{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:01:48Z","timestamp":1757617308399,"version":"3.44.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T00:00:00Z","timestamp":1735257600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T00:00:00Z","timestamp":1735257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Natural Science Foundation Project of China","award":["62001247","62001247","62001247","62001247"],"award-info":[{"award-number":["62001247","62001247","62001247","62001247"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. &amp; Cyber."],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s13042-024-02510-y","type":"journal-article","created":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T02:50:46Z","timestamp":1735267846000},"page":"4295-4306","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Single image deraining via nonlinear recursive Conv-Transformer"],"prefix":"10.1007","volume":"16","author":[{"given":"Zhenyuan","family":"Liang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Songhao","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiwei","family":"Liang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,12,27]]},"reference":[{"issue":"11","key":"2510_CR1","doi-asserted-by":"publisher","first-page":"4059","DOI":"10.1109\/TPAMI.2020.2995190","volume":"43","author":"W Yang","year":"2020","unstructured":"Yang W, Tan RT, Wang S, Fang Y, Liu J (2020) Single image deraining: from model-based to data-driven and beyond. IEEE Trans Pattern Anal Mach Intell 43(11):4059\u20134077","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"5","key":"2510_CR2","doi-asserted-by":"publisher","first-page":"1767","DOI":"10.1007\/s13042-023-01996-2","volume":"15","author":"D Nimma","year":"2024","unstructured":"Nimma D, Zhou Z (2024) IntelPVT: intelligent patch-based pyramid vision transformers for object detection and classification. Mach Learn Cybern 15(5):1767\u20131778","journal-title":"Mach Learn Cybern"},{"key":"2510_CR3","doi-asserted-by":"crossref","unstructured":"Wang H,\u00a0Zhu Y,\u00a0Adam H,\u00a0Yuille AL,\u00a0Chen L (2021:) MaX-DeepLab:\u00a0end-to-end\u00a0panoptic segmentation\u00a0with\u00a0mask\u00a0transformers. In: IEEE conference on computer vision and pattern recognition, 5463\u20135474","DOI":"10.1109\/CVPR46437.2021.00542"},{"key":"2510_CR4","doi-asserted-by":"crossref","unstructured":"Chen X,\u00a0Yan B,\u00a0Zhu J,\u00a0Wang D,\u00a0Yang X,\u00a0Lu H (2021) Transformer tracking. In: IEEE conference on computer vision and pattern recognition, 8126\u20138135","DOI":"10.1109\/CVPR46437.2021.00803"},{"issue":"12","key":"2510_CR5","doi-asserted-by":"publisher","first-page":"5765","DOI":"10.1007\/s13042-024-02277-2","volume":"15","author":"B Wang","year":"2024","unstructured":"Wang B, Zhang Y, Long W, Cui Z (2024) Joint features-guided linear transformer and CNN for efficient image super-resolution. Mach Learn Cybern 15(12):5765\u20135780","journal-title":"Mach Learn Cybern"},{"key":"2510_CR6","unstructured":"Jiang Y,\u00a0Chang S,\u00a0Wang Z (2021) TransGAN:\u00a0two\u00a0pure\u00a0transformers\u00a0can\u00a0make one\u00a0strong GAN, and\u00a0that\u00a0can\u00a0scale\u00a0up. In: Annual conference on neural information processing systems, 14745\u201314758"},{"key":"2510_CR7","doi-asserted-by":"crossref","unstructured":"Chen H,\u00a0Wang Y,\u00a0Guo T,\u00a0Xu C,\u00a0Deng Y, et al (2021) Pre-trained image processing transformer. IN: IEEE conference on computer vision and pattern recognition, 12299\u201312310","DOI":"10.1109\/CVPR46437.2021.01212"},{"key":"2510_CR8","unstructured":"Dosovitskiy A, Beyer L, Kolesnikov