{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T06:29:39Z","timestamp":1776752979734,"version":"3.51.2"},"reference-count":51,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Mathematical morphology is a powerful tool for image processing tasks. The main difficulty in designing mathematical morphological algorithm is deciding the order of operators\/filters and the corresponding structuring elements (SEs). In this work, we develop morphological network composed of alternate sequences of dilation and erosion layers, which depending on learned SEs, may form opening or closing layers. These layers in the right order along with linear combination (of their outputs) are useful in extracting image features and processing them. Structuring elements in the network are learned by back-propagation method guided by minimization of the loss function. Efficacy of the proposed network is established by applying it to two interesting image restoration problems, namely<jats:italic>de-raining<\/jats:italic>and<jats:italic>de-hazing<\/jats:italic>. Results are comparable to that of many state-of-the-art algorithms for most of the images. It is also worth mentioning that the number of network parameters to handle is much less than that of popular convolutional neural network for similar tasks. The source code can be found here<jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/github.com\/ranjanZ\/Mophological-Opening-Closing-Net\">https:\/\/github.com\/ranjanZ\/Mophological-Opening-Closing-Net<\/jats:ext-link><\/jats:p>","DOI":"10.1515\/mathm-2020-0103","type":"journal-article","created":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T03:47:55Z","timestamp":1600141675000},"page":"87-107","source":"Crossref","is-referenced-by-count":26,"title":["Image Restoration by Learning Morphological Opening-Closing Network"],"prefix":"10.1515","volume":"4","author":[{"given":"Ranjan","family":"Mondal","sequence":"first","affiliation":[{"name":"Indian Statistical Institute , Kolkata , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moni Shankar","family":"Dey","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology , Bombay , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bhabatosh","family":"Chanda","sequence":"additional","affiliation":[{"name":"Indian Statistical Institute , Kolkata , India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2020,9,11]]},"reference":[{"key":"2022042712261288296_j_mathm-2020-0103_ref_001_w2aab3b7c10b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"[1] Codruta O Ancuti, Cosmin Ancuti, Radu Timofte, and Christophe De Vleeschouwer. O-haze: a dehazing benchmark with real hazy and haze-free outdoor images. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 754\u2013762, 2018.10.1109\/CVPRW.2018.00119","DOI":"10.1109\/CVPRW.2018.00119"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_002_w2aab3b7c10b1b6b1ab1ab2Aa","doi-asserted-by":"crossref","unstructured":"[2] Cosmin Ancuti, Codruta O Ancuti, and Christophe De Vleeschouwer. D-hazy: A dataset to evaluate quantitatively dehazing algorithms. In 2016 IEEE International Conference on Image Processing (ICIP), pages 2226\u20132230. IEEE, 2016.10.1109\/ICIP.2016.7532754","DOI":"10.1109\/ICIP.2016.7532754"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_003_w2aab3b7c10b1b6b1ab1ab3Aa","unstructured":"[3] Cosmin Ancuti, Codruta O Ancuti, Radu Timofte, Luc Van Gool, Lei Zhang, Ming-Hsuan Yang, Vishal M Patel, He Zhang, Vishwanath A Sindagi, Ruhao Zhao, et al. Ntire 2018 challenge on image dehazing: Methods and results. In CVPR Workshops, volume 1, 2018.10.1109\/CVPRW.2018.00134"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_004_w2aab3b7c10b1b6b1ab1ab4Aa","doi-asserted-by":"crossref","unstructured":"[4] Jesus Angulo. A mathematical morphology approach to cell shape analysis. In Progress in Industrial Mathematics at ECMI 2006, pages 543\u2013547. Springer, 2008.10.1007\/978-3-540-71992-2_87","DOI":"10.1007\/978-3-540-71992-2_87"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_005_w2aab3b7c10b1b6b1ab1ab5Aa","doi-asserted-by":"crossref","unstructured":"[5] Amy Bearman, Olga Russakovsky, Vittorio Ferrari, and Li Fei-Fei. What\u2019s the point: Semantic segmentation with point supervision. In European conference on computer vision, pages 549\u2013565. Springer, 2016.10.1007\/978-3-319-46478-7_34","DOI":"10.1007\/978-3-319-46478-7_34"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_006_w2aab3b7c10b1b6b1ab1ab6Aa","doi-asserted-by":"crossref","unstructured":"[6] D. Berman, T. Treibitz, and S. Avidan. Non-local Image Dehazing. