |
[11] | Wiersma, D. S., Nat. Photon., 7, 188 (2013) · doi:10.1038/nphoton.2013.29 |
[12] | Boonzajer Flaes, D. E.; Stopka, J.; Turtaev, S.; De Boer, J. F.; Tyc, T.; Čižmár, T., Phys. Rev. Lett., 120 (2018) · doi:10.1103/physrevlett.120.233901 |
[13] | Di Battista, D.; Ancora, D.; Zhang, H.; Lemonaki, K.; Marakis, E.; Liapis, E.; Tzortzakis, S.; Zacharakis, G., Optica, 3, 1237-1240 (2016) · doi:10.1364/optica.3.001237 |
[14] | Chaigne, T.; Katz, O.; Boccara, A. C.; Fink, M.; Bossy, E.; Gigan, S., Nat. Photon., 8, 58 (2014) · doi:10.1038/nphoton.2013.307 |
[15] | Frostig, H.; Small, E.; Daniel, A.; Oulevey, P.; Derevyanko, S.; Silberberg, Y., Optica, 4, 1073-1079 (2017) · doi:10.1364/optica.4.001073 |
[16] | Penrose, R., On best approximate solutions of linear matrix equations, Math. Proc. Camb. Phil. Soc., 52, 17-19 (1956) · Zbl 0070.12501 · doi:10.1017/s0305004100030929 |
[17] | Tyagi, P.; Marruzzo, A.; Pagnani, A.; Antenucci, F.; Leuzzi, L., Phys. Rev. B, 94 (2016) · doi:10.1103/physrevb.94.024203 |
[18] | Ravikumar, P.; Wainwright, M. J.; Lafferty, J. D., Ann. Stat., 38, 1287-1319 (2010) · Zbl 1189.62115 · doi:10.1214/09-aos691 |
[19] | Ekeberg, M.; Lövkvist, C.; Lan, Y.; Weigt, M.; Aurell, E., Phys. Rev. E, 87 (2013) · doi:10.1103/physreve.87.012707 |
[20] | Decelle, A.; Ricci-Tersenghi, F., Phys. Rev. Lett., 112 (2014) · doi:10.1103/physrevlett.112.070603 |
[21] | Bianchi, S.; Di Leonardo, R., Lab Chip, 12, 635 (2012) · doi:10.1039/c1lc20719a |
[22] | Kim, D.; Moon, J.; Kim, M.; Yang, T. D.; Kim, J.; Chung, E.; Choi, W., Opt. Lett., 39, 1921-1924 (2014) · doi:10.1364/ol.39.001921 |
[23] | Ancora, D.; Dominici, L.; Gianfrate, A.; Cazzato, P.; De Giorgi, M.; Ballarini, D.; Sanvitto, D.; Leuzzi, L., Photonics Res., 10 (2021) · doi:10.1364/PR.462578 |
[24] | Sharma, M. K.; Metzler, C. A.; Nagesh, S.; Baraniuk, R. G.; Cossairt, O.; Veeraraghavan, A., IEEE Trans. Comput. Imaging, 6, 95-108 (2019) · doi:10.1109/TCI.2019.2919257 |
[25] | Calisesi, G.; Ghezzi, A.; Ancora, D.; D’Andrea, C.; Valentini, G.; Farina, A.; Bassi, A., Prog. Biophys. Mol. Biol., 168, 66-80 (2021) · doi:10.1016/j.pbiomolbio.2021.06.004 |
[26] | Barber, D., Bayesian Reasoning and Machine Learning (2012), Cambridge: Cambridge University Press, Cambridge · Zbl 1267.68001 |
[27] | Marruzzo, A.; Tyagi, P.; Antenucci, F.; Pagnani, A.; Leuzzi, L., SciPost Phys., 5, 002 (2018) · doi:10.21468/scipostphys.5.1.002 |
[28] | Schmidt, M., minFunc: unconstrained differentiable multivariate optimization in Matlab (2005) |
[29] | Anderson, D.; Burnham, K., Model Selection and Multi-Model Inference, vol 63 (2004), New York: Springer, New York |
[30] | Akaike, H., IEEE Trans. Autom. Control, 19, 716-723 (1974) · Zbl 0314.62039 · doi:10.1109/tac.1974.1100705 |
[31] | Hurvich, C. M.; Tsai, C-L, Biometrika, 76, 297-307 (1989) · Zbl 0669.62085 · doi:10.1093/biomet/76.2.297 |
[32] | Schwarz, G., Ann. Stat., 6, 461-464 (1978) · Zbl 0379.62005 · doi:10.1214/aos/1176344136 |
[33] | Franz, S.; Ricci-Tersenghi, F.; Rocchi, J. (2019) |
[34] | Antenucci, F.; Crisanti, A.; Leuzzi, L., Phys. Rev. A, 91 (2015) · doi:10.1103/physreva.91.053816 |
[35] | Antenucci, F.; Crisanti, A.; Ibáñez-Berganza, M.; Marruzzo, A.; Leuzzi, L., Phil. Mag., 96, 704 (2016) · doi:10.1080/14786435.2016.1145359 |
[36] | Antenucci, F., Statistical Physics of Wave Interactions (2016), Berlin: Springer, Berlin |
[37] | Sreeram, V.; Agathoklis, P., IEEE Trans. Circuits Syst. I, 41, 234-237 (1994) · doi:10.1109/81.273922 |
[38] | Popoff, S.; Lerosey, G.; Fink, M.; Boccara, A. C.; Gigan, S., Nat. Commun., 1, 81 (2010) · doi:10.1038/ncomms1078 |
[39] | Di Battista, D.; Ancora, D.; Leonetti, M.; Zacharakis, G., Appl. Phys. Lett., 109 (2016) · doi:10.1063/1.4962955 |
[40] | Leonetti, M.; Karbasi, S.; Mafi, A.; Conti, C., Phys. Rev. Lett., 112 (2014) · doi:10.1103/physrevlett.112.193902 |
[41] | Di Battista, D.; Ancora, D.; Zacharakis, G.; Ruocco, G.; Leonetti, M., Opt. Express, 26, 15594-15608 (2018) · doi:10.1364/oe.26.015594 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.