A, Weissenborn D, Zhai X, et al (2021) An image is worth 16x16 words: transformers for image recognition at scale. International conference on learning representations, 1\u201321"},{"key":"2510_CR9","doi-asserted-by":"crossref","unstructured":"Liu Z,\u00a0Lin Y,\u00a0Cao Y,\u00a0Hu H,\u00a0Wei Y, et al (2021) Swin\u00a0transformer:\u00a0hierarchical\u00a0vision\u00a0transformer\u00a0using\u00a0shifted\u00a0windows. In: IEEE conference on computer vision, 9992\u201310002","DOI":"10.1109\/ICCV48922.2021.00986"},{"key":"2510_CR10","doi-asserted-by":"crossref","unstructured":"Li Y,\u00a0Tan RT,\u00a0Guo X,\u00a0Lu J,\u00a0Brown MS (2016) Rain\u00a0streak\u00a0removal\u00a0using\u00a0layer\u00a0priors. In: IEEE conference on computer vision and pattern recognition, 2736\u20132744","DOI":"10.1109\/CVPR.2016.299"},{"key":"2510_CR11","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1016\/j.apm.2018.03.001","volume":"59","author":"L Deng","year":"2018","unstructured":"Deng L, Huang T, Zhao X, Jiang T (2018) A directional global sparse model for single image rain removal. Appl Math Model 59:662\u2013679","journal-title":"Appl Math Model"},{"key":"2510_CR12","doi-asserted-by":"crossref","unstructured":"Zhu L,\u00a0Fu C,\u00a0Lischinski D,\u00a0Heng P (2017) Joint\u00a0bi-layer\u00a0optimization\u00a0for\u00a0single-image rain\u00a0streak\u00a0removal. In: IEEE conference on computer vision, 2545\u20132553","DOI":"10.1109\/ICCV.2017.276"},{"issue":"4","key":"2510_CR13","doi-asserted-by":"publisher","first-page":"1742","DOI":"10.1109\/TIP.2011.2179057","volume":"21","author":"L Kang","year":"2011","unstructured":"Kang L, Lin C, Yuhsiang Fu (2011) Automatic single image based rain streaks removal via image decomposition. IEEE Trans Image Process 21(4):1742\u20131755","journal-title":"IEEE Trans Image Process"},{"issue":"8","key":"2510_CR14","doi-asserted-by":"publisher","first-page":"3936","DOI":"10.1109\/TIP.2017.2708502","volume":"26","author":"Y Wang","year":"2017","unstructured":"Wang Y, Liu S, Chen C, Zeng B (2017) A hierarchical approach for rain or snow removing in a single-color image. IEEE Trans Image Process 26(8):3936\u20133950","journal-title":"IEEE Trans Image Process"},{"key":"2510_CR15","doi-asserted-by":"crossref","unstructured":"Luo Y, Xu Y, Ji H (2015) Removing rain from a single image via discriminative sparse coding. In: IEEE conference on computer vision, 3397\u20133405","DOI":"10.1109\/ICCV.2015.388"},{"key":"2510_CR16","doi-asserted-by":"crossref","unstructured":"Fu X,\u00a0Huang J,\u00a0Ding X,\u00a0Liao Y,\u00a0Paisley JW (2017) Clearing\u00a0the\u00a0skies:\u00a0a\u00a0deep\u00a0network\u00a0architecture for\u00a0single image\u00a0rain\u00a0removal. In: IEEE transactions on image processing, 2944\u20132956","DOI":"10.1109\/TIP.2017.2691802"},{"key":"2510_CR17","doi-asserted-by":"crossref","unstructured":"Yang W, Tan RT, Feng J, Guo Z, Yan S, et al (2017) Joint rain detection and removal from a single image with contextualized deep networks. In: IEEE conference on computer vision and pattern recognition, 1357\u20131366","DOI":"10.1109\/CVPR.2017.183"},{"key":"2510_CR18","doi-asserted-by":"crossref","unstructured":"Hu X, Fu C, Zhu L, Heng P (2019) Depth-attentional features for single-image rain removal. In: IEEE conference on computer vision and pattern recognition, 8022\u20138031","DOI":"10.1109\/CVPR.2019.00821"},{"key":"2510_CR19","doi-asserted-by":"crossref","unstructured":"Ren D, Zuo W, Hu Q, Zhu P, Meng D (2019) Progressive image deraining networks: a better and simpler baseline. In: IEEE conference on computer vision and pattern recognition, 