{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T16:36:50Z","timestamp":1779381410525,"version":"3.53.1"},"reference-count":77,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T00:00:00Z","timestamp":1753315200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T00:00:00Z","timestamp":1753315200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"EPSRC","doi-asserted-by":"crossref","award":["International PhD Scholarship"],"award-info":[{"award-number":["International PhD Scholarship"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000266","name":"EPSRC","doi-asserted-by":"crossref","award":["EP\/V029428\/1, EPSRC Grants EP\/S026045\/1 and EP\/T003553\/1, EP\/N014588\/1, EP\/T017961\/1"],"award-info":[{"award-number":["EP\/V029428\/1, EPSRC Grants EP\/S026045\/1 and EP\/T003553\/1, EP\/N014588\/1, EP\/T017961\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Philip Leverhulme Prize"},{"name":"Royal Society Wolfson Fellowship"},{"name":"Wellcome Innovator Awards","award":["215733\/Z\/19\/Z ,221633\/Z\/20\/Z"],"award-info":[{"award-number":["215733\/Z\/19\/Z ,221633\/Z\/20\/Z"]}]},{"name":"European Union Horizon 2020 research and innovation programme","award":["Marie Sk lodowska-Curie Grant agreement No. 777826 NoMADS"],"award-info":[{"award-number":["Marie Sk lodowska-Curie Grant agreement No. 777826 NoMADS"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We propose a new operator sketching paradigm for designing efficient iterative data-driven reconstruction (IDR) schemes, such as plug-and-play algorithms and deep unrolling networks. These IDR schemes are the state-of-the-art solutions for imaging inverse problems. However, for high-dimensional imaging tasks, such as X-ray CT, PET and MRI imaging, these IDR schemes typically become inefficient in terms of computation, due to the need to compute the high-dimensional forward and adjoint operators multiple times. In this work, we introduce a universal dimensionality reduction framework for accelerating IDR schemes in solving imaging inverse problems, based on leveraging the sketching techniques from stochastic optimization. Using this framework, we derive several accelerated IDR schemes, including the plug-and-play multistage sketched gradient (PnP-MS2G) and sketching-based primal\u2013dual (LSPD and SkLSPD) deep unrolling networks. Meanwhile, to fully accelerate PnP schemes when the denoisers are computationally expensive, we further propose novel stochastic lazy denoising schemes (Lazy-PnP and Lazy-PnP-EQ), leveraging the ProxSkip scheme in optimization and equivariant image denoisers, to significantly enhance the practicality and efficiency of PnP algorithms. We provide theoretical analysis for recovery guarantees of instances of the proposed framework. Our numerical experiments on natural image processing and tomographic image reconstruction demonstrate the remarkable effectiveness of our sketched IDR schemes.\n<\/jats:p>","DOI":"10.1007\/s10851-025-01263-9","type":"journal-article","created":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T09:40:53Z","timestamp":1753350053000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Practical Operator Sketching Framework for Accelerating Iterative Data-Driven Solutions in Linear Inverse Problems"],"prefix":"10.1007","volume":"67","author":[{"given":"Junqi","family":"Tang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guixian","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Subhadip","family":"Mukherjee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carola-Bibiane","family":"Sch\u00f6nlieb","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,7,24]]},"reference":[{"key":"1263_CR1","doi-asserted-by":"crossref","unstructured":"Tang, J., Mukherjee, S., Sch\u00f6nlieb, C.-B.: Iterative operator sketching framework for large-scale imaging inverse problems. ICASSP-2025 (accepted\/in press) (2024)","DOI":"10.1109\/ICASSP49660.2025.10890355"},{"key":"1263_CR2","unstructured":"Tang, J., Mukherjee, S., Sch\u00f6nlieb, C.