{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T00:28:15Z","timestamp":1786408095517,"version":"build-2736575974"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T00:00:00Z","timestamp":1782777600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T00:00:00Z","timestamp":1786406400000},"content-version":"vor","delay-in-days":42,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/100000002","name":"U.S. Department of Health & Human Services | National Institutes of Health","doi-asserted-by":"publisher","award":["R35GM148237"],"award-info":[{"award-number":["R35GM148237"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["PHY- 2310610"],"award-info":[{"award-number":["PHY- 2310610"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Commun"],"DOI":"10.1038\/s41467-026-74615-7","type":"journal-article","created":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T22:37:38Z","timestamp":1782859058000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A physics-informed alternative to Richardson-Lucy deconvolution across SNR regimes without iteration cutoffs"],"prefix":"10.1038","volume":"17","author":[{"given":"Zachary H.","family":"Hendrix","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2060-6398","authenticated-orcid":false,"given":"Peter T.","family":"Brown","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5131-1330","authenticated-orcid":false,"given":"Rory","family":"Kruithoff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-2191-2091","authenticated-orcid":false,"given":"Tim","family":"Flanagan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Douglas P.","family":"Shepherd","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8482-782X","authenticated-orcid":false,"given":"Ayush","family":"Saurabh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5408-0718","authenticated-orcid":false,"given":"Steve","family":"Press\u00e9","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,30]]},"reference":[{"key":"74615_CR1","unstructured":"Goodman, J. W. Introduction to Fourier Optics (Roberts and Company Publishers, 2005)."},{"key":"74615_CR2","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1364\/JOSA.62.000055","volume":"62","author":"WH Richardson","year":"1972","unstructured":"Richardson, W. H. Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62, 55 (1972).","journal-title":"J. Opt. Soc. Am."},{"key":"74615_CR3","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1086\/111605","volume":"79","author":"L Lucy","year":"1974","unstructured":"Lucy, L. An iterative technique for the rectification of observed distributions. Astron. J. 79, 745 (1974).","journal-title":"Astron. J."},{"key":"74615_CR4","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1364\/OPTICA.448287","volume":"9","author":"V Mannam","year":"2022","unstructured":"Mannam, V. et al. Real-time image denoising of mixed Poisson\u2013Gaussian noise in fluorescence microscopy images using ImageJ. Optica 9, 335 (2022).","journal-title":"Optica"},{"key":"74615_CR5","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-56241-x","volume":"16","author":"Y Liu","year":"2025","unstructured":"Liu, Y., Panezai, S., Wang, Y. & Stallinga, S. Noise amplification and ill-convergence of Richardson\u2013Lucy deconvolution. Nat. Commun. 16, 911 (2025).","journal-title":"Nat. Commun."},{"key":"74615_CR6","unstructured":"Burg, J. P. Maximum Entropy Spectral Analysis (Stanford Univ., 1975)."},{"key":"74615_CR7","first-page":"409","volume":"108","author":"H Bi","year":"1994","unstructured":"Bi, H. & Boerner, G. When does the Richardson-Lucy deconvolution converge? Astron. Astrophys. Suppl. Ser. 108, 409 (1994).","journal-title":"Astron. Astrophys. Suppl. Ser."},{"key":"74615_CR8","doi-asserted-by":"publisher","first-page":"3842","DOI":"10.1109\/TIP.2018.2819821","volume":"27","author":"W Meiniel","year":"2018","unstructured":"Meiniel, W., Olivo-Marin, J.-C. & Angelini, E. D. Denoising of microscopy images: a review of the state-of-the-art, and a new sparsity-based method. IEEE Trans. Image Process. 27, 3842 (2018).","journal-title":"IEEE Trans. Image Process."