Eckart, A. & Genzel, R. Stellar proper motions in the central 0.1 pc of the Galaxy. *Monthly Notices of the Royal Astronomical Society* **284**, 576–598 (1997).

M. Solan et al., Towards a greater understanding of pattern, scale and process in marine benthic systems: a picture is worth a thousand worms. J. Exp. Mar. Biol. Ecol. **285–286**, 313–338 (2003)

Google Scholar

Tan, R. T. Visibility in bad weather from a single image. in *2008 IEEE Conference on Computer Vision and Pattern Recognition* 1–8 (2008). https://doi.org/10.1109/CVPR.2008.4587643.

V. Ntziachristos, Going deeper than microscopy: the optical imaging frontier in biology. Nat. Methods **7**, 603–614 (2010)

Google Scholar

N. Ji, D.E. Milkie, E. Betzig, Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues. Nat. Methods **7**, 141–147 (2010)

Google Scholar

K. He, J. Sun, X. Tang, Single Image Haze Removal Using Dark Channel Prior. IEEE Trans. Pattern Anal. Mach. Intell. **33**, 2341–2353 (2011)

Google Scholar

J. Bertolotti et al., Non-invasive imaging through opaque scattering layers. Nature **491**, 232–234 (2012)

ADS
Google Scholar

A.P. Mosk, A. Lagendijk, G. Lerosey, M. Fink, Controlling waves in space and time for imaging and focusing in complex media. Nat. Photonics **6**, 283–292 (2012)

ADS
Google Scholar

O. Katz, P. Heidmann, M. Fink, S. Gigan, Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations. Nature Photon **8**, 784–790 (2014)

ADS
Google Scholar

S.-C. Huang, B.-H. Chen, Y.-J. Cheng, An Efficient Visibility Enhancement Algorithm for Road Scenes Captured by Intelligent Transportation Systems. IEEE Trans. Intell. Transp. Syst. **15**, 2321–2332 (2014)

Google Scholar

S. Li, M. Deng, J. Lee, A. Sinha, G. Barbastathis, Imaging through glass diffusers using densely connected convolutional networks. Optica, OPTICA **5**, 803–813 (2018)

ADS
Google Scholar

Y. Li, Y. Xue, L. Tian, Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media. Optica **5**, 1181 (2018)

ADS
Google Scholar

D.B. Lindell, G. Wetzstein, Three-dimensional imaging through scattering media based on confocal diffuse tomography. Nat Commun **11**, 4517 (2020)

ADS
Google Scholar

J.W. Goodman, W.H. Huntley, D.W. Jackson, M. Lehmann, Wavefront-reconstruction imaging through random media. Appl. Phys. Lett. **8**, 311–313 (1966)

ADS
Google Scholar

H. Kogelnik, K.S. Pennington, Holographic Imaging Through a Random Medium. J. Opt. Soc. Am. **58**, 273 (1968)

Google Scholar

S. Popoff, G. Lerosey, M. Fink, A.C. Boccara, S. Gigan, Image transmission through an opaque material. Nat Commun **1**, 81 (2010)

ADS
Google Scholar

J. Li et al., Conjugate adaptive optics in widefield microscopy with an extended-source wavefront sensor. Optica **2**, 682 (2015)

ADS
Google Scholar

E. Edrei, G. Scarcelli, Optical imaging through dynamic turbid media using the Fourier-domain shower-curtain effect. Optica **3**, 71 (2016)

ADS
Google Scholar

X. Li, J.A. Greenberg, M.E. Gehm, Single-shot multispectral imaging through a thin scatterer. Optica, OPTICA **6**, 864–871 (2019)

ADS
Google Scholar

M. Jang et al., Relation between speckle decorrelation and optical phase conjugation (OPC)-based turbidity suppression through dynamic scattering media: a study on in vivo mouse skin. Biomed. Opt. Express **6**, 72 (2015)

Google Scholar

S.G. Narasimhan, S.K. Nayar, Contrast restoration of weather degraded images. IEEE Trans. Pattern Anal. Mach. Intell. **25**, 713–724 (2003)