-B.: Accelerating deep unrolling networks via dimensionality reduction. arXiv preprint arXiv:2208.14784 (2022)"},{"key":"1263_CR3","unstructured":"Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: Proceedings of 3rd International Conference on Learning Representations (2015)"},{"key":"1263_CR4","unstructured":"Johnson, R., Zhang, T.: Accelerating stochastic gradient descent using predictive variance reduction. In: Advances in Neural Information Processing Systems, pp. 315\u2013323 (2013)"},{"issue":"1","key":"1263_CR5","first-page":"8194","volume":"18","author":"Z Allen-Zhu","year":"2017","unstructured":"Allen-Zhu, Z.: Katyusha: The first direct acceleration of stochastic gradient methods. J. Mach. Learn. Res. 18(1), 8194\u20138244 (2017)","journal-title":"J. Mach. Learn. Res."},{"issue":"4","key":"1263_CR6","doi-asserted-by":"publisher","first-page":"2783","DOI":"10.1137\/17M1134834","volume":"28","author":"A Chambolle","year":"2018","unstructured":"Chambolle, A., Ehrhardt, M.J., Richtarik, P., Schonlieb, C.-B.: Stochastic primal-dual hybrid gradient algorithm with arbitrary sampling and imaging applications. SIAM J. Optim. 28(4), 2783\u20132808 (2018)","journal-title":"SIAM J. Optim."},{"key":"1263_CR7","unstructured":"Andrychowicz, M., Denil, M., Gomez, S., Hoffman, M.W., Pfau, D., Schaul, T., Shillingford, B., De\u00a0Freitas, N.: Learning to learn by gradient descent by gradient descent. In: Advances in Neural Information Processing Systems, pp. 3981\u20133989 (2016)"},{"key":"1263_CR8","doi-asserted-by":"crossref","unstructured":"Li, Y., Zhang, K., Wang, J., Kumar, S.: Learning adaptive random features. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 4229\u20134236 (2019)","DOI":"10.1609\/aaai.v33i01.33014229"},{"key":"1263_CR9","unstructured":"Woodworth, B.E., Srebro, N.: Tight complexity bounds for optimizing composite objectives. In: Advances in Neural Information Processing Systems, pp. 3639\u20133647 (2016)"},{"issue":"1\u20132","key":"1263_CR10","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s10107-010-0434-y","volume":"133","author":"G Lan","year":"2012","unstructured":"Lan, G.: An optimal method for stochastic composite optimization. Math. Program. 133(1\u20132), 365\u2013397 (2012)","journal-title":"Math. Program."},{"key":"1263_CR11","unstructured":"Lan, G., Zhou, Y.: An optimal randomized incremental gradient method. arXiv preprint arXiv:1507.02000 (2015)"},{"key":"1263_CR12","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1017\/S096249291600009X","volume":"25","author":"A Chambolle","year":"2016","unstructured":"Chambolle, A., Pock, T.: An introduction to continuous optimization for imaging. Acta Numer 25, 161\u2013319 (2016)","journal-title":"Acta Numer"},{"key":"1263_CR13","doi-asserted-by":"crossref","unstructured":"Buzug, T.M.: Computed tomography. In: Springer Handbook of Medical Technology, pp. 311\u2013342. Springer, Berlin (2011)","DOI":"10.1007\/978-3-540-74658-4_16"},{"key":"1263_CR14","volume-title":"Magnetic Resonance Imaging: Theory and Practice","author":"MT Vlaardingerbroek","year":"2013","unstructured":"Vlaardingerbroek, M.T., Boer, J.A.: Magnetic Resonance Imaging: Theory and Practice. Springer, Berlin (2013)"},{"issue":"1","key":"1263_CR15","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1109\/79.560323","volume":"14","author":"JM Ollinger","year":"1997","unstructured":"Ollinger, J.M., Fessler, J.A.: Positron-emission tomography. IEEE Signal Process. Mag. 14(1), 43\u201355 (1997)","journal-title":"IEEE Signal Process. Mag."},{"issue":"3","key":"1263_CR16","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1214\/aoms\/1177729586","volume":"22","author":"H Robbins","year":"1951","unstructured":"Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 22(3), 400\u2013407 (1951)","journal-title":"Ann. Math. Stat."