{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T02:52:47Z","timestamp":1781491967243,"version":"3.54.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T00:00:00Z","timestamp":1781481600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T00:00:00Z","timestamp":1781481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12571472"],"award-info":[{"award-number":["12571472"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Open Project of Key Laboratory of Mathematics and Information Networks","award":["KF202401"],"award-info":[{"award-number":["KF202401"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1007\/s10851-026-01307-8","type":"journal-article","created":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T02:20:05Z","timestamp":1781490005000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Two-view CBCT Reconstruction via Preconditioned Gradient Descent with Plug-and-play Diffusion Anatomical Prior"],"prefix":"10.1007","volume":"68","author":[{"given":"Ji","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qilong","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Lv","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yikun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Tong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Ji","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,15]]},"reference":[{"issue":"7","key":"1307_CR1","doi-asserted-by":"publisher","first-page":"2916","DOI":"10.1002\/mp.14170","volume":"47","author":"G Chen","year":"2020","unstructured":"Chen, G., Hong, X., Ding, Q., Zhang, Y., Chen, H., Fu, S., Zhao, Y., Zhang, X., Ji, H., Wang, G., et al.: AirNet: fused analytical and iterative reconstruction with deep neural network regularization for sparse-data CT. Med. Phys. 47(7), 2916\u20132930 (2020)","journal-title":"Med. Phys."},{"issue":"17","key":"1307_CR2","doi-asserted-by":"publisher","first-page":"175020","DOI":"10.1088\/1361-6560\/ab9f60","volume":"65","author":"G Chen","year":"2020","unstructured":"Chen, G., Zhao, Y., Huang, Q., Gao, H.: 4D-AirNet: a temporally-resolved CBCT slice reconstruction method synergizing analytical and iterative method with deep learning. Phys. Med. Biol. 65(17), 175020 (2020)","journal-title":"Phys. Med. Biol."},{"issue":"11","key":"1307_CR3","doi-asserted-by":"publisher","first-page":"8168","DOI":"10.1002\/mp.17328","volume":"51","author":"X Chen","year":"2024","unstructured":"Chen, X., Qiu, R.L., Peng, J., Shelton, J.W., Chang, C.W., Yang, X., Kesarwala, A.H.: CBCT-based synthetic CT image generation using a diffusion model for CBCT-guided lung radiotherapy. Med. Phys. 51(11), 8168\u20138178 (2024)","journal-title":"Med. Phys."},{"key":"1307_CR4","unstructured":"Chung, H., Kim, J., Mccann, M.T., Klasky, M.L., Ye, J.C.: Diffusion posterior sampling for general noisy inverse problems. In: The Eleventh International Conference on Learning Representations, (2022)"},{"issue":"12","key":"1307_CR5","doi-asserted-by":"publisher","first-page":"14687","DOI":"10.1088\/1361-6560\/ab831a","volume":"65","author":"Q Ding","year":"2020","unstructured":"Ding, Q., Chen, G., Zhang, X., Huang, Q., Ji, H., Gao, H.: Low-dose CT with deep learning regularization via proximal forward backward splitting. Phys. Med. Biol. 65(12), 14687 (2020)","journal-title":"Phys. Med. Biol."},{"key":"1307_CR6","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1109\/TCI.2021.3093003","volume":"7","author":"Q Ding","year":"2021","unstructured":"Ding, Q., Nan, Y., Gao, H., Ji, H.: Deep learning with adaptive hyper-parameters for low-dose CT image reconstruction. IEEE Trans. Comput. Imaging 7, 648\u2013660 (2021)","journal-title":"IEEE Trans. Comput. Imaging"},{"issue":"15","key":"1307_CR7","doi-asserted-by":"publisher","first-page":"155008","DOI":"10.1088\/1361-6560\/ad5d47","volume":"69","author":"W Du","year":"2024","unstructured":"Du, W., Cui, H., He, L., Chen, H., Zhang, Y., Yang, H.: Structure-aware diffusion for low-dose CT imaging. Phys. Med. Biol. 69(15), 155008 (2024)","journal-title":"Phys. Med. Biol."