},{"key":"74615_CR9","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1186\/s42492-019-0016-7","volume":"2","author":"L Fan","year":"2019","unstructured":"Fan, L., Zhang, F., Fan, H. & Zhang, C. Brief review of image denoising techniques. Vis. Comput. Ind. Biomed. Art. 2, 7 (2019).","journal-title":"Vis. Comput. Ind. Biomed. Art."},{"key":"74615_CR10","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin, L. I., Osher, S. & Fatemi, E. Nonlinear total variation based noise removal algorithms. Phys. D Nonlinear Phenom. 60, 259 (1992).","journal-title":"Phys. D Nonlinear Phenom."},{"key":"74615_CR11","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1038\/nbt.4115","volume":"36","author":"X Huang","year":"2018","unstructured":"Huang, X. et al. Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy. Nat. Biotechnol. 36, 451 (2018).","journal-title":"Nat. Biotechnol."},{"key":"74615_CR12","doi-asserted-by":"publisher","first-page":"1337","DOI":"10.1038\/s41587-020-0560-x","volume":"38","author":"M Guo","year":"2020","unstructured":"Guo, M. et al. Rapid image deconvolution and multiview fusion for optical microscopy. Nat. Biotechnol. 38, 1337\u20131346 (2020).","journal-title":"Nat. Biotechnol."},{"key":"74615_CR13","doi-asserted-by":"publisher","first-page":"2342","DOI":"10.1038\/s41592-024-02475-4","volume":"21","author":"X Ruan","year":"2024","unstructured":"Ruan, X. et al. Image processing tools for petabyte-scale light sheet microscopy data. Nat. Methods 21, 2342\u20132352 (2024).","journal-title":"Nat. Methods"},{"key":"74615_CR14","doi-asserted-by":"publisher","first-page":"3126","DOI":"10.1109\/TIP.2016.2562563","volume":"25","author":"N Eslahi","year":"2016","unstructured":"Eslahi, N. & Aghagolzadeh, A. Compressive sensing image restoration using adaptive curvelet thresholding and nonlocal sparse regularization. IEEE Trans. Image Process. 25, 3126 (2016).","journal-title":"IEEE Trans. Image Process."},{"key":"74615_CR15","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1002\/jemt.20294","volume":"69","author":"N Dey","year":"2006","unstructured":"Dey, N. et al. Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution. Microsc. Res. Tech. 69, 260 (2006).","journal-title":"Microsc. Res. Tech."},{"key":"74615_CR16","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1002\/mrm.27993","volume":"83","author":"Y Blunck","year":"2020","unstructured":"Blunck, Y. et al. Compressed sensing effects on quantitative analysis of undersampled human brain sodium MRI. Magn. Reson. Med. 83, 1025 (2020).","journal-title":"Magn. Reson. Med."},{"key":"74615_CR17","doi-asserted-by":"publisher","first-page":"606","DOI":"10.1038\/s41587-021-01092-2","volume":"40","author":"W Zhao","year":"2022","unstructured":"Zhao, W. et al. Sparse deconvolution improves the resolution of live-cell super-resolution fluorescence microscopy. Nat. Biotechnol. 40, 606 (2022).","journal-title":"Nat. Biotechnol."},{"key":"74615_CR18","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1109\/MSP.2022.3199595","volume":"40","author":"US Kamilov","year":"2023","unstructured":"Kamilov, U. S., Bouman, C. A., Buzzard, G. T. & Wohlberg, B. Plug-and-play methods for integrating physical and learned models in computational imaging: theory, algorithms, and applications. IEEE Signal Process. Mag. 40, 85 (2023).","journal-title":"IEEE Signal Process. Mag."},{"key":"74615_CR19","doi-asserted-by":"crossref","unstructured":"Ulyanov, D., Vedaldi, A. & Lempitsky, V. Deep image prior. In Proc. IEEE Conference on Computer Vision and Pattern Recognition 9446 (IEEE, 2018).","DOI":"10.1109\/CVPR.2018.00984"},{"key":"74615_CR20","doi-asserted-by":"crossref","unstructured":"Ma, L. et al. Deblur-NeRF: neural radiance fields from blurry images. In Proc. IEEE\/CVF Conference on Computer Vision and Pattern Recognition 12861 (IEEE, 2022).","DOI":"10.1109\/CVPR52688.2022.01252"},{"key":"74615_CR21","doi-asserted-by":"crossref","unstructured":"Ni, S. et al. Application of physics-informed neural networks in removing telescope beam effects. Astrophys. J. 990, 122 (2025).","DOI":"10.3847\/1538-4357\/adf223"},{"key":"74615_CR22","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-48575-9","volume":"15","author":"C Qiao","year":"2024","unstructured":"Qiao, C. et al. Zero-shot learning enables instant denoising and super-resolution in optical fluorescence microscopy. Nat. Commun. 