},{"issue":"9","key":"1263_CR17","doi-asserted-by":"publisher","first-page":"5096","DOI":"10.1109\/TIT.2015.2450722","volume":"61","author":"M Pilanci","year":"2015","unstructured":"Pilanci, M., Wainwright, M.J.: Randomized sketches of convex programs with sharp guarantees. IEEE Trans. Inf. Theory 61(9), 5096\u20135115 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"1263_CR18","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s00211-010-0331-6","volume":"117","author":"P Drineas","year":"2011","unstructured":"Drineas, P., Mahoney, M.W., Muthukrishnan, S., Sarl\u00f3s, T.: Faster least squares approximation. Numer. Math. 117(2), 219\u2013249 (2011)","journal-title":"Numer. Math."},{"key":"1263_CR19","unstructured":"Avron, H., Sindhwani, V., Woodruff, D.: Sketching structured matrices for faster nonlinear regression. In: Advances in Neural Information Processing Systems, pp. 2994\u20133002 (2013)"},{"issue":"1","key":"1263_CR20","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1109\/TMI.2014.2350962","volume":"34","author":"D Kim","year":"2015","unstructured":"Kim, D., Ramani, S., Fessler, J.A.: Combining ordered subsets and momentum for accelerated X-ray CT image reconstruction. IEEE Trans. Med. Imaging 34(1), 167\u2013178 (2015)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"3","key":"1263_CR21","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1109\/TCI.2019.2893568","volume":"5","author":"Y Sun","year":"2019","unstructured":"Sun, Y., Wohlberg, B., Kamilov, U.S.: An online plug-and-play algorithm for regularized image reconstruction. IEEE Trans. Comput. Imaging 5(3), 395\u2013408 (2019)","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"1263_CR22","unstructured":"Tang, J., Golbabaee, M., Davies, M.E.: Gradient projection iterative sketch for large-scale constrained least-squares. In: Proceedings of the 34th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 70, pp. 3377\u20133386. PMLR (2017)"},{"issue":"53","key":"1263_CR23","first-page":"1","volume":"17","author":"M Pilanci","year":"2016","unstructured":"Pilanci, M., Wainwright, M.J.: Iterative hessian sketch: fast and accurate solution approximation for constrained least-squares. J. Mach. Learn. Res. 17(53), 1\u201338 (2016)","journal-title":"J. Mach. Learn. Res."},{"issue":"6","key":"1263_CR24","doi-asserted-by":"publisher","first-page":"1322","DOI":"10.1109\/TMI.2018.2799231","volume":"37","author":"J Adler","year":"2018","unstructured":"Adler, J., \u00d6ktem, O.: Learned primal-dual reconstruction. IEEE Trans. Med. Imaging 37(6), 1322\u20131332 (2018)","journal-title":"IEEE Trans. Med. Imaging"},{"key":"1263_CR25","doi-asserted-by":"crossref","unstructured":"Zhang, J., Ghanem, B.: ISTA-Net: interpretable optimization-inspired deep network for image compressive sensing. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1828\u20131837 (2018)","DOI":"10.1109\/CVPR.2018.00196"},{"key":"1263_CR26","unstructured":"Sun, J., Li, H., Xu, Z., et al.: Deep ADMM-Net for compressive sensing MRI. In: Advances in Neural Information Processing Systems, vol. 29 (2016)"},{"issue":"5","key":"1263_CR27","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1109\/TMI.2021.3054167","volume":"40","author":"J Xiang","year":"2021","unstructured":"Xiang, J., Dong, Y., Yang, Y.: FISTA-Net: learning a fast iterative shrinkage thresholding network for inverse problems in imaging. IEEE Trans. Med. Imaging 40(5), 1329\u20131339 (2021)","journal-title":"IEEE Trans. Med. Imaging"},{"key":"1263_CR28","unstructured":"Mukherjee, S., Carioni, M., \u00d6ktem, O., Sch\u00f6nlieb, C.-B.: End-to-end reconstruction meets data-driven regularization for inverse problems. arXiv preprint arXiv:2106.03538 (2021)"},{"key":"1263_CR29","unstructured":"Mukherjee, S., Dittmer, S., Shumaylov, Z., Lunz, S., \u00d6ktem, O., Sch\u00f6nlieb, C.-B.: Learned convex regularizers for inverse problems. arXiv preprint arXiv:2008.02839 (2020)"},{"issue":"11","key":"1263_CR30","doi-asserted-by":"publisher","first-page":"2419","DOI":"10.1109\/TIP.2009.2028250","volume":"18","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18(11), 2419\u20132434 (2009)","journal-title":"IEEE Trans. Image Process."