},{"key":"1307_CR8","doi-asserted-by":"crossref","unstructured":"Friedrich, P., Wolleb, J., Bieder, F., Durrer, A., Cattin, P.C.(2024): WDM: 3D wavelet diffusion models for high-resolution medical image synthesis. In: MICCAI Workshop on Deep Generative Models, Springer. pp. 11\u201321","DOI":"10.1007\/978-3-031-72744-3_2"},{"issue":"11","key":"1307_CR9","doi-asserted-by":"publisher","first-page":"7110","DOI":"10.1118\/1.4761867","volume":"39","author":"H Gao","year":"2012","unstructured":"Gao, H.: Fast parallel algorithms for the X-ray transform and its adjoint. Med. Phys. 39(11), 7110\u20137120 (2012)","journal-title":"Med. Phys."},{"issue":"19","key":"1307_CR10","doi-asserted-by":"publisher","first-page":"7187","DOI":"10.1088\/0031-9155\/61\/19\/7187","volume":"61","author":"H Gao","year":"2016","unstructured":"Gao, H.: Fused analytical and iterative reconstruction (air) via modified proximal forward-backward splitting: a FDK-based iterative image reconstruction example for CBCT. Phys. Med. Biol. 61(19), 7187 (2016)","journal-title":"Phys. Med. Biol."},{"issue":"11","key":"1307_CR11","doi-asserted-by":"publisher","first-page":"6943","DOI":"10.1118\/1.4762288","volume":"39","author":"H Gao","year":"2012","unstructured":"Gao, H., Li, R., Lin, Y., Xing, L.: 4D cone beam CT via spatiotemporal tensor framelet. Med. Phys. 39(11), 6943\u20136946 (2012)","journal-title":"Med. Phys."},{"issue":"1","key":"1307_CR12","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1002\/mp.12671","volume":"45","author":"H Gao","year":"2018","unstructured":"Gao, H., Zhang, Y., Ren, L., Yin, F.F.: Principal component reconstruction (PCR) for cine CBCT with motion learning from 2D fluoroscopy. Med. Phys. 45(1), 167\u2013177 (2018)","journal-title":"Med. Phys."},{"issue":"107","key":"1307_CR13","first-page":"680","volume":"236","author":"R Ge","year":"2022","unstructured":"Ge, R., He, Y., Xia, C., Xu, C., Sun, W., Yang, G., Li, J., Wang, Z., Yu, H., Zhang, D.: X-CTRSNet: 3D cervical vertebra CT reconstruction and segmentation directly from 2D X-ray images. Knowl.-Based Syst. 236(107), 680 (2022)","journal-title":"Knowl.-Based Syst."},{"key":"1307_CR14","first-page":"6840","volume":"33","author":"J Ho","year":"2020","unstructured":"Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Adv. neural info. process. syst. 33, 6840\u20136851 (2020)","journal-title":"Adv. neural info. process. syst."},{"key":"1307_CR15","first-page":"1","volume":"72","author":"D Hu","year":"2023","unstructured":"Hu, D., Zhang, Y., Li, W., Zhang, W., Reddy, K., Ding, Q., Zhang, X., Chen, Y., Gao, H.: SEA-net: Structure-enhanced attention network for limited-angle CBCT reconstruction of clinical projection data. IEEE Trans. Instrum. Meas. 72, 1\u201313 (2023)","journal-title":"IEEE Trans. Instrum. Meas."},{"issue":"1","key":"1307_CR16","doi-asserted-by":"publisher","first-page":"7303","DOI":"10.1038\/s41598-023-34341-2","volume":"13","author":"F Khader","year":"2023","unstructured":"Khader, F., M\u00fcller-Franzes, G., Tayebi Arasteh, S., Han, T., Haarburger, C., Schulze-Hagen, M., Schad, P., Engelhardt, S., Bae\u00dfler, B., Foersch, S., et al.: Denoising diffusion probabilistic models for 3D medical image generation. Sci. Rep. 13(1), 7303 (2023)","journal-title":"Sci. Rep."},{"key":"1307_CR17","doi-asserted-by":"crossref","unstructured":"Lee, S., Chung, H., Park, M., Park, J., Ryu, W.S., Ye, J.C.: Improving 3D imaging with pre-trained perpendicular 2D diffusion models. In: ICCV, pp. 10,710\u201310,720 (2023)","DOI":"10.1109\/ICCV51070.2023.00983"},{"issue":"23","key":"1307_CR18","doi-asserted-by":"publisher","first-page":"235003","DOI":"10.1088\/1361-6560\/abc303","volume":"65","author":"Y Lei","year":"2020","unstructured":"Lei, Y., Tian, Z., Wang, T., Higgins, K., Bradley, J.D., Curran, W.J., Liu, T., Yang, X.: Deep learning-based real-time volumetric imaging for lung stereotactic body radiation therapy: a proof of concept study. Phys. Med. Biol. 65(23), 235003 (2020)","journal-title":"Phys. Med. Biol."