{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:01:10Z","timestamp":1760058070606,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Project Program of the Guangxi Key Laboratory of Digital Infrastructure","award":["GXDIOP2023007","AB24010340"],"award-info":[{"award-number":["GXDIOP2023007","AB24010340"]}]},{"name":"The Guangxi Key Research and Development Program","award":["GXDIOP2023007","AB24010340"],"award-info":[{"award-number":["GXDIOP2023007","AB24010340"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the advancement of technology, the information hiding capacity has significantly increased, allowing a cover image to conceal one or more secret images. However, this high hiding capacity often leads to contour shadows and color distortions, making the high-quality recovery of secret images extremely challenging. Existing image hiding algorithms based on Invertible Neural Networks (INNs) often discard useful information during the hiding process, resulting in poor quality of the recovered secret images, especially in multi-image hiding scenarios. The theoretical symmetry of INNs ensures the lossless reversibility of the embedder and decoder, but the lost information generated in practical image steganography disrupts this symmetry. To address this issue, we propose an INN-based image steganography framework that overcomes the limitations of current INN methods in image steganography applications. Our framework can embed multiple full-size secret images into cover images of the same size and utilize the correlation between the lost information and the secret and cover images to generate the lost information by combining the auxiliary model of the Dense\u2013Channel\u2013Spatial Attention Module to restore the symmetry of reversible neural networks, thereby improving the quality of the recovered images. In addition, we employ a multi-stage progressive training strategy to improve the recovery of lost information, thereby achieving high-quality secret image recovery. To further enhance the security of the hiding process, we introduced a multi-scale wavelet loss function into the loss function. Our method significantly improves the quality of image recovery in single-image steganography tasks across multiple datasets (DIV2K, COCO, ImageNet), with a PSNR reaching up to 50.37 dB (an improvement of over 3 dB compared to other methods). The results show that our method outperforms other state-of-the-art (SOTA) image hiding techniques on different datasets and achieves strong performance in multi-image hiding as well.<\/jats:p>","DOI":"10.3390\/sym17030456","type":"journal-article","created":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T11:02:31Z","timestamp":1742295751000},"page":"456","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Recovery-Enhanced Image Steganography Framework with Auxiliary Model Based on Invertible Neural Networks"],"prefix":"10.3390","volume":"17","author":[{"given":"Lin","family":"Huo","sequence":"first","affiliation":[{"name":"School of Computer and Electronic Information, Guangxi University, Nanning 530004, China"},{"name":"China-ASEAN School of Economics, Guangxi University, Nanning 530004, China"},{"name":"China-ASEAN Collaborative Innovation Center for Regional Development, Guangxi University, Nanning 530004, China"}]},{"given":"Kai","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer and Electronic Information, Guangxi University, Nanning 530004, China"}]},{"given":"Jie","family":"Wei","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Digital Infrastructure, Guangxi Information Center, Nanning 530000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MC.1998.4655281","article-title":"Exploring steganography: Seeing the unseen","volume":"31","author":"Johnson","year":"1998","journal-title":"Computer"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1109\/83.777088","article-title":"Spread spectrum image steganography","volume":"8","author":"Marvel","year":"1999","journal-title":"IEEE Trans. Image Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/978-3-642-16435-4_13","article-title":"Using High-Dimensional Image Models to Perform Highly Undetectable Steganography","volume":"6387","author":"Filler","year":"2010","journal-title":"Lect. Notes Comput. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Holub, V., and Fridrich, J. (2012, January 2\u20135). Designing Steganographic Distortion Using Directional Filters. Proceedings of the IEEE Workshop on Information Forensic and Security, Costa Adeje, Spain.","DOI":"10.1109\/WIFS.2012.6412655"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1687-417X-2014-1","article-title":"Universal distortion function for steganography in an arbitrary domain","volume":"2014","author":"Holub","year":"2014","journal-title":"Eurasip J. Inf. Secur."