{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T04:10:06Z","timestamp":1771301406238,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T00:00:00Z","timestamp":1631664000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61775121, 11574311"],"award-info":[{"award-number":["61775121, 11574311"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014103","name":"key research and development program of Shandong Province","doi-asserted-by":"publisher","award":["2018GGX101002"],"award-info":[{"award-number":["2018GGX101002"]}],"id":[{"id":"10.13039\/100014103","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2019QF006"],"award-info":[{"award-number":["ZR2019QF006"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Multi-image encryption technology is a vital branch of optical encryption technology. The traditional encryption method can only encrypt a small number of images, which greatly restricts its application in practice. In this paper, a new multi-image encryption method based on sinusoidal stripe coding frequency multiplexing and deep learning is proposed to realize the encryption of a greater number of images. In the process of encryption, several images are grouped, and each image in each group is first encoded with a random matrix and then modulated with a specific sinusoidal stripe; therefore, the dominant frequency of each group of images can be separated in the Fourier frequency domain. Each group is superimposed and scrambled to generate the final ciphertext. In the process of decryption, deep learning is used to improve the quality of decrypted image and the decryption speed. Specifically, the obtained ciphertext can be sent into the trained neural network and then the plaintext image can be reconstructed directly. Experimental analysis shows that when 32 images are encrypted, the CC of the decrypted result can reach more than 0.99. The efficiency of the proposed encryption method is proved in terms of histogram analysis, adjacent pixels correlation analysis, anti-noise attack analysis and resistance to occlusion attacks analysis. The encryption method has the advantages of large amount of information, good robustness and fast decryption speed.<\/jats:p>","DOI":"10.3390\/s21186178","type":"journal-article","created":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T12:00:44Z","timestamp":1631707244000},"page":"6178","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Multi-Image Encryption Based on Sinusoidal Coding Frequency Multiplexing and Deep Learning"],"prefix":"10.3390","volume":"21","author":[{"given":"Qi","family":"Li","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Qingdao 266237, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6439-1862","authenticated-orcid":false,"given":"Xiangfeng","family":"Meng","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Qingdao 266237, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3577-3428","authenticated-orcid":false,"given":"Yongkai","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Qingdao 266237, China"}]},{"given":"Huazheng","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Qingdao 266237, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1364\/AOP.1.000589","article-title":"Optical image compression and encryption methods","volume":"1","author":"Alfalou","year":"2009","journal-title":"Adv. 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