},{"issue":"3","key":"1307_CR19","doi-asserted-by":"publisher","first-page":"613","DOI":"10.3934\/ipi.2024047","volume":"19","author":"J Li","year":"2024","unstructured":"Li, J., Wang, C.: Diffusion posterior sampling for magnetic resonance imaging. Inverse Probl. Imaging 19(3), 613\u2013631 (2024)","journal-title":"Inverse Probl. Imaging"},{"issue":"2","key":"1307_CR20","doi-asserted-by":"publisher","first-page":"1468","DOI":"10.1137\/24M1688321","volume":"18","author":"J Li","year":"2025","unstructured":"Li, J., Wang, C.: Efficient diffusion posterior sampling for noisy inverse problems. SIAM J. Imag. Sci. 18(2), 1468\u20131492 (2025). https:\/\/doi.org\/10.1137\/24M1688321","journal-title":"SIAM J. Imag. Sci."},{"key":"1307_CR21","unstructured":"Liu, X., Gong, C.: Flow straight and fast: Learning to generate and transfer data with rectified flow. In: The Eleventh International Conference on Learning Representations, (2023)"},{"issue":"2","key":"1307_CR22","doi-asserted-by":"publisher","first-page":"1083","DOI":"10.1109\/TMI.2024.3473970","volume":"44","author":"Z Liu","year":"2024","unstructured":"Liu, Z., Fang, Y., Li, C., Wu, H., Liu, Y., Shen, D., Cui, Z.: Geometry-aware attenuation learning for sparse-view CBCT reconstruction. IEEE Trans. Med. Imaging 44(2), 1083\u20131097 (2024)","journal-title":"IEEE Trans. Med. Imaging"},{"key":"1307_CR23","first-page":"5775","volume":"35","author":"C Lu","year":"2022","unstructured":"Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., Zhu, J.: DPM-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. Adv. Neural. Inf. Process. Syst. 35, 5775\u20135787 (2022)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"1307_CR24","doi-asserted-by":"crossref","unstructured":"Pan, S., Lo, S.Y., Chang, C.W., Salari, E., Wang, T., Roper, J., Kesarwala, A.H., Yang, X.: Patient-specific 3D volumetric cbct image reconstruction with single X-ray projection using denoising diffusion probabilistic model. In: Medical Imaging 2024: Imaging Informatics for Healthcare, Research, and Applications, 12931: 136\u2013143. SPIE (2024)","DOI":"10.1117\/12.3006561"},{"key":"1307_CR25","doi-asserted-by":"publisher","unstructured":"Pan, S., Peng, J., Gao, Y., Lo, S.Y., Luan, T., Li, J., Wang, T., Chang, C.W., Tian, Z., Yang, X.: CBCT reconstruction using single X-ray projection with cycle-domain geometry-integrated denoising diffusion probabilistic models. IEEE Transactions on Medical Imaging pp. 1\u20131 (2025). https:\/\/doi.org\/10.1109\/TMI.2025.3556402","DOI":"10.1109\/TMI.2025.3556402"},{"key":"1307_CR26","unstructured":"Peng, X., Zheng, Z., Dai, W., Xiao, N., Li, C., Zou, J., Xiong, H.: Improving diffusion models for inverse problems using optimal posterior covariance. In: Salakhutdinov, R., Kolter, Z., Heller, K., Weller, A., Oliver, N., Scarlett, J., Berkenkamp, F. (eds.) Proceedings of the 41st International Conference on Machine Learning, Proceedings of Machine Learning Research, 235: 40347\u201340370. PMLR (2024)"},{"issue":"11","key":"1307_CR27","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1038\/s41551-019-0466-4","volume":"3","author":"L Shen","year":"2019","unstructured":"Shen, L., Zhao, W., Xing, L.: Patient-specific reconstruction of volumetric computed tomography images from a single projection view via deep learning. Nat. Biomed. Eng. 3(11), 880\u2013888 (2019)","journal-title":"Nat. Biomed. Eng."