},{"key":"1263_CR31","unstructured":"Nesterov, Y.: Gradient methods for minimizing composite objective function. Technical Report, UCL (2007)"},{"issue":"11","key":"1263_CR32","doi-asserted-by":"publisher","first-page":"2835","DOI":"10.1088\/0031-9155\/44\/11\/311","volume":"44","author":"H Erdogan","year":"1999","unstructured":"Erdogan, H., Fessler, J.A.: Ordered subsets algorithms for transmission tomography. Phys. Med. Biol. 44(11), 2835 (1999)","journal-title":"Phys. Med. Biol."},{"issue":"4","key":"1263_CR33","doi-asserted-by":"publisher","first-page":"2057","DOI":"10.1137\/140961791","volume":"24","author":"L Xiao","year":"2014","unstructured":"Xiao, L., Zhang, T.: A proximal stochastic gradient method with progressive variance reduction. SIAM J. Optim. 24(4), 2057\u20132075 (2014)","journal-title":"SIAM J. Optim."},{"key":"1263_CR34","unstructured":"Defazio, A., Bach, F., Lacoste-Julien, S.: SAGA: a fast incremental gradient method with support for non-strongly convex composite objectives. In: Advances in Neural Information Processing Systems, pp. 1646\u20131654 (2014)"},{"key":"1263_CR35","unstructured":"Tang, J., Golbabaee, M., Bach, F., Davies, M.E.: Rest-Katyusha: exploiting the solution\u2019s structure via scheduled restart schemes. In: Advances in Neural Information Processing Systems 31, pp. 427\u2013438. Curran Associates, Inc. (2018)"},{"issue":"4","key":"1263_CR36","doi-asserted-by":"publisher","first-page":"1932","DOI":"10.1137\/20M1387213","volume":"14","author":"D Driggs","year":"2021","unstructured":"Driggs, D., Tang, J., Liang, J., Davies, M., Sch\u00f6nlieb, C.-B.: A stochastic proximal alternating minimization for nonsmooth and nonconvex optimization. SIAM J. Imag. Sci. 14(4), 1932\u20131970 (2021)","journal-title":"SIAM J. Imag. Sci."},{"key":"1263_CR37","doi-asserted-by":"crossref","unstructured":"Tang, J., Egiazarian, K., Davies, M.: The limitation and practical acceleration of stochastic gradient algorithms in inverse problems. In: ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 7680\u20137684 (2019). IEEE","DOI":"10.1109\/ICASSP.2019.8683368"},{"key":"1263_CR38","doi-asserted-by":"publisher","first-page":"1471","DOI":"10.1109\/TCI.2020.3032101","volume":"6","author":"J Tang","year":"2020","unstructured":"Tang, J., Egiazarian, K., Golbabaee, M., Davies, M.: The practicality of stochastic optimization in imaging inverse problems. IEEE Trans. Comput. Imaging 6, 1471\u20131485 (2020)","journal-title":"IEEE Trans. Comput. Imaging"},{"issue":"1","key":"1263_CR39","doi-asserted-by":"publisher","DOI":"10.1088\/2057-1976\/2\/1\/015008","volume":"2","author":"D Karimi","year":"2016","unstructured":"Karimi, D., Ward, R.K.: A hybrid stochastic-deterministic gradient descent algorithm for image reconstruction in cone-beam computed tomography. Biomed. Phys. Eng. Express 2(1), 015008 (2016)","journal-title":"Biomed. Phys. Eng. Express"},{"issue":"9","key":"1263_CR40","doi-asserted-by":"publisher","first-page":"4509","DOI":"10.1109\/TIP.2017.2713099","volume":"26","author":"KH Jin","year":"2017","unstructured":"Jin, K.H., McCann, M.T., Froustey, E., Unser, M.: Deep convolutional neural network for inverse problems in imaging. IEEE Trans. Image Process. 26(9), 4509\u20134522 (2017)","journal-title":"IEEE Trans. Image Process."},{"issue":"7","key":"1263_CR41","doi-asserted-by":"publisher","first-page":"3142","DOI":"10.1109\/TIP.2017.2662206","volume":"26","author":"K Zhang","year":"2017","unstructured":"Zhang, K., Zuo, W., Chen, Y., Meng, D., Zhang, L.: Beyond a Gaussian denoiser: residual learning of deep CNN for image denoising. IEEE Trans. Image Process. 26(7), 3142\u20133155 (2017)","journal-title":"IEEE Trans. Image Process."