15, 4180 (2024).","journal-title":"Nat. Commun."},{"key":"74615_CR23","unstructured":"Xu, L., Ren, J. S., Liu, C. & Jia, J. Deep convolutional neural network for image deconvolution. Adv. Neural Inform. Process. Syst. 27 (2014)."},{"key":"74615_CR24","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1364\/OPTICA.442438","volume":"9","author":"K Yanny","year":"2022","unstructured":"Yanny, K., Monakhova, K., Shuai, R. W. & Waller, L. Deep learning for fast spatially varying deconvolution. Optica 9, 96 (2022).","journal-title":"Optica"},{"key":"74615_CR25","doi-asserted-by":"publisher","first-page":"1427","DOI":"10.1038\/s41592-022-01652-7","volume":"19","author":"Y Li","year":"2022","unstructured":"Li, Y. et al. Incorporating the image formation process into deep learning improves network performance. Nat. Methods 19, 1427 (2022).","journal-title":"Nat. Methods"},{"key":"74615_CR26","unstructured":"Manton, J., York, A., Becker, J. & Russell, C. Data-driven parameter-free optimal deconvolution using Richardson-Lucy iterations and gradient consensus as a stopping criterion https:\/\/colab.research.google.com\/drive\/1mfVNSCaYHz1g56g92xBkIoa8190XNJpJ (2023)."},{"key":"74615_CR27","doi-asserted-by":"crossref","unstructured":"Khatana, V., Saraswat, G., Patel, S. & Salapaka, M. V. Gradient-consensus method for distributed optimization in directed multi-agent networks. In 2020 American Control Conference (ACC) 4689 (IEEE, 2020).","DOI":"10.23919\/ACC45564.2020.9147544"},{"key":"74615_CR28","doi-asserted-by":"publisher","first-page":"044005","DOI":"10.1088\/1361-6420\/ab5ede","volume":"36","author":"RR Lederman","year":"2020","unstructured":"Lederman, R. R., And\u00e9n, J. & Singer, A. Hyper-molecules: on the representation and recovery of dynamical structures for applications in flexible macro-molecules in cryo-em. Inverse Probl. 36, 044005 (2020).","journal-title":"Inverse Probl."},{"key":"74615_CR29","unstructured":"Bishop, C. M. & Nasrabadi, N. M. Pattern Recognition and Machine Learning Vol. 4 (Springer, 2006)."},{"key":"74615_CR30","doi-asserted-by":"crossref","unstructured":"Press\u00e9, S. & Sgouralis, I. Data Modeling for the Sciences: Applications, Basics, Computations (Cambridge Univ. Press, 2023).","DOI":"10.1017\/9781009089555"},{"key":"74615_CR31","doi-asserted-by":"crossref","unstructured":"Saurabh, A. et al. Approaching maximum resolution in structured illumination microscopy via accurate noise modeling. npj Imaging 3, 5 (2025).","DOI":"10.1038\/s44303-024-00066-8"},{"key":"74615_CR32","unstructured":"https:\/\/github.com\/JuliaImages\/TestImages.jl."},{"key":"74615_CR33","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1038\/s41586-021-03977-3","volume":"599","author":"L Heinrich","year":"2021","unstructured":"Heinrich, L. et al. Whole-cell organelle segmentation in volume electron microscopy. Nature 599, 141\u2013146 (2021).","journal-title":"Nature"},{"key":"74615_CR34","doi-asserted-by":"publisher","unstructured":"FIB-SEM Technology Group. Isotropic 3D electron microscopy reference data of wild-type, interphase HeLa cell (jrc_hela-3). https:\/\/doi.org\/10.25378\/janelia.13114244.v2 (2024).","DOI":"10.25378\/janelia.13114244.v2"},{"key":"74615_CR35","unstructured":"Saurabh, A. BayesianDeconvolution https:\/\/github.com\/LabPresse\/BayesianDeconvolution (2024)."},{"key":"74615_CR36","doi-asserted-by":"publisher","first-page":"e53671","DOI":"10.1371\/journal.pone.0053671","volume":"8","author":"M Hirsch","year":"2013","unstructured":"Hirsch, M., Wareham, R. J., Martin-Fernandez, M. L., Hobson, M. P. & Rolfe, D. J. A stochastic model for electron multiplication charge-coupled devices\u2013from theory to practice. PLoS ONE 8, e53671 (2013).","journal-title":"PLoS ONE"},{"key":"74615_CR37","doi-asserted-by":"publisher","first-page":"9603","DOI":"10.1364\/OE.386168","volume":"28","author":"PC Konda","year":"2020","unstructured":"Konda, P. C. et al. Fourier ptychography: current applications and future promises. Opt. Express 28, 9603 (2020).","journal-title":"Opt. Express"},{"key":"74615_CR38","doi-asserted-by":"publisher","first-page":"1196","DOI":"10.1137\/16M1101684","volume":"10","author":"L Calatroni","year":"2017","unstructured":"Calatroni, L., De Los Reyes, J. C. & Sch\u00f6nlieb, C.