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1674\u20131682, June 2016. 10.1109\/CVPR.2016.185.10.1109\/CVPR.2016.185","DOI":"10.1109\/CVPR.2016.185"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_007_w2aab3b7c10b1b6b1ab1ab7Aa","doi-asserted-by":"crossref","unstructured":"[7] Alan C Bovik. Handbook of image and video processing. 2005.10.1201\/9781420027822.ch14","DOI":"10.1201\/9781420027822.ch14"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_008_w2aab3b7c10b1b6b1ab1ab8Aa","doi-asserted-by":"crossref","unstructured":"[8] Bolun Cai, Xiangmin Xu, Kui Jia, Chunmei Qing, and Dacheng Tao. Dehazenet: An end-to-end system for single image haze removal. IEEE Transactions on Image Processing, 25(11):5187\u20135198, 2016.","DOI":"10.1109\/TIP.2016.2598681"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_009_w2aab3b7c10b1b6b1ab1ab9Aa","unstructured":"[9] Nick Efford. Digital image processing: a practical introduction using java (with CD-ROM). Addison-Wesley Longman Publishing Co., Inc., 2000."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_010_w2aab3b7c10b1b6b1ab1ac10Aa","doi-asserted-by":"crossref","unstructured":"[10] Raanan Fattal. Dehazing using color-lines. ACM transactions on graphics (TOG), 34(1):13, 2014.10.1145\/2651362","DOI":"10.1145\/2651362"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_011_w2aab3b7c10b1b6b1ab1ac11Aa","doi-asserted-by":"crossref","unstructured":"[11] Raanan Fattal. Dehazing Using Color-Lines. ACM Trans. Graph., 34(1):13:1\u201313:14, December 2014. ISSN 0730-0301. 10.1145\/2651362. URL http:\/\/doi.acm.org\/10.1145\/2651362.10.1145\/2651362","DOI":"10.1145\/2651362"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_012_w2aab3b7c10b1b6b1ab1ac12Aa","doi-asserted-by":"crossref","unstructured":"[12] Richard J Feehs and Gonzalo R Arce. Multidimensional morphological edge detection. In Visual Communications and Image Processing II, volume 845, pages 285\u2013292. International Society for Optics and Photonics, 1987.10.1117\/12.976517","DOI":"10.1117\/12.976517"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_013_w2aab3b7c10b1b6b1ab1ac13Aa","doi-asserted-by":"crossref","unstructured":"[13] Gianni Franchi, Amin Fehri, and Angela Yao. Deep morphological networks. Pattern Recognition, page 107246, 2020.10.1016\/j.patcog.2020.107246","DOI":"10.1016\/j.patcog.2020.107246"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_014_w2aab3b7c10b1b6b1ab1ac14Aa","doi-asserted-by":"crossref","unstructured":"[14] Xueyang Fu, Jiabin Huang, Xinghao Ding, Yinghao Liao, and John Paisley. Clearing the skies: A deep network architecture for single-image rain removal. IEEE TIP, 26(6):2944\u20132956, 2017.","DOI":"10.1109\/TIP.2017.2691802"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_015_w2aab3b7c10b1b6b1ab1ac15Aa","unstructured":"[15] Xueyang Fu, Jiabin Huang, Delu Zeng, Yue Huang, Xinghao Ding, and John Paisley. Removing rain from single images via a deep detail network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3855\u20133863, 2017."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_016_w2aab3b7c10b1b6b1ab1ac16Aa","doi-asserted-by":"crossref","unstructured":"[16] Ross Girshick. Fast r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 1440\u20131448, 2015.10.1109\/ICCV.2015.169","DOI":"10.1109\/ICCV.2015.169"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_017_w2aab3b7c10b1b6b1ab1ac17Aa","unstructured":"[17] Xavier Glorot and Yoshua Bengio. Understanding the diflculty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pages 249\u2013256, 2010."