},{"key":"1307_CR28","unstructured":"Song, J., Vahdat, A., Mardani, M., Kautz, J.: Pseudoinverse-guided diffusion models for inverse problems. In: International Conference on Learning Representations, (2022)"},{"key":"1307_CR29","unstructured":"Song, Y., Shen, L., Xing, L., Ermon, S.: Solving inverse problems in medical imaging with score-based generative models. In: International Conference on Learning Representations, (2021)"},{"key":"1307_CR30","unstructured":"Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., Poole, B.: Score-based generative modeling through stochastic differential equations. In: International Conference on Learning Representations, (2020)"},{"key":"1307_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.compmedimag.2022.102067","volume":"98","author":"Z Tan","year":"2022","unstructured":"Tan, Z., Li, J., Tao, H., Li, S., Hu, Y.: XctNet: Reconstruction network of volumetric images from a single X-ray image. Comput. Med. Imaging Graph. 98, 102,067 (2022)","journal-title":"Comput. Med. Imaging Graph."},{"key":"1307_CR32","doi-asserted-by":"crossref","unstructured":"Wang, X., Ou, Z., Jin, P., Xie, J., Teng, Z., Xu, L., Du, J., Ding, M., Chen, Y., Niu, T.(2024): Four-dimensional cone-beam CT reconstruction via diffusion model and motion compensation. In: IEEE Trans. Rad. Plasma Med. Sci. 9(2): 191-201","DOI":"10.1109\/TRPMS.2024.3449155"},{"issue":"13","key":"1307_CR33","doi-asserted-by":"publisher","first-page":"135008","DOI":"10.1088\/1361-6560\/ad580d","volume":"69","author":"J Xie","year":"2024","unstructured":"Xie, J., Shao, H.C., Li, Y., Zhang, Y.: Prior frequency guided diffusion model for limited angle (LA)-CBCT reconstruction. Phys. Med. Biol. 69(13), 135008 (2024)","journal-title":"Phys. Med. Biol."},{"key":"1307_CR34","doi-asserted-by":"crossref","unstructured":"Ying, X., Guo, H., Ma, K., Wu, J., Weng, Z., Zheng, Y.: X2CT-GAN: reconstructing CT from biplanar X-rays with generative adversarial networks, pp. 10619\u201310628. CVPR (2019)","DOI":"10.1109\/CVPR.2019.01087"},{"key":"1307_CR35","doi-asserted-by":"crossref","unstructured":"Zang, G., Idoughi, R., Li, R., Wonka, P., Heidrich, W.: Intratomo: self-supervised learning-based tomography via sinogram synthesis and prediction. In: ICCV, pp. 1960\u20131970. (2021)","DOI":"10.1109\/ICCV48922.2021.00197"},{"issue":"10","key":"1307_CR36","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."},{"key":"1307_CR37","unstructured":"Zhang, Q., Chen, Y.: Fast sampling of diffusion models with exponential integrator. In: The Eleventh International Conference on Learning Representations"},{"issue":"1","key":"1307_CR38","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1109\/TMI.2024.3439573","volume":"44","author":"Y Zhang","year":"2024","unstructured":"Zhang, Y., Hu, D., Li, W., Zhang, W., Chen, G., Chen, R.C., Chen, Y., Gao, H.: 2V-CBCT: Two-orthogonal-projection based CBCT reconstruction and dose calculation for radiation therapy using real projection data. IEEE Trans. Med. Imaging 44(1), 284\u2013296 (2024)","journal-title":"IEEE Trans. Med. Imaging"},{"key":"1307_CR39","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Zhang, K., Liang, J., Cao, J., Wen, B., Timofte, R., Van Gool, L.: Denoising diffusion models for plug-and-play image restoration. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition Workshops, pp. 1219\u20131229. (2023)","DOI":"10.1109\/CVPRW59228.2023.00129"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-026-01307-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10851-026-01307-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-026-01307-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T02:20:16Z","timestamp":1781490016000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10851-026-01307-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,15]]},"references-count":39,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["1307"],"URL":"https:\/\/doi.org\/10.1007\/s10851-026-01307-8","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,15]]},"assertion":[{"value":"14 January 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2026","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":"33"}}