-B. Infimal convolution of data discrepancies for mixed noise removal. SIAM J. Imaging Sci. 10, 1196\u20131233 (2017).","journal-title":"SIAM J. Imaging Sci."},{"key":"74615_CR39","doi-asserted-by":"publisher","first-page":"968","DOI":"10.1007\/s10851-022-01100-3","volume":"64","author":"B Toader","year":"2022","unstructured":"Toader, B. et al. Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise. J. Math. Imaging Vis. 64, 968 (2022).","journal-title":"J. Math. Imaging Vis."},{"key":"74615_CR40","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1109\/TCI.2017.2700203","volume":"3","author":"Y Marnissi","year":"2017","unstructured":"Marnissi, Y., Zheng, Y., Chouzenoux, E. & Pesquet, J.-C. A variational Bayesian approach for image restoration\u2014application to image deblurring with Poisson-Gaussian noise. IEEE Trans. Comput. Imaging 3, 722 (2017).","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"74615_CR41","doi-asserted-by":"crossref","unstructured":"Aetesam, H. A proximal approach to image deconvolution under mixed Poisson\u2013Gaussian noise. In Computer Vision, Pattern Recognition, Image Processing, and Graphics (eds Subudhi, B. N., Rout, R. K. & Sengar, B. S.) Ch. 27, 344\u2013358 (Springer, 2026).","DOI":"10.1007\/978-3-032-08508-5_27"},{"key":"74615_CR42","doi-asserted-by":"crossref","unstructured":"Biquard, M., Chabert, M., Genin, F., Latry, C. & Oberlin, T. PG-DPIR: an efficient plug-and-play method for high-count Poisson\u2013Gaussian inverse problems. In 2025 33rd European Signal Processing Conference (EUSIPCO) 696\u2013700 (IEEE, 2025).","DOI":"10.23919\/EUSIPCO63237.2025.11226422"},{"key":"74615_CR43","doi-asserted-by":"publisher","first-page":"3910","DOI":"10.1039\/b509983h","volume":"7","author":"DJ Earl","year":"2005","unstructured":"Earl, D. J. & Deem, M. W. Parallel tempering: Theory, applications, and new perspectives. Phys. Chem. Chem. Phys. 7, 3910 (2005).","journal-title":"Phys. Chem. Chem. Phys."},{"key":"74615_CR44","doi-asserted-by":"publisher","first-page":"3700","DOI":"10.1364\/BOE.422703","volume":"12","author":"PT Brown","year":"2021","unstructured":"Brown, P. T., Kruithoff, R., Seedorf, G. J. & Shepherd, D. P. Multicolor structured illumination microscopy and quantitative control of polychromatic light with a digital micromirror device. Biomed. Opt. Express 12, 3700 (2021).","journal-title":"Biomed. Opt. Express"},{"key":"74615_CR45","doi-asserted-by":"publisher","first-page":"eadr8004","DOI":"10.1126\/sciadv.adr8004","volume":"11","author":"PT Brown","year":"2025","unstructured":"Brown, P. T. et al. Fourier synthesis optical diffraction tomography for kilohertz rate volumetric imaging. Sci. Adv. 11, eadr8004 (2025).","journal-title":"Sci. Adv."},{"key":"74615_CR46","doi-asserted-by":"publisher","first-page":"99","DOI":"10.21105\/jcon.00099","volume":"1","author":"F Wechsler","year":"2023","unstructured":"Wechsler, F. & Heintzmann, R. DeconvOptim.jl - signal deconvolution with Julia. Proc. JuliaCon Conf. 1, 99 (2023).","journal-title":"Proc. JuliaCon Conf."},{"key":"74615_CR47","unstructured":"https:\/\/scikit-image.org\/docs\/stable\/auto_examples\/filters\/plot_deconvolution."}],"container-title":["Nature Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41467-026-74615-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41467-026-74615-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41467-026-74615-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T23:32:09Z","timestamp":1786404729000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41467-026-74615-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,30]]},"references-count":47,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["74615"],"URL":"https:\/\/doi.org\/10.1038\/s41467-026-74615-7","relation":{},"ISSN":["2041-1723"],"issn-type":[{"value":"2041-1723","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,30]]},"assertion":[{"value":"6 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Ethics"}}],"article-number":"8162"}}