},{"issue":"8","key":"1263_CR42","doi-asserted-by":"publisher","first-page":"2080","DOI":"10.1109\/TIP.2007.901238","volume":"16","author":"K Dabov","year":"2007","unstructured":"Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080\u20132095 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"1263_CR43","doi-asserted-by":"crossref","unstructured":"Tachella, J., Tang, J., Davies, M.: The neural tangent link between CNN denoisers and non-local filters. In: IEEE\/CVF Conference on Computer Vision and Pattern Recognition (2021)","DOI":"10.1109\/CVPR46437.2021.00851"},{"key":"1263_CR44","doi-asserted-by":"crossref","unstructured":"Egiazarian, K., Foi, A., Katkovnik, V.: Compressed sensing image reconstruction via recursive spatially adaptive filtering. In: 2007 IEEE International Conference on Image Processing, vol. 1, p. 549 (2007). IEEE","DOI":"10.1109\/ICIP.2007.4379013"},{"key":"1263_CR45","doi-asserted-by":"crossref","unstructured":"Venkatakrishnan, S.V., Bouman, C.A., Wohlberg, B.: Plug-and-play priors for model based reconstruction. In: 2013 IEEE Global Conference on Signal and Information Processing, pp. 945\u2013948 (2013). IEEE","DOI":"10.1109\/GlobalSIP.2013.6737048"},{"issue":"4","key":"1263_CR46","doi-asserted-by":"publisher","first-page":"1804","DOI":"10.1137\/16M1102884","volume":"10","author":"Y Romano","year":"2017","unstructured":"Romano, Y., Elad, M., Milanfar, P.: The little engine that could: regularization by denoising (red). SIAM J. Imag. Sci. 10(4), 1804\u20131844 (2017)","journal-title":"SIAM J. Imag. Sci."},{"issue":"1","key":"1263_CR47","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1109\/TCI.2018.2880326","volume":"5","author":"ET Reehorst","year":"2018","unstructured":"Reehorst, E.T., Schniter, P.: Regularization by denoising: clarifications and new interpretations. IEEE Trans. Comput. Imaging 5(1), 52\u201367 (2018)","journal-title":"IEEE Trans. Comput. Imaging"},{"issue":"2","key":"1263_CR48","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1137\/23M157185X","volume":"17","author":"HY Tan","year":"2024","unstructured":"Tan, H.Y., Mukherjee, S., Tang, J., Sch\u00f6nlieb, C.-B.: Provably convergent plug-and-play quasi-newton methods. SIAM J. Imag. Sci. 17(2), 785\u2013819 (2024)","journal-title":"SIAM J. Imag. Sci."},{"issue":"3","key":"1263_CR49","doi-asserted-by":"publisher","first-page":"1374","DOI":"10.1137\/20M1337168","volume":"14","author":"R Cohen","year":"2021","unstructured":"Cohen, R., Elad, M., Milanfar, P.: Regularization by denoising via fixed-point projection (red-pro). SIAM J. Imag. Sci. 14(3), 1374\u20131406 (2021)","journal-title":"SIAM J. Imag. Sci."},{"key":"1263_CR50","unstructured":"Tang, J., Davies, M.: A fast stochastic plug-and-play ADMM for imaging inverse problems. arXiv preprint arXiv:2006.11630 (2020)"},{"key":"1263_CR51","doi-asserted-by":"crossref","unstructured":"Sun, Y., Wu, Z., Wohlberg, B., Kamilov, U.S.: Scalable plug-and-play ADMM with convergence guarantees. arXiv preprint arXiv:2006.03224 (2020)","DOI":"10.1109\/TCI.2021.3094062"},{"key":"1263_CR52","doi-asserted-by":"crossref","unstructured":"Papoutsellis, E., Kereta, Z., Papafitsoros, K.: Why do we regularise in every iteration for imaging inverse problems? arXiv preprint arXiv:2411.00688 (2024)","DOI":"10.1007\/978-3-031-92366-1_4"},{"key":"1263_CR53","doi-asserted-by":"crossref","unstructured":"Terris, M., Moreau, T., Pustelnik, N., Tachella, J.: Equivariant plug-and-play image reconstruction. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp. 25255\u201325264 (2024)","DOI":"10.1109\/CVPR52733.2024.02386"},{"issue":"1","key":"1263_CR54","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s10851-010-0251-1","volume":"40","author":"A Chambolle","year":"2011","unstructured":"Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"key":"1263_CR55","unstructured":"Gregor, K., LeCun, Y.: Learning fast approximations of sparse coding. In: Proceedings of the 27th International Conference on International Conference on Machine Learning, pp. 399\u2013406 (2010)"},{"issue":"1","key":"1263_CR56","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1137\/15M1021106","volume":"27","author":"M Pilanci","year":"2017","unstructured":"Pilanci, M., Wainwright, M.J.: Newton sketch: a near linear-time optimization algorithm with linear-quadratic convergence. SIAM J. Optim. 