3937\u20133946","DOI":"10.1109\/CVPR.2019.00406"},{"key":"2510_CR20","doi-asserted-by":"crossref","unstructured":"Jiang K,\u00a0Wang Z,\u00a0Yi P,\u00a0Chen C,\u00a0Huang B, et al (2020) Multi-scale progressive fusion network for single image deraining. In: IEEE conference on computer vision and pattern recognition, 8343\u20138352","DOI":"10.1109\/CVPR42600.2020.00837"},{"key":"2510_CR21","doi-asserted-by":"crossref","unstructured":"Qian R, Tan RT, Yang W, Su J, Liu J (2018) Attentive generative adversarial network for raindrop removal from a single image. In: IEEE conference on computer vision and pattern recognition, 2482\u20132491","DOI":"10.1109\/CVPR.2018.00263"},{"key":"2510_CR22","doi-asserted-by":"crossref","unstructured":"Wei W,\u00a0Meng D,\u00a0Zhao Q,\u00a0Xu Z, Wu Y (2019) Semi-supervised\u00a0transfer\u00a0learning\u00a0for\u00a0image\u00a0rain\u00a0removal. In: IEEE conference on computer vision and pattern recognition, 3877\u20133886","DOI":"10.1109\/CVPR.2019.00400"},{"key":"2510_CR23","doi-asserted-by":"crossref","unstructured":"Yasarla R,\u00a0Sindagi VA,\u00a0Patel VM (2020) Syn2Real\u00a0transfer\u00a0learning\u00a0for\u00a0image\u00a0deraining\u00a0using\u00a0gaussian\u00a0processes. In: IEEE conference on computer vision and pattern recognition, 2726\u20132736","DOI":"10.1109\/CVPR42600.2020.00280"},{"key":"2510_CR24","doi-asserted-by":"crossref","unstructured":"Ye Y,\u00a0Chang Y,\u00a0Zhou H,\u00a0Yan L. (2021) Closing the loop: joint rain generation and removal via disentangled image translation. In: IEEE conference on computer vision and pattern recognition, 2053\u20132062","DOI":"10.1109\/CVPR46437.2021.00209"},{"key":"2510_CR25","doi-asserted-by":"crossref","unstructured":"Li X, Wu J, Lin Z, Liu H, Zha H (2018) Recurrent squeeze and excitation context aggregation net for single image deraining. In: European conference on computer vision, 254\u2013269","DOI":"10.1007\/978-3-030-01234-2_16"},{"key":"2510_CR26","doi-asserted-by":"publisher","first-page":"6852","DOI":"10.1109\/TIP.2020.2994443","volume":"29","author":"D Ren","year":"2020","unstructured":"Ren D, Shang W, Zhu P, Qinghua Hu, Meng D et al (2020) Single image deraining using bilateral recurrent network. IEEE Trans Image Process 29:6852\u20136863","journal-title":"IEEE Trans Image Process"},{"key":"2510_CR27","doi-asserted-by":"crossref","unstructured":"Xiao J,\u00a0Fu X, Liu A, Wu F, Jun Zha Z (2022) Image De-Raining Transformer. Accepted by IEEE transactions on pattern analysis and machine intelligence","DOI":"10.1109\/TPAMI.2022.3183612"},{"key":"2510_CR28","doi-asserted-by":"crossref","unstructured":"Jiang K,\u00a0Wang Z,\u00a0Chen C,\u00a0Wang Z,\u00a0Cui L, et al (2022) Magic ELF: image deraining meets association learning and transformer. In: ACM conference on multimedia, 827\u2013836.","DOI":"10.1145\/3503161.3547760"},{"key":"2510_CR29","doi-asserted-by":"crossref","unstructured":"Chen X,\u00a0Li H,\u00a0Li M,\u00a0Pan J. (2023) Learning a Sparse transformer network for effective image deraining. IEEE conference on computer vision and pattern recognition, 5896\u20135905","DOI":"10.1109\/CVPR52729.2023.00571"},{"key":"2510_CR30","doi-asserted-by":"publisher","first-page":"1927","DOI":"10.1109\/TIP.2023.3256763","volume":"32","author":"Y Song","year":"2023","unstructured":"Song Y, He Z, Qian H, Xin Du (2023) Vision transformers for single image dehazing. IEEE Trans Image Process 32:1927\u20131941","journal-title":"IEEE Trans Image Process"},{"key":"2510_CR31","doi-asserted-by":"crossref","unstructured":"Tu Z,\u00a0Talebi H,\u00a0Zhang H,\u00a0YangF,\u00a0Milanfar P,\u00a0et al (2022) MAXIM:\u00a0multi-axis\u00a0MLP\u00a0for\u00a0image processing. In: IEEE conference on computer vision and pattern recognition, 5759\u20135770","DOI":"10.1109\/CVPR52688.2022.00568"},{"key":"2510_CR32","doi-asserted-by":"crossref","unstructured":"Zamir SW,\u00a0Arora A,\u00a0Khan S,\u00a0Hayat M,\u00a0Shahbaz Khan F, et al (2022) Restormer: efficient transformer for high-resolution image restoration. In: IEEE conference on computer vision and pattern recognition, 5718\u20135729","DOI":"10.1109\/CVPR52688.2022.00564"},{"key":"2510_CR33","unstructured":"Kingma DP, Ba J (2015) Adam: a method for stochastic optimization. In: International conference on learning representations, 1\u201315"},{"issue":"11","key":"2510_CR34","doi-asserted-by":"publisher","first-page":"2599","DOI":"10.1109\/TPAMI.2018.2865304","volume":"41","author":"W Lai","year":"2018","unstructured":"Lai W, Huang J, Ahuja N, Yang M (2018) Fast and accurate image super-resolution with deep laplacian pyramid networks. IEEE Trans Pattern Anal Mach Intell 41(11):2599\u20132613","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"2510_CR35","doi-asserted-by":"crossref","unstructured":"Wang T Y, Yang X, Xu K, et al (2019) Spatial attentive single-image deraining with a high-quality real rain dataset. In: IEEE conference on computer vision and pattern recognition, 12270\u201312279.","DOI":"10.1109\/CVPR.2019.01255"},{"key":"2510_CR36","doi-asserted-by":"crossref","unstructured":"Wang T,\u00a0Yang X,\u00a0Xu K,\u00a0Chen S,\u00a0Zhang Q, et al (2020) A model-driven deep neural network for single image rain removal. In: IEEE conference on computer vision and pattern recognition, 3100\u20133109.","DOI":"10.1109\/CVPR42600.2020.00317"},{"key":"2510_CR37","doi-asserted-by":"crossref","unstructured":"Zamir SW,\u00a0Arora A,\u00a0Khan SH,\u00a0Hayat M,\u00a0Shahbaz Khan F, et al (2021) Multi-stage progressive image restoration. In: IEEE conference on computer vision and pattern recognition, 14821\u201314831","DOI":"10.1109\/CVPR46437.2021.01458"},{"key":"2510_CR38","doi-asserted-by":"crossref","unstructured":"Chen C, Li H (2021) Robust representation learning with feedback for single image deraining. In: IEEE conference on computer vision and pattern recognition, 7742\u20137751","DOI":"10.1109\/CVPR46437.2021.00765"},{"key":"2510_CR39","unstructured":"Gao H, Dang D (2023) Mixed hierarchy network for image restoration. CoRR\u2002abs\/2302.09554"},{"key":"2510_CR40","doi-asserted-by":"crossref","unstructured":"Chen X, Pan J, Lu J, Fan Z, Li H (2023) Hybrid CNN-transformer feature fusion for single image deraining. In: AAAI conference on artificial intelligence, 378\u2013386","DOI":"10.1609\/aaai.v37i1.25111"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-024-02510-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-024-02510-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-024-02510-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T03:01:25Z","timestamp":1757127685000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-024-02510-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,27]]},"references-count":40,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["2510"],"URL":"https:\/\/doi.org\/10.1007\/s13042-024-02510-y","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"type":"print","value":"1868-8071"},{"type":"electronic","value":"1868-808X"}],"subject":[],"published":{"date-parts":[[2024,12,27]]},"assertion":[{"value":"12 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 December 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","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"}}]}}