Google Scholar

E.A. Bucher, Computer Simulation of Light Pulse Propagation for Communication Through Thick Clouds. Appl. Opt. **12**, 2391 (1973)

ADS
Google Scholar

A. Lopez, E. Nezry, R. Touzi, H. Laur, Structure detection and statistical adaptive speckle filtering in SAR images. Int. J. Remote Sens. **14**, 1735–1758 (1993)

Google Scholar

Lohmann, A. W., Weigelt, G. & Wirnitzer, B. Speckle masking in astronomy: triple correlation theory and applications. *Appl. Opt., AO* **22**, 4028–4037 (1983).

Roggemann, M. C., Welsh, B. M. & Hunt, B. R. *Imaging Through Turbulence*. (CRC Press, 1996).

J.S. Jaffe, K.D. Moore, J. Mclean, M.R. Strand, Underwater optical imaging: Status and prospects. Oceanography **14**, 64–66 (2001)

Google Scholar

Schettini, R. & Corchs, S. Underwater Image Processing: State of the Art of Restoration and Image Enhancement Methods. *EURASIP Journal on Advances in Signal Processing* **2010**, (2010).

Z. Jia et al., A two-step approach to see-through bad weather for surveillance video quality enhancement. Mach. Vis. Appl. **23**, 1059–1082 (2012)

Google Scholar

Tarel, J.-P. & Hautière, N. Fast visibility restoration from a single color or gray level image. in *2009 IEEE 12th International Conference on Computer Vision* 2201–2208 (2009). https://doi.org/10.1109/ICCV.2009.5459251.

M. Johnson-Roberson et al., High-Resolution Underwater Robotic Vision-Based Mapping and Three-Dimensional Reconstruction for Archaeology. Journal of Field Robotics **34**, 625–643 (2017)

Google Scholar

Hao, Z., You, S., Li, Y., Li, K. & Lu, F. Learning From Synthetic Photorealistic Raindrop for Single Image Raindrop Removal. in *Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops* 0–0 (2019).

Majer, F., Yan, Z., Broughton, G., Ruichek, Y. & Krajník, T. Learning to see through haze: Radar-based Human Detection for Adverse Weather Conditions. in *2019 European Conference on Mobile Robots (ECMR)* 1–7 (2019). doi:https://doi.org/10.1109/ECMR.2019.8870954.

Popoff, S. M. *et al.* Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media. *Physical Review Letters* **104**, (2010).

Goodman, J. W. *Speckle Phenomena in Optics: Theory and Applications*. (Roberts and Company Publishers, 2007).

D.B. Conkey, A.M. Caravaca-Aguirre, R. Piestun, High-speed scattering medium characterization with application to focusing light through turbid media. Opt. Express **20**, 1733 (2012)

ADS
Google Scholar

Wang, K. *et al.* Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue. *Nature Communications* **6**, (2015).

I.M. Vellekoop, A.P. Mosk, Focusing coherent light through opaque strongly scattering media. Opt. Lett. **32**, 2309 (2007)

ADS
Google Scholar

I.M. Vellekoop, A. Lagendijk, A.P. Mosk, Exploiting disorder for perfect focusing. Nat. Photonics **4**, 320–322 (2010)

Google Scholar

R. Horstmeyer, H. Ruan, C. Yang, Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nat. Photonics **9**, 563–571 (2015)

ADS
Google Scholar

M. Nixon et al., Real-time wavefront shaping through scattering media by all-optical feedback. Nat. Photonics **7**, 919–924 (2013)

ADS
Google Scholar

O. Katz, E. Small, Y. Silberberg, Looking around corners and through thin turbid layers in real time with scattered incoherent light. Nat. Photonics **6**, 549–553 (2012)

ADS
Google Scholar

S. Feng, C. Kane, P.A. Lee, A.D. Stone, Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media. Phys. Rev. Lett. **61**, 834–837 (1988)

ADS
Google Scholar

I. Freund, M. Rosenbluh, S. Feng, Memory Effects in Propagation of Optical Waves through Disordered Media. Phys. Rev. Lett. **61**, 2328–2331 (1988)

ADS
Google Scholar

Edrei, E. & Scarcelli, G. Memory-effect based deconvolution microscopy for super-resolution imaging through scattering media. *Scientific Reports* **6**, (2016).

