{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:13:53Z","timestamp":1760116433308,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T00:00:00Z","timestamp":1730937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Commission Horizon 2020 Framework Program","award":["861584","20190910"],"award-info":[{"award-number":["861584","20190910"]}]},{"name":"Taishan Distinguished Professor Fund","award":["861584","20190910"],"award-info":[{"award-number":["861584","20190910"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Due to channel noise and random atmospheric turbulence, retrieved satellite images are always distorted and degraded and so require further restoration before use in various applications. The latest quaternion-based weighted nuclear norm minimization (QWNNM) model, which utilizes the idea of low-rank matrix approximation and the quaternion representation of multi-channel satellite images, can achieve image restoration and enhancement. However, the QWNNM model ignores the impact of noise on similarity measurement, lacks the utilization of residual image information, and fixes the number of iterations. In order to address these drawbacks, we propose three adaptive strategies: adaptive noise-resilient block matching, adaptive feedback of residual image, and adaptive iteration stopping criterion in a new adaptive QWNNM model. Both simulation experiments with known noise\/blurring and real environment experiments with unknown noise\/blurring demonstrated that the effectiveness of adaptive QWNNM models outperformed the original QWNNM model and other state-of-the-art satellite image restoration models in very different technique approaches.<\/jats:p>","DOI":"10.3390\/rs16224152","type":"journal-article","created":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T09:24:13Z","timestamp":1730971453000},"page":"4152","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Satellite Image Restoration via an Adaptive QWNNM Model"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6492-0812","authenticated-orcid":false,"given":"Xudong","family":"Xu","sequence":"first","affiliation":[{"name":"Interdisciplinary Data Mining Group, School of Mathematics, Shandong University, Jinan 250100, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6449-4332","authenticated-orcid":false,"given":"Zhihua","family":"Zhang","sequence":"additional","affiliation":[{"name":"Interdisciplinary Data Mining Group, School of Mathematics, Shandong University, Jinan 250100, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3609-1963","authenticated-orcid":false,"given":"M. James C.","family":"Crabbe","sequence":"additional","affiliation":[{"name":"Wolfson College, Oxford University, Oxford OX2 6UD, UK"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2538","DOI":"10.1109\/TCSVT.2019.2927603","article-title":"Exemplar-Based Denoising: A Unified Low-Rank Recovery Framework","volume":"30","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2046","DOI":"10.1109\/TCSVT.2019.2923816","article-title":"Low Rank and Sparse Decomposition for Image and Video Applications","volume":"30","author":"Zarmehi","year":"2020","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2023","DOI":"10.1109\/TVCG.2017.2702738","article-title":"Patch-Based Image Inpainting via Two-Stage Low Rank Approximation","volume":"24","author":"Guo","year":"2018","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1145\/2184319.2184343","article-title":"Exact Matrix Completion via Convex Optimization","volume":"55","author":"Recht","year":"2012","journal-title":"Commun. ACM"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TIT.2010.2044061","article-title":"The Power of Convex Relaxation: Near-Optimal Matrix Completion","volume":"56","author":"Candes","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1137\/080738970","article-title":"A Singular Value Thresholding Algorithm for Matrix Completion","volume":"20","author":"Cai","year":"2010","journal-title":"SIAM J. Optim."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s11263-016-0930-5","article-title":"Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision","volume":"121","author":"Gu","year":"2017","journal-title":"Int. J. Comput. Vis."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1109\/TIP.2008.919370","article-title":"SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding","volume":"17","author":"Luisier","year":"2008","journal-title":"IEEE Trans. Image Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2080","DOI":"10.1109\/TIP.2007.901238","article-title":"Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering","volume":"16","author":"Dabov","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_10","unstructured":"Carmeli, A., and Turek, J. (2013). Quaternion K-SVD for Color Image Denoising. Tech. Isr. Inst. Technol. Tech. Rep., Available online: https:\/\/api.semanticscholar.org\/CorpusID:15559041."