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/j.patcog.2003.08.007","article-title":"Hiding data in images by simple LSB substitution","volume":"37","author":"Chan","year":"2004","journal-title":"Pattern Recognit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1016\/j.sigpro.2008.12.017","article-title":"Reversible image hiding scheme using predictive coding and histogram shifting","volume":"89","author":"Tsai","year":"2009","journal-title":"Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1016\/S0167-8655(02)00402-6","article-title":"A steganographic method for images by pixel-value differencing","volume":"24","author":"Wu","year":"2003","journal-title":"Pattern Recognit. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Pan, F., Li, J., and Yang, X. (2011, January 9\u201311). Image steganography method based on PVD and modulus function. Proceedings of the 2011 International Conference on Electronics, Communications and Control (ICECC), Ningbo, China.","DOI":"10.1109\/ICECC.2011.6067590"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4639","DOI":"10.1007\/s12652-022-04366-y","article-title":"A secure data hiding approach based on least-significant-bit and nature-inspired optimization techniques","volume":"14","author":"Hameed","year":"2023","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Fridrich, J. (2007, January 20\u201321). Statistically undetectable jpeg steganography: Dead ends challenges, and opportunities. Proceedings of the 9th Workshop on Multimedia & Security, Dallas, TX, USA.","DOI":"10.1145\/1288869.1288872"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sallee, P. (2003). Model-Based Steganography, Springer.","DOI":"10.1007\/978-3-540-24624-4_12"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/MSECP.2003.1203220","article-title":"Hide and seek: An introduction to steganography","volume":"1","author":"Provos","year":"2003","journal-title":"IEEE Secur. Priv."},{"key":"ref_14","unstructured":"Hetzl, S., and Mutzel, P. (2005, January 19\u201321). A Graph\u2013Theoretic Approach to Steganography. Proceedings of the Communications & Multimedia Security, Ifip Tc-6 Tc-11 International Conference, CMS, Salzburg, Austria."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2768","DOI":"10.1016\/j.ins.2007.02.019","article-title":"Reversible hiding in DCT-based compressed images","volume":"177","author":"Chang","year":"2007","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s00521-014-1702-1","article-title":"Artificial neural network for steganography","volume":"26","author":"Husien","year":"2015","journal-title":"Neural Comput. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.cose.2016.11.016","article-title":"Exploring the learning capabilities of convolutional neural networks for robust image watermarking","volume":"65","author":"Kandi","year":"2017","journal-title":"Comput. Secur."},{"key":"ref_18","unstructured":"Mun, S.M., Nam, S.H., Jang, H.U., Kim, D., and Lee, H.K. (2017). A Robust Blind Watermarking Using Convolutional Neural Network. arXiv."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhu, J., Kaplan, R., Johnson, J., and Fei-Fei, L. (2018, January 8\u201314). HiDDeN: Hiding Data With Deep Networks. Proceedings of the Computer Vision\u2014ECCV 2018: 15th European Conference, Munich, Germany.","DOI":"10.1007\/978-3-030-01267-0_40"},{"key":"ref_20","unstructured":"Baluja, S. (2017, January 4\u20139). Hiding Images in Plain Sight: Deep Steganography. Proceedings of the Neural Information Processing Systems, Long Beach, CA, USA."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Jing, J., Deng, X., Xu, M., Wang, J., and Guan, Z. (2021, January 11\u201317). HiNet: Deep Image Hiding by Invertible Network. Proceedings of the 2021 IEEE\/CVF International Conference on Computer Vision (ICCV), Montreal, BC, Canada.","DOI":"10.1109\/ICCV48922.2021.00469"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Lu, S.P., Wang, R., Zhong, T., and Rosin, P.L. (2021, January 19\u201325). Large-capacity Image Steganography Based on Invertible Neural Networks. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Virtual.","DOI":"10.1109\/CVPR46437.2021.01067"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Fang, H., Qiu, Y., Chen, K., Zhang, J., Zhang, W., and Chang, E.C. (2023, January 7\u201314). Flow-Based Robust Watermarking with Invertible Noise Layer for Black-Box Distortions. Proceedings of the AAAI Conference on Artificial Intelligence, Washington, DC, USA.","DOI":"10.1609\/aaai.v37i4.25633"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1109\/TPAMI.2022.3141725","article-title":"DeepMIH: Deep invertible network for multiple image hiding","volume":"45","author":"Guan","year":"2022","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3137","DOI":"10.1109\/TMM.2023.3307970","article-title":"iSCMIS: Spatial-Channel Attention Based Deep Invertible Network for Multi-Image Steganography","volume":"26","author":"Li","year":"2023","journal-title":"IEEE Trans. Multimed."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"103719","DOI":"10.1016\/j.ipm.2024.103719","article-title":"Lossless image steganography: Regard steganography as super-resolution","volume":"61","author":"Wang","year":"2024","journal-title":"Inf. Process. Manag."