W. Yang, G. Li, G. Situ, Imaging through scattering media with the auxiliary of a known reference object. Sci. Rep. **8**, 9614 (2018)

ADS
Google Scholar

He, H., Guan, Y. & Zhou, J. Image restoration through thin turbid layers by correlation with a known object. *Opt. Express, OE* **21**, 12539–12545 (2013).

X. Wang et al., Prior-information-free single-shot scattering imaging beyond the memory effect. Opt. Lett. **44**, 1423 (2019)

ADS
Google Scholar

Yang, M. *et al.* Deep hybrid scattering image learning. *J. Phys. D: Appl. Phys.* **52**, 115105 (2019).

Lyu, M., Wang, H., Li, G., Zheng, S. & Situ, G. Learning-based lensless imaging through optically thick scattering media. *AP* **1**, 036002 (2019).

Y. Rivenson et al., Deep learning microscopy. Optica, OPTICA **4**, 1437–1443 (2017)

ADS
Google Scholar

Y. Rivenson et al., Deep Learning Enhanced Mobile-Phone Microscopy. ACS Photonics (2018). https://doi.org/10.1021/acsphotonics.8b00146

Article
Google Scholar

E. Nehme, L.E. Weiss, T. Michaeli, Y. Shechtman, Deep-STORM: super-resolution single-molecule microscopy by deep learning. Optica, OPTICA **5**, 458–464 (2018)

ADS
Google Scholar

H. Wang et al., Deep learning enables cross-modality super-resolution in fluorescence microscopy. Nat. Methods **16**, 103–110 (2019)

Google Scholar

Y. Rivenson et al., Virtual histological staining of unlabelled tissue-autofluorescence images via deep learning. Nat Biomed Eng **3**, 466–477 (2019)

Google Scholar

Y. Wu et al., Three-dimensional virtual refocusing of fluorescence microscopy images using deep learning. Nat. Methods **16**, 1323–1331 (2019)

Google Scholar

Y. Wu et al., Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery. Optica **5**, 704 (2018)

ADS
Google Scholar

Wu, Y. *et al.* Bright-field holography: cross-modality deep learning enables snapshot 3D imaging with bright-field contrast using a single hologram. *Light: Science & Applications* **8**, 1–7 (2019).

T. Liu et al., Deep learning-based super-resolution in coherent imaging systems. Sci. Rep. **9**, 1–13 (2019)

ADS
Google Scholar

Liu, T. *et al.* Deep learning-based color holographic microscopy. *Journal of Biophotonics* **12**, e201900107 (2019).

G. Barbastathis, A. Ozcan, G. Situ, On the use of deep learning for computational imaging. Optica, OPTICA **6**, 921–943 (2019)

ADS
Google Scholar

Wang, F. *et al.* Phase imaging with an untrained neural network. *Light: Science & Applications* **9**, 77 (2020).

Malkiel, I. *et al.* Plasmonic nanostructure design and characterization via Deep Learning. *Light: Science & Applications* **7**, (2018).

D. Liu, Y. Tan, E. Khoram, Z. Yu, Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures. ACS Photonics **5**, 1365–1369 (2018)

Google Scholar

Peurifoy, J. *et al.* Nanophotonic particle simulation and inverse design using artificial neural networks. *Science Advances* **4**, eaar4206 (2018).

W. Ma, F. Cheng, Y. Liu, Deep-Learning-Enabled On-Demand Design of Chiral Metamaterials. ACS Nano **12**, 6326–6334 (2018)

Google Scholar

Luo, Y. *et al.* Design of task-specific optical systems using broadband diffractive neural networks. *Light: Science & Applications* **8**, 1–14 (2019).