27(1), 205\u2013245 (2017)","journal-title":"SIAM J. Optim."},{"key":"1263_CR57","doi-asserted-by":"crossref","unstructured":"Tang, J., Golbabaee, M., Davies, M.: Exploiting the structure via sketched gradient algorithms. In: 2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP), pp. 1305\u20131309 (2017). IEEE","DOI":"10.1109\/GlobalSIP.2017.8309172"},{"issue":"1\u20132","key":"1263_CR58","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/0400000060","volume":"10","author":"DP Woodruff","year":"2014","unstructured":"Woodruff, D.P., et al.: Sketching as a tool for numerical linear algebra. Found. Trends Theor. Comput. Sci. 10(1\u20132), 1\u2013157 (2014)","journal-title":"Found. Trends Theor. Comput. Sci."},{"key":"1263_CR59","doi-asserted-by":"crossref","unstructured":"Xu, X., Liu, J., Sun, Y., Wohlberg, B., Kamilov, U.S.: Boosting the performance of plug-and-play priors via denoiser scaling. arXiv preprint arXiv:2002.11546 (2020)","DOI":"10.1109\/IEEECONF51394.2020.9443410"},{"key":"1263_CR60","unstructured":"Mishchenko, K., Malinovsky, G., Stich, S., Richt\u00e1rik, P.: Proxskip: Yes! local gradient steps provably lead to communication acceleration! finally! In: International Conference on Machine Learning, pp. 15750\u201315769 (2022). PMLR"},{"issue":"10","key":"1263_CR61","doi-asserted-by":"publisher","first-page":"6360","DOI":"10.1109\/TPAMI.2021.3088914","volume":"44","author":"K Zhang","year":"2021","unstructured":"Zhang, K., Li, Y., Zuo, W., Zhang, L., Van Gool, L., Timofte, R.: Plug-and-play image restoration with deep denoiser prior. IEEE Trans. Pattern Anal. Mach. Intell. 44(10), 6360\u20136376 (2021)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"12","key":"1263_CR62","doi-asserted-by":"publisher","first-page":"1872","DOI":"10.1109\/LSP.2017.2763583","volume":"24","author":"US Kamilov","year":"2017","unstructured":"Kamilov, U.S., Mansour, H., Wohlberg, B.: A plug-and-play priors approach for solving nonlinear imaging inverse problems. IEEE Signal Process. Lett. 24(12), 1872\u20131876 (2017)","journal-title":"IEEE Signal Process. Lett."},{"issue":"8","key":"1263_CR63","doi-asserted-by":"publisher","first-page":"1108","DOI":"10.1109\/LSP.2017.2710233","volume":"24","author":"S Ono","year":"2017","unstructured":"Ono, S.: Primal-dual plug-and-play image restoration. IEEE Signal Process. Lett. 24(8), 1108\u20131112 (2017)","journal-title":"IEEE Signal Process. Lett."},{"issue":"6","key":"1263_CR64","doi-asserted-by":"publisher","first-page":"1088","DOI":"10.1109\/JSTSP.2020.2998402","volume":"14","author":"J Liu","year":"2020","unstructured":"Liu, J., Sun, Y., Eldeniz, C., Gan, W., An, H., Kamilov, U.S.: Rare: image reconstruction using deep priors learned without groundtruth. IEEE J. Sel. Topics Signal Process. 14(6), 1088\u20131099 (2020)","journal-title":"IEEE J. Sel. Topics Signal Process."},{"key":"1263_CR65","doi-asserted-by":"crossref","unstructured":"Rick\u00a0Chang, J., Li, C.-L., Poczos, B., Vijaya\u00a0Kumar, B., Sankaranarayanan, A.C.: One network to solve them all\u2014solving linear inverse problems using deep projection models. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 5888\u20135897 (2017)","DOI":"10.1109\/ICCV.2017.627"},{"key":"1263_CR66","doi-asserted-by":"publisher","first-page":"598","DOI":"10.1109\/TCI.2021.3085534","volume":"7","author":"J Liu","year":"2021","unstructured":"Liu, J., Sun, Y., Gan, W., Xu, X., Wohlberg, B., Kamilov, U.S.: SGD-Net: efficient model-based deep learning with theoretical guarantees. IEEE Trans. Comput. Imaging 7, 598\u2013610 (2021)","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"1263_CR67","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1214\/12-STS400","volume":"27","author":"SN Negahban","year":"2012","unstructured":"Negahban, S.N., Ravikumar, P., Wainwright, M.J., Yu, B.: A unified framework for high-dimensional analysis of m-estimators with decomposable regularizers. Stat. Sci. 27, 538\u2013557 (2012)","journal-title":"Stat. Sci."