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"ur Rehman, A., Rahim, R., Nadeem, S., and ul Hussain, S. (2018, January 8\u201314). End-to-End Trained CNN Encoder-Decoder Networks for Image Steganography. Proceedings of the Computer Vision\u2014ECCV 2018 Workshops, Munich, Germany.","DOI":"10.1007\/978-3-030-11018-5_64"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Weng, X., Li, Y., Chi, L., and Mu, Y. (2019, January 10\u201313). High-Capacity Convolutional Video Steganography with Temporal Residual Modeling. Proceedings of the 2019 on International Conference on Multimedia Retrieval, Ottawa, ON, Canada.","DOI":"10.1145\/3323873.3325011"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1109\/TPAMI.2019.2901877","article-title":"Hiding Images Within Images","volume":"42","author":"Baluja","year":"2019","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"9451","DOI":"10.1109\/TNNLS.2022.3175627","article-title":"Composition-Aware Image Steganography Through Adversarial Self-Generated Supervision","volume":"34","author":"Zheng","year":"2023","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"123540","DOI":"10.1016\/j.eswa.2024.123540","article-title":"High invisibility image steganography with wavelet transform and generative adversarial network","volume":"249","author":"Yao","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6128","DOI":"10.1109\/TCSVT.2023.3348291","article-title":"Invisible and Steganalysis-Resistant Deep Image Hiding Based on One-Way Adversarial Invertible Networks","volume":"34","author":"Hu","year":"2024","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_33","unstructured":"Dinh, L., Krueger, D., and Bengio, Y. (2014). NICE: Non-linear Independent Components Estimation. arXiv."},{"key":"ref_34","unstructured":"Dinh, L., Sohl-Dickstein, J., and Bengio, S. (2016). Density estimation using Real NVP. arXiv."},{"key":"ref_35","unstructured":"Kingma, D.P., and Dhariwal, P. (2018). Glow: Generative Flow with Invertible 1x1 Convolutions. arXiv."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Van der Ouderaa, T.F.A., and Worrall, D.E. (2019, January 15\u201320). Reversible GANs for Memory-efficient Image-to-Image Translation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00485"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Xiao, M., Zheng, S., Liu, C., Wang, Y., He, D., Ke, G., Bian, J., Lin, Z., and Liu, T.Y. (2020, January 23\u201328). Invertible Image Rescaling. Proceedings of the Computer Vision\u2014ECCV 2020: 16th European Conference, Glasgow, UK.","DOI":"10.1007\/978-3-030-58452-8_8"},{"key":"ref_38","unstructured":"Wang, Y., Xiao, M., Liu, C., Zheng, S., and Liu, T.Y. (2020). Modeling Lost Information in Lossy Image Compression. arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Xu, Y., Mou, C., Hu, Y.F., Xie, J., and Zhang, J. (2022, January 19\u201320). Robust Invertible Image Steganography. Proceedings of the 2022 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA.","DOI":"10.1109\/CVPR52688.2022.00772"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Wang, X., Yu, K., Wu, S., Gu, J., Liu, Y., Dong, C., Loy, C.C., Qiao, Y., and Tang, X. (2018). ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks, Springer.","DOI":"10.1007\/978-3-030-11021-5_5"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Agustsson, E., and Timofte, R. (2017, January 21\u201326). NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study. Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), Honolulu, HI, USA.","DOI":"10.1109\/CVPRW.2017.150"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11263-015-0816-y","article-title":"ImageNet Large Scale Visual Recognition Challenge","volume":"115","author":"Russakovsky","year":"2015","journal-title":"Int. J. Comput. Vis."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Lin, T.Y., Maire, M., Belongie, S.J., Hays, J., Perona, P., Ramanan, D., Doll\u00e1r, P., and Zitnick, C.L. (2014, January 6\u201312). Microsoft COCO: Common Objects in Context. Proceedings of the European Conference on Computer Vision, Zurich, Switzerland.","DOI":"10.1007\/978-3-319-10602-1_48"},{"key":"ref_44","unstructured":"Kingma, D., and Ba, J. (2014). Adam: A Method for Stochastic Optimization. arXiv."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process"},{"key":"ref_46","unstructured":"Boehm, B. (2014). StegExpose\u2014A Tool for Detecting LSB Steganography. arXiv."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/456\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:56:05Z","timestamp":1760028965000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/456"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,18]]},"references-count":46,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030456"],"URL":"https:\/\/doi.org\/10.3390\/sym17030456","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,3,18]]}}}