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1109\/TIP.2015.2397314","article-title":"Vector Sparse Representation of Color Image Using Quaternion Matrix Analysis","volume":"24","author":"Xu","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.ijleo.2018.08.013","article-title":"An improved non-local means filter for color image denoising","volume":"173","author":"Wang","year":"2018","journal-title":"Opt.-Int. J. Light Electron Opt."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3868","DOI":"10.1109\/TIP.2022.3176133","article-title":"Non-Local Robust Quaternion Matrix Completion for Large-Scale Color Image and Video Inpainting","volume":"31","author":"Jia","year":"2022","journal-title":"IEEE Trans. Image Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.neucom.2018.12.034","article-title":"Quaternion-Based Weighted Nuclear Norm Minimization for Color Image Denoising","volume":"332","author":"Yu","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"108665","DOI":"10.1016\/j.patcog.2022.108665","article-title":"Quaternion-Based Weighted Nuclear Norm Minimization for Color Image Restoration","volume":"128","author":"Huang","year":"2022","journal-title":"Pattern Recognit."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Huang, C., Li, J., and Gao, G. (2023). Review of Quaternion-Based Color Image Processing Methods. Mathematics, 11.","DOI":"10.3390\/math11092056"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/TIP.2021.3128321","article-title":"Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm","volume":"31","author":"Miao","year":"2022","journal-title":"IEEE Trans. Image Process."},{"key":"ref_18","first-page":"15","article-title":"Salient Region Detection Based on Frequency Domain Analysis for Remote Sensing Image","volume":"14","author":"Maheswari","year":"2023","journal-title":"Adv. Electron. Electr. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"32827","DOI":"10.1007\/s11042-023-14866-4","article-title":"Quaternion Discrete Orthogonal Hahn Moments Convolutional Neural Network for Color Image Classification and Face Recognition","volume":"82","author":"Mesbah","year":"2023","journal-title":"Multimed. Tools Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s10915-024-02671-6","article-title":"Quaternion-Aware Low-Rank Prior for Blind Color Image Deblurring","volume":"101","author":"Zhang","year":"2024","journal-title":"J. Sci. Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1412","DOI":"10.1109\/JBHI.2023.3346529","article-title":"Quaternion Cross-Modality Spatial Learning for Multi-Modal Medical Image Segmentation","volume":"28","author":"Chen","year":"2024","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"22705","DOI":"10.1007\/s11042-023-14474-2","article-title":"Image Super Resolution via Combination of Two Dimensional Quaternion Valued Singular Spectrum Analysis Based Denoising, Empirical Mode Decomposition Based Denoising and Discrete Cosine Transform Based Denoising Methods","volume":"82","author":"Cheng","year":"2023","journal-title":"Multimed. Tools Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"104781","DOI":"10.1016\/j.dsp.2024.104781","article-title":"Quaternion Optimized Model with Sparseness for Color Image Recovery","volume":"156","author":"Yang","year":"2025","journal-title":"Digit. Signal Prog."},{"key":"ref_24","unstructured":"MacQueen, J. (July, January 21). Some Methods for Classification and Analysis of Multivariate Observations. Proceedings of the fifth Berkeley Symposium on Mathematical Statistics & Probability, Berkeley, CA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2907","DOI":"10.1073\/pnas.96.6.2907","article-title":"Interpreting Patterns of Gene Expression with Self-Organizing Maps: Methods and Application to Hematopoietic Differentiation","volume":"96","author":"Tamayo","year":"1999","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1253\/jcj.62.750","article-title":"Fuzzy Cluster Analysis: A New Method to Predict Future Cardiac Events in Patients with Positive Stress Tests","volume":"62","author":"Peters","year":"1998","journal-title":"Jpn Circ. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/TIT.1982.1056457","article-title":"On the Structure of Vector Quantizers","volume":"28","author":"Gersho","year":"1982","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_28","first-page":"1","article-title":"Robust Principal Component Analysis?","volume":"58","author":"Li","year":"2011","journal-title":"J. ACM"},{"key":"ref_29","unstructured":"Liu, R., Lin, Z., Fernando, D.L.T., and Su, Z. (2012, January 16\u201321). Fixed-Rank Representation for Unsupervised Visual Learning. Proceedings of the 2012 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Providence, RI, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0024-3795(95)00543-9","article-title":"Quaternions and Matrices of Quaternions","volume":"251","author":"Zhang","year":"1997","journal-title":"Linear Algebra