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_018_w2aab3b7c10b1b6b1ab1ac18Aa","doi-asserted-by":"crossref","unstructured":"[18] Kaiming He, Jian Sun, and Xiaoou Tang. Single image haze removal using dark channel prior. IEEE transactions on pattern analysis and machine intelligence, 33(12):2341\u20132353, 2010.10.1109\/TPAMI.2010.16820820075","DOI":"10.1109\/TPAMI.2010.168"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_019_w2aab3b7c10b1b6b1ab1ac19Aa","doi-asserted-by":"crossref","unstructured":"[19] Kaiming He, Jian Sun, and Xiaoou Tang. Single Image Haze Removal Using Dark Channel Prior. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(12):2341\u20132353, December 2011. ISSN 0162-8828. 10.1109\/TPAMI.2010.168.10.1109\/TPAMI.2010.168","DOI":"10.1109\/TPAMI.2010.168"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_020_w2aab3b7c10b1b6b1ab1ac20Aa","unstructured":"[20] Kaiming He, Georgia Gkioxari, Piotr Doll\u00e1r, and Ross Girshick. Mask r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 2961\u20132969, 2017."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_021_w2aab3b7c10b1b6b1ab1ac21Aa","doi-asserted-by":"crossref","unstructured":"[21] HJAM Heijmans, Michael Buckley, and Hugues Talbot. Path-based morphological openings. In 2004 International Conference on Image Processing, 2004. ICIP\u201904., volume 5, pages 3085\u20133088. IEEE, 2004.","DOI":"10.1109\/ICIP.2004.1421765"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_022_w2aab3b7c10b1b6b1ab1ac22Aa","unstructured":"[22] Harald Koschmieder. Theorie der horizontalen sichtweite. Beitrage zur Physik der freien Atmosphare, pages 33\u201353, 1924."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_023_w2aab3b7c10b1b6b1ab1ac23Aa","unstructured":"[23] Boyi Li, Xiulian Peng, Zhangyang Wang, Jizheng Xu, and Dan Feng. Aod-net: All-in-one dehazing network. In Proceedings of the IEEE International Conference on Computer Vision, pages 4770\u20134778, 2017."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_024_w2aab3b7c10b1b6b1ab1ac24Aa","unstructured":"[24] Boyi Li, Xiulian Peng, Zhangyang Wang, Jizheng Xu, and Dan Feng. AOD-Net: All-In-One Dehazing Network. In Proceedings of the IEEE International Conference on Computer Vision, pages 4770\u20134778, 2017."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_025_w2aab3b7c10b1b6b1ab1ac25Aa","doi-asserted-by":"crossref","unstructured":"[25] Yu Li, Robby T Tan, Xiaojie Guo, Jiangbo Lu, and Michael S Brown. Rain streak removal using layer priors. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2736\u20132744, 2016.10.1109\/CVPR.2016.299","DOI":"10.1109\/CVPR.2016.299"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_026_w2aab3b7c10b1b6b1ab1ac26Aa","doi-asserted-by":"crossref","unstructured":"[26] Yu Luo, Yong Xu, and Hui Ji. Removing rain from a single image via discriminative sparse coding. In Proceedings of the IEEE International Conference on Computer Vision, pages 3397\u20133405, 2015.10.1109\/ICCV.2015.388","DOI":"10.1109\/ICCV.2015.388"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_027_w2aab3b7c10b1b6b1ab1ac27Aa","unstructured":"[27] Gili Mendel. Optical character recognition using morphological attributes. 1993."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_028_w2aab3b7c10b1b6b1ab1ac28Aa","doi-asserted-by":"crossref","unstructured":"[28] Gaofeng Meng, Ying Wang, Jiangyong Duan, Shiming Xiang, and Chunhong Pan. Eflcient image dehazing with boundary constraint and contextual regularization. In Proceedings of the IEEE international conference on computer vision, pages 617\u2013624, 2013.10.1109\/ICCV.2013.82","DOI":"10.1109\/ICCV.2013.82"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_029_w2aab3b7c10b1b6b1ab1ac29Aa","doi-asserted-by":"crossref","unstructured":"[29] Ranjan Mondal, Sanchayan Santra, and Bhabatosh Chanda. Image dehazing by joint estimation of transmittance and airlight using bi-directional consistency loss minimized fcn. In CVPR Workshops, pages 920\u2013928, 2018.10.1109\/CVPRW.2018.00137","DOI":"10.1109\/CVPRW.2018.00137"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_030_w2aab3b7c10b1b6b1ab1ac30Aa","doi-asserted-by":"crossref","unstructured":"[30] Ranjan Mondal, Deepayan Chakraborty, and Bhabatosh Chanda. Learning 