},{"issue":"5","key":"1263_CR68","doi-asserted-by":"publisher","first-page":"2452","DOI":"10.1214\/12-AOS1032","volume":"40","author":"A Agarwal","year":"2012","unstructured":"Agarwal, A., Negahban, S., Wainwright, M.J.: Fast global convergence rates of gradient methods for high-dimensional statistical recovery. Ann. Stat. 40(5), 2452\u20132482 (2012)","journal-title":"Ann. Stat."},{"key":"1263_CR69","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1146\/annurev-statistics-022513-115643","volume":"1","author":"MJ Wainwright","year":"2014","unstructured":"Wainwright, M.J.: Structured regularizers for high-dimensional problems: statistical and computational issues. Annu. Rev. Stat. Appl. 1, 233\u2013253 (2014)","journal-title":"Annu. Rev. Stat. Appl."},{"issue":"6","key":"1263_CR70","doi-asserted-by":"publisher","first-page":"4129","DOI":"10.1109\/TIT.2017.2773497","volume":"64","author":"S Oymak","year":"2017","unstructured":"Oymak, S., Recht, B., Soltanolkotabi, M.: Sharp time-data tradeoffs for linear inverse problems. IEEE Trans. Inf. Theory 64(6), 4129\u20134158 (2017)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"1263_CR71","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1007\/s10208-012-9135-7","volume":"12","author":"V Chandrasekaran","year":"2012","unstructured":"Chandrasekaran, V., Recht, B., Parrilo, P.A., Willsky, A.S.: The convex geometry of linear inverse problems. Found. Comput. Math. 12(6), 805\u2013849 (2012)","journal-title":"Found. Comput. Math."},{"key":"1263_CR72","doi-asserted-by":"crossref","unstructured":"Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image restoration by sparse 3d transform-domain collaborative filtering. In: Image Processing: Algorithms and Systems VI, vol. 6812, p. 681207 (2008). International Society for Optics and Photonics","DOI":"10.1117\/12.766355"},{"key":"1263_CR73","unstructured":"Mason, J.H.: Quantitative cone-beam computed tomography reconstruction for radiotherapy planning (2018)"},{"issue":"6Part35","key":"1263_CR74","first-page":"3759","volume":"43","author":"C McCollough","year":"2016","unstructured":"McCollough, C.: TU-FG-207A-04: overview of the low dose CT grand challenge. Med. Phys. 43(6Part35), 3759\u20133760 (2016)","journal-title":"Med. Phys."},{"issue":"4","key":"1263_CR75","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","volume":"13","author":"Z Wang","year":"2004","unstructured":"Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600\u2013612 (2004)","journal-title":"IEEE Trans. Image Process."},{"key":"1263_CR76","unstructured":"Hu, Y., Delbracio, M., Milanfar, P., Kamilov, U.S.: A restoration network as an implicit prior. arXiv preprint arXiv:2310.01391 (2023)"},{"key":"1263_CR77","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.1109\/TCI.2021.3118944","volume":"7","author":"D Gilton","year":"2021","unstructured":"Gilton, D., Ongie, G., Willett, R.: Deep equilibrium architectures for inverse problems in imaging. IEEE Trans. Comput. Imaging 7, 1123\u20131133 (2021)","journal-title":"IEEE Trans. Comput. Imaging"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-025-01263-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10851-025-01263-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-025-01263-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T23:12:25Z","timestamp":1757286745000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10851-025-01263-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,24]]},"references-count":77,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["1263"],"URL":"https:\/\/doi.org\/10.1007\/s10851-025-01263-9","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,24]]},"assertion":[{"value":"20 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"There are no conflict of interest to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This declaration is not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}],"article-number":"46"}}