Its Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"30628","DOI":"10.1109\/ACCESS.2020.2973044","article-title":"Robust Dual-Color Watermarking Based on Quaternion Singular Value Decomposition","volume":"8","author":"Chen","year":"2020","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.neucom.2015.07.153","article-title":"Quaternion Discrete Cosine Transformation Signature Analysis in Crowd Scenes for Abnormal Event Detection","volume":"204","author":"Guo","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Schauerte, B., and Stiefelhagen, R. (2012, January 9\u201311). Predicting Human Gaze Using Quaternion DCT Image Signature Saliency and Face Detection. Proceedings of the 2012 IEEE Workshop on the Applications of Computer Vision (WACV), Breckenridge, CO, USA.","DOI":"10.1109\/WACV.2012.6163035"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1109\/TPAMI.1986.4767851","article-title":"A Computational Approach to Edge Detection","volume":"PAMI-8","author":"Canny","year":"1986","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1109\/TIP.2018.2871597","article-title":"Fast Adaptive Bilateral Filtering","volume":"28","author":"Gavaskar","year":"2019","journal-title":"IEEE Trans. Image Process. Publ. IEEE Signal Process. Soc."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Ono, S., and Yamada, I. (2014, January 23\u201328). Decorrelated Vectorial Total Variation. Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, USA.","DOI":"10.1109\/CVPR.2014.521"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Makinen, Y., Azzari, L., and Foi, A. (2019, January 22\u201325). Exact Transform-Domain Noise Variance for Collaborative Filtering of Stationary Correlated Noise. Proceedings of the 2019 IEEE International Conference on Image Processing (ICIP), Taipei, Taiwan.","DOI":"10.1109\/ICIP.2019.8802964"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"133076","DOI":"10.1109\/ACCESS.2020.3010127","article-title":"Optimized Wavelet-Based Satellite Image De-Noising with Multi-Population Differential Evolution-Assisted Harris Hawks Optimization Algorithm","volume":"8","author":"Golilarz","year":"2020","journal-title":"IEEE Access"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"8195","DOI":"10.1007\/s11760-024-03461-1","article-title":"Remote Sensing Image Denoising Based on Deformable Convolution and Attention-Guided Filtering in Progressive Framework","volume":"18","author":"Liu","year":"2024","journal-title":"Signal Image Video Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2508","DOI":"10.1049\/ipr2.12236","article-title":"Remote Sensing Image Super-resolution Based on Convolutional Blind Denoising Adaptive Dense Connection","volume":"15","author":"Yang","year":"2021","journal-title":"IET Image Process."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Yang, Y., and Newsam, S. (2010, January 2\u20135). Bag-of-Visual-Words and Spatial Extensions for Land-Use Classification. Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, San Jose, CA, USA.","DOI":"10.1145\/1869790.1869829"},{"key":"ref_42","first-page":"103","article-title":"Estimating PSNR in High Definition H.264\/AVC Video Sequences Using Artificial Neural Networks","volume":"17","author":"Slanina","year":"2008","journal-title":"Radioengineering"},{"key":"ref_43","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_44","doi-asserted-by":"crossref","first-page":"2378","DOI":"10.1109\/TIP.2011.2109730","article-title":"FSIM: A Feature Similarity Index for Image Quality Assessment","volume":"20","author":"Zhang","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"ref_45","unstructured":"Wald, L. (2010). Data Fusion. Definitions and Architectures-Fusion of Images of Different Spatial Resolutions, Presses des MINES."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3339","DOI":"10.1109\/TIP.2012.2191563","article-title":"Blind Image Quality Assessment: A Natural Scene Statistics Approach in the DCT Domain","volume":"21","author":"Saad","year":"2012","journal-title":"IEEE Trans. Image Process."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.image.2018.05.009","article-title":"Generalized Gaussian Scale Mixtures: A Model for Wavelet Coefficients of Natural Images","volume":"66","author":"Gupta","year":"2018","journal-title":"Signal Process. Image Commun."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1109\/TNNLS.2017.2649101","article-title":"Learning a No-Reference Quality Assessment Model of Enhanced Images with Big Data","volume":"29","author":"Gu","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/22\/4152\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:28:15Z","timestamp":1760113695000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/22\/4152"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,7]]},"references-count":48,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["rs16224152"],"URL":"https:\/\/doi.org\/10.3390\/rs16224152","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,11,7]]}}}