2d morphological network for old document image binarization. In 2019 International Conference on Document Analysis and Recognition (ICDAR), pages 65\u201370. IEEE, 2019.10.1109\/ICDAR.2019.00020","DOI":"10.1109\/ICDAR.2019.00020"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_031_w2aab3b7c10b1b6b1ab1ac31Aa","doi-asserted-by":"crossref","unstructured":"[31] Ranjan Mondal, Pulak Purkait, Sanchayan Santra, and Bhabatosh Chanda. Morphological networks for image de-raining. In International Conference on Discrete Geometry for Computer Imagery, pages 262\u2013275. Springer, 2019.10.1007\/978-3-030-14085-4_21","DOI":"10.1007\/978-3-030-14085-4_21"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_032_w2aab3b7c10b1b6b1ab1ac32Aa","unstructured":"[32] Ranjan Mondal, Sanchayan Santra, and Bhabatosh Chanda. Dense Morphological Network: An Universal Function Approximator. arXiv e-prints, art. arXiv:1901.00109, January 2019."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_033_w2aab3b7c10b1b6b1ab1ac33Aa","doi-asserted-by":"crossref","unstructured":"[33] Susanta Mukhopadhyay and Bhabatosh Chanda. A multiscale morphological approach to local contrast enhancement. Signal Processing, 80(4):685\u2013696, 2000.10.1016\/S0165-1684(99)00161-9","DOI":"10.1016\/S0165-1684(99)00161-9"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_034_w2aab3b7c10b1b6b1ab1ac34Aa","unstructured":"[34] Hyeonwoo Noh, Seunghoon Hong, and Bohyung Han. Learning deconvolution network for semantic segmentation. In Proceedings of the IEEE international conference on computer vision, pages 1520\u20131528, 2015."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_035_w2aab3b7c10b1b6b1ab1ac35Aa","doi-asserted-by":"crossref","unstructured":"[35] Bryan A Plummer, Liwei Wang, Chris M Cervantes, Juan C Caicedo, Julia Hockenmaier, and Svetlana Lazebnik. Flickr30k entities: Collecting region-to-phrase correspondences for richer image-to-sentence models. In Proceedings of the IEEE international conference on computer vision, pages 2641\u20132649, 2015.10.1109\/ICCV.2015.303","DOI":"10.1109\/ICCV.2015.303"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_036_w2aab3b7c10b1b6b1ab1ac36Aa","unstructured":"[36] Kendall Preston Jr and Michael JB Duff. Modern cellular automata: theory and applications. Springer Science & Business Media, 2013."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_037_w2aab3b7c10b1b6b1ab1ac37Aa","unstructured":"[37] Joseph Redmon and Ali Farhadi. Yolov3: An incremental improvement. arXiv preprint arXiv:1804.02767, 2018."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_038_w2aab3b7c10b1b6b1ab1ac38Aa","doi-asserted-by":"crossref","unstructured":"[38] Wenqi Ren, Si Liu, Hua Zhang, Jinshan Pan, Xiaochun Cao, and Ming-Hsuan Yang. Single image dehazing via multi-scale convolutional neural networks. In European conference on computer vision, pages 154\u2013169. Springer, 2016.10.1007\/978-3-319-46475-6_10","DOI":"10.1007\/978-3-319-46475-6_10"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_039_w2aab3b7c10b1b6b1ab1ac39Aa","doi-asserted-by":"crossref","unstructured":"[39] Wenqi Ren, Si Liu, Hua Zhang, Jinshan Pan, Xiaochun Cao, and Ming-Hsuan Yang. Single Image Dehazing via Multi-scale Convolutional Neural Networks. In Computer Vision - ECCV 2016, Lecture Notes in Computer Science, pages 154\u2013169. Springer, Cham, October 2016. 10.1007\/978-3-319-46475-6_10.10.1007\/978-3-319-46475-6_10","DOI":"10.1007\/978-3-319-46475-6_10"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_040_w2aab3b7c10b1b6b1ab1ac40Aa","doi-asserted-by":"crossref","unstructured":"[40] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In International Conference on Medical image computing and computer-assisted intervention, pages 234\u2013241. Springer, 2015.10.1007\/978-3-319-24574-4_28","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_041_w2aab3b7c10b1b6b1ab1ac41Aa","unstructured":"[41] A Rosenfeld. Ac kak digital picture processing vol. 2, 1982."