M. Veli et al., Terahertz pulse shaping using diffractive surfaces. Nat. Commun. **12**, 37 (2021)

ADS
Google Scholar

D. Psaltis, D. Brady, X.G. Gu, S. Lin, Holography in artificial neural networks. Nature **343**, 325–330 (1990)

ADS
Google Scholar

Y. Shen et al., Deep learning with coherent nanophotonic circuits. Nat. Photonics **11**, 441–446 (2017)

ADS
Google Scholar

Chang, J., Sitzmann, V., Dun, X., Heidrich, W. & Wetzstein, G. Hybrid optical-electronic convolutional neural networks with optimized diffractive optics for image classification. *Scientific Reports* **8**, (2018).

X. Lin et al., All-optical machine learning using diffractive deep neural networks. Science **361**, 1004 (2018)

ADS
MathSciNet
MATH
Google Scholar

N.M. Estakhri, B. Edwards, N. Engheta, Inverse-designed metastructures that solve equations. Science **363**, 1333–1338 (2019)

ADS
MathSciNet
MATH
Google Scholar

J. Li, D. Mengu, Y. Luo, Y. Rivenson, A. Ozcan, Class-specific differential detection in diffractive optical neural networks improves inference accuracy. Adv. Photon. **1**, 1 (2019)

Google Scholar

D. Mengu, Y. Luo, Y. Rivenson, A. Ozcan, Analysis of Diffractive Optical Neural Networks and Their Integration With Electronic Neural Networks. IEEE J. Sel. Top. Quantum Electron. **26**, 1–14 (2020)

Google Scholar

Mengu, D. *et al.* Misalignment resilient diffractive optical networks. *Nanophotonics* **0**, (2020).

Li, J. *et al.* Spectrally encoded single-pixel machine vision using diffractive networks. *Science Advances* **7**, eabd7690 (2021).

O. Kulce, D. Mengu, Y. Rivenson, A. Ozcan, All-optical information-processing capacity of diffractive surfaces. Light Sci Appl **10**, 25 (2021)

Google Scholar

B. Rahmani, D. Loterie, G. Konstantinou, D. Psaltis, C. Moser, Multimode optical fiber transmission with a deep learning network. Light Sci Appl **7**, 1–11 (2018)

Google Scholar

Bai, B. *et al.* Pathological crystal imaging with single-shot computational polarized light microscopy. *Journal of Biophotonics* **13**, e201960036 (2020).

T. Liu et al., Deep Learning-Based Holographic Polarization Microscopy. ACS Photonics **7**, 3023–3034 (2020)

Google Scholar

LeCun, Y. *et al.* Handwritten Digit Recognition with a Back-Propagation Network. in *Advances in Neural Information Processing Systems 2* (ed. Touretzky, D. S.) 396–404 (Morgan-Kaufmann, 1990).

Benesty, J., Chen, J., Huang, Y. & Cohen, I. Pearson Correlation Coefficient. in *Noise Reduction in Speech Processing* vol. 2 1–4 (Springer Berlin Heidelberg, 2009).

Wu, T., Dong, J., Shao, X. & Gigan, S. Imaging through a thin scattering layer and jointly retrieving the point-spread-function using phase-diversity. *Opt. Express, OE* **25**, 27182–27194 (2017).

X. Xu et al., Imaging of objects through a thin scattering layer using a spectrally and spatially separated reference. Opt. Express **26**, 15073 (2018)

ADS
Google Scholar

Hofer, M., Soeller, C., Brasselet, S. & Bertolotti, J. Wide field fluorescence epi-microscopy behind a scattering medium enabled by speckle correlations. *Opt. Express, OE* **26**, 9866–9881 (2018).

S. Lowenthal, D. Joyeux, Speckle Removal by a Slowly Moving Diffuser Associated with a Motionless Diffuser. J. Opt. Soc. Am. **61**, 847 (1971)

ADS
Google Scholar

Kingma, D. P. & Ba, J. Adam: A Method for Stochastic Optimization. arXiv:1412.6980. [cs] (2014).

Rahman, M. S. S., Li, J., Mengu, D., Rivenson, Y. & Ozcan, A. Ensemble learning of diffractive optical networks. *Light: Science & Applications* **10**, 14 (2021).