},{"key":"2022042712261288296_j_mathm-2020-0103_ref_042_w2aab3b7c10b1b6b1ab1ac42Aa","doi-asserted-by":"crossref","unstructured":"[42] Dan Schonfeld and John Goutsias. Optimal morphological pattern restoration from noisy binary images. IEEE Transactions on Pattern Analysis & Machine Intelligence, (1):14\u201329, 1991.10.1109\/34.67627","DOI":"10.1109\/34.67627"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_043_w2aab3b7c10b1b6b1ab1ac43Aa","doi-asserted-by":"crossref","unstructured":"[43] Stanley R Sternberg. Grayscale morphology. Computer vision, graphics, and image processing, 35(3):333\u2013355, 1986.10.1016\/0734-189X(86)90004-6","DOI":"10.1016\/0734-189X(86)90004-6"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_044_w2aab3b7c10b1b6b1ab1ac44Aa","doi-asserted-by":"crossref","unstructured":"[44] Ketan Tang, Jianchao Yang, and Jue Wang. Investigating haze-relevant features in a learning framework for image dehazing. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2995\u20133000, 2014.10.1109\/CVPR.2014.383","DOI":"10.1109\/CVPR.2014.383"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_045_w2aab3b7c10b1b6b1ab1ac45Aa","doi-asserted-by":"crossref","unstructured":"[45] Luc Vincent. Morphological area openings and closings for grey-scale images. In Shape in Picture, pages 197\u2013208. Springer, 1994.10.1007\/978-3-662-03039-4_13","DOI":"10.1007\/978-3-662-03039-4_13"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_046_w2aab3b7c10b1b6b1ab1ac46Aa","doi-asserted-by":"crossref","unstructured":"[46] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE TIP, 13(4):600\u2013612, 2004.","DOI":"10.1109\/TIP.2003.819861"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_047_w2aab3b7c10b1b6b1ab1ac47Aa","doi-asserted-by":"crossref","unstructured":"[47] He Zhang and Vishal M Patel. Densely connected pyramid dehazing network. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3194\u20133203, 2018.10.1109\/CVPR.2018.00337","DOI":"10.1109\/CVPR.2018.00337"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_048_w2aab3b7c10b1b6b1ab1ac48Aa","doi-asserted-by":"crossref","unstructured":"[48] He Zhang, Vishwanath Sindagi, and Vishal M Patel. Multi-scale single image dehazing using perceptual pyramid deep network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 902\u2013911, 2018.10.1109\/CVPRW.2018.00135","DOI":"10.1109\/CVPRW.2018.00135"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_049_w2aab3b7c10b1b6b1ab1ac49Aa","doi-asserted-by":"crossref","unstructured":"[49] Kai Zhang, Wangmeng Zuo, Yunjin Chen, Deyu Meng, and Lei Zhang. Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising. IEEE Transactions on Image Processing, 26(7):3142\u20133155, 2017.","DOI":"10.1109\/TIP.2017.2662206"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_050_w2aab3b7c10b1b6b1ab1ac50Aa","doi-asserted-by":"crossref","unstructured":"[50] Kai Zhang, Wangmeng Zuo, and Lei Zhang. Ffdnet: Toward a fast and flexible solution for cnn-based image denoising. IEEE Transactions on Image Processing, 27(9):4608\u20134622, 2018.","DOI":"10.1109\/TIP.2018.2839891"},{"key":"2022042712261288296_j_mathm-2020-0103_ref_051_w2aab3b7c10b1b6b1ab1ac51Aa","doi-asserted-by":"crossref","unstructured":"[51] Qingsong Zhu, Jiaming Mai, and Ling Shao. A fast single image haze removal algorithm using color attenuation prior. IEEE transactions on image processing, 24(11):3522\u20133533, 2015.10.1109\/TIP.2015.244619126099141","DOI":"10.1109\/TIP.2015.2446191"}],"container-title":["Mathematical Morphology - Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/mathm\/4\/1\/article-p87.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2020-0103\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2020-0103\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T20:31:47Z","timestamp":1723581107000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2020-0103\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,1]]},"references-count":51,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,3,25]]},"published-print":{"date-parts":[[2020,1,1]]}},"alternative-id":["10.1515\/mathm-2020-0103"],"URL":"https:\/\/doi.org\/10.1515\/mathm-2020-0103","relation":{},"ISSN":["2353-3390"],"issn-type":[{"value":"2353-3390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,1]]}}}