{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:21:18Z","timestamp":1760242878114,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,17]],"date-time":"2016-10-17T00:00:00Z","timestamp":1476662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Basic Research Program of China","award":["2013CB329402"],"award-info":[{"award-number":["2013CB329402"]}]},{"name":"Cheung Kong Scholars and Innovative Research Team in University","award":["IRT_15R53"],"award-info":[{"award-number":["IRT_15R53"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>During the acquisition process hyperspectral images (HSI) are inevitably corrupted by various noises, which greatly influence their visual impression and subsequent applications. In this paper, a novel Bayesian approach integrating hierarchical sparse learning and spectral-spatial information is proposed for HSI denoising. Based on the structure correlations, spectral bands with similar and continuous features are segmented into the same band-subset. To exploit local similarity, each subset is then divided into overlapping cubic patches. All patches can be regarded as consisting of clean image component, Gaussian noise component and sparse noise component. The first term is depicted by a linear combination of dictionary elements, where Gaussian process with Gamma distribution is applied to impose spatial consistency on dictionary. The last two terms are utilized to fully depict the noise characteristics. Furthermore, the sparseness of the model is adaptively manifested through Beta-Bernoulli process. Calculated by Gibbs sampler, the proposed model can directly predict the noise and dictionary without priori information of the degraded HSI. The experimental results on both synthetic and real HSI demonstrate that the proposed approach can better suppress the existing various noises and preserve the structure\/spectral-spatial information than the compared state-of-art approaches.<\/jats:p>","DOI":"10.3390\/s16101718","type":"journal-article","created":{"date-parts":[[2016,10,17]],"date-time":"2016-10-17T10:33:16Z","timestamp":1476700396000},"page":"1718","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Hierarchical Sparse Learning with Spectral-Spatial Information for Hyperspectral Imagery Denoising"],"prefix":"10.3390","volume":"16","author":[{"given":"Shuai","family":"Liu","sequence":"first","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi\u2019an 710071, China"},{"name":"Joint International Research Laboratory of Intelligent Perception and Computation, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Licheng","family":"Jiao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi\u2019an 710071, China"},{"name":"Joint International Research Laboratory of Intelligent Perception and Computation, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuyuan","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi\u2019an 710071, China"},{"name":"Joint International Research Laboratory of Intelligent Perception and Computation, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,17]]},"reference":[{"key":"ref_1","first-page":"112","article-title":"Multi-and Hyperspectral geologic remote sensing: A review","volume":"14","author":"Hecker","year":"2012","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"010901","DOI":"10.1117\/1.JBO.19.1.010901","article-title":"Medical hyperspectral imaging: A review","volume":"19","author":"Lu","year":"2014","journal-title":"J. Biomed. Opt."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"10639","DOI":"10.3390\/s120810639","article-title":"Hyperspectral analysis of soil nitrogen, carbon, carbonate, and organic matter using regression trees","volume":"12","author":"Gmur","year":"2012","journal-title":"Sensors"},{"key":"ref_4","unstructured":"Lam, A., Sato, I., and Sato, Y. (2012, January 11\u201315). Denoising hyperspectral images using spectral domain statistics. Proceedings of the IEEE International Conference on Pattern Recognition (ICPR\u201912), Tsukuba, Japan."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7059","DOI":"10.1364\/AO.53.007059","article-title":"Adaptive noise estimation from highly textured hyperspectral images","volume":"53","author":"Fu","year":"2014","journal-title":"Appl. Opt."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4889","DOI":"10.1080\/01431160802653724","article-title":"Denoising and dimensionality reduction of hyper-spectral imagery using wavelet packets, neighbour shrinking and principal component analysis","volume":"30","author":"Chen","year":"2009","journal-title":"Int. J. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2419","DOI":"10.1109\/TIP.2009.2028250","article-title":"Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems","volume":"18","author":"Beck","year":"2009","journal-title":"IEEE Trans. Image Process."},{"key":"ref_8","unstructured":"Buades, A., Coll, B., and Morel, J.M. (2005, January 7\u201312). A non-local algorithm for image denoising. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR\u201905), San Diego, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4311","DOI":"10.1109\/TSP.2006.881199","article-title":"K-SVD: An algorithm for designing overcomplete dictionaries for Sparse Representation","volume":"54","author":"Aharon","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2080","DOI":"10.1109\/TIP.2007.901238","article-title":"Image denoising by sparse 3Dtransform-domain collaborative filtering","volume":"16","author":"Dabov","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1109\/JSTSP.2011.2132692","article-title":"Noise reduction of hyperspectral images using kernel non-negative Tucker decomposition","volume":"5","author":"Karami","year":"2011","journal-title":"IEEEJ. Sel. Top. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1109\/TGRS.2010.2075937","article-title":"Denoising of hyperspectral imagery using principal component analysis and wavelet shrinkage","volume":"49","author":"Chen","year":"2011","journal-title":"IEEE Trans. Geosci.Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1002\/jmri.22003","article-title":"Adaptive non-local means denoising of MR images with spatially varying noise levels","volume":"31","author":"Pierrick","year":"2010","journal-title":"J. Magn. Reson. Imaging"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1109\/JSTARS.2012.2232904","article-title":"Hyperspectral imagery restoration using nonlocal spectral-spatial structured sparse representation with noise estimation","volume":"6","author":"Qian","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_15","first-page":"442","article-title":"Hyperspectral Image Denoising Using Spatio-Spectral Total Variation","volume":"13","author":"Aggarwal","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3660","DOI":"10.1109\/TGRS.2012.2185054","article-title":"Hyperspectral image denoising employing a spectral\u2013spatial adaptive total variation model","volume":"50","author":"Yuan","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.sigpro.2014.12.023","article-title":"Hyperspectral image recovery employing a multidimensional nonlocal total variation model","volume":"111","author":"Li","year":"2015","journal-title":"Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Liao, D.P., Ye, M.C., Jia, S., and Qian, Y.T. (2013, January 21\u201326). Noise reduction of hyperspectral imagery based on nonlocal tensor factorization. Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Melbourne, Australia.","DOI":"10.1109\/IGARSS.2013.6721352"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1109\/TIP.2012.2210725","article-title":"Nonlocal transform-domain filter for volumetric data denoising and reconstruction","volume":"22","author":"Maggioni","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3025","DOI":"10.1109\/JSTARS.2015.2402675","article-title":"Hyperspectral Image Denoising Using a Spatial\u2013Spectral Monte Carlo Sampling Approach","volume":"8","author":"Xu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1109\/TNNLS.2013.2293061","article-title":"Jointly learning the hybrid CRF and MLR model for simultaneous denoising and classification of hyperspectral imagery","volume":"25","author":"Zhong","year":"2014","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1109\/TGRS.2013.2259245","article-title":"Hyperspectral image denoising with a spatial\u2013spectral view fusion strategy","volume":"52","author":"Yuan","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1561\/0600000058","article-title":"Sparse Modeling for Image and Vision Processing","volume":"8","author":"Mairal","year":"2014","journal-title":"Found. Trends Comput. Graph. Vis."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wu, D., Zhang, Y., and Chen, Y. (2015, January 26\u201331). 3D sparse coding based denoising of hyperspectral images. Proceedings of the 2015 IEEE International Geoscience and Remote Sensing Symposium, Milan, Italy.","DOI":"10.1109\/IGARSS.2015.7326476"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1137\/110837486","article-title":"Dictionary learning for noisy and incomplete hyperspectral images","volume":"5","author":"Xing","year":"2012","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5425","DOI":"10.1109\/TGRS.2016.2564639","article-title":"Noise Removal from Hyperspectral Image with Joint Spectral-Spatial Distributed Sparse Representation","volume":"54","author":"Li","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2621","DOI":"10.1109\/TGRS.2014.2363101","article-title":"Multitask sparse nonnegative matrix factorization for joint spectral\u2013spatial hyperspectral imagery denoising","volume":"53","author":"Ye","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Rasti, B., Sveinsson, J.R., Ulfarsson, M.O., and Benediktsson, J.A. (2013, January 21\u201326). Hyperspectral image denoising using a new linear model and Sparse Regularization. Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Melbourne, Australia.","DOI":"10.1109\/IGARSS.2013.6721191"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1109\/TGRS.2015.2489218","article-title":"Coupled Sparse Denoising and Unmixing with Low-Rank Constraint for Hyperspectral Image","volume":"54","author":"Yang","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3062","DOI":"10.1109\/JSTARS.2014.2370062","article-title":"Spectral nonlocal restoration of hyperspectral images with low-rank property","volume":"8","author":"Zhu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4729","DOI":"10.1109\/TGRS.2013.2284280","article-title":"Hyperspectral image restoration using low-rank matrix recovery","volume":"52","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/TGRS.2015.2452812","article-title":"Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration","volume":"54","author":"He","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Makantasis, K., Karantzalos, K., Doulamis, A., and Doulamis, N. (2015, January 26\u201331). Deep supervised learning for hyperspectral data classification through convolutional neural networks. Proceedings of the 2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Milan, Italy.","DOI":"10.1109\/IGARSS.2015.7326945"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1587\/transinf.2014EDL8246","article-title":"Learning deep dictionary for hyperspectral image denoising","volume":"7","author":"Huo","year":"2015","journal-title":"IEICE Trans. Inf. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1002\/cpa.20132","article-title":"For most large underdetermined systems of linear equations the minimal -norm solution is also the sparsest solution","volume":"59","author":"Donoho","year":"2006","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1109\/TPAMI.2011.156","article-title":"Task-driven dictionary learning","volume":"34","author":"Mairal","year":"2012","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_37","unstructured":"Shah, A., David, K., and Ghahramani, Z.B. (2015, January 6\u201311). An empirical study of stochastic variational inference algorithms for the beta Bernoulli process. Proceedings of the 32nd International Conference on Machine Learning (ICML\u201815), Lille, France."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1913","DOI":"10.1109\/TNNLS.2014.2361052","article-title":"Learning stable multilevel dictionaries for sparse representations","volume":"26","author":"Thiagarajan","year":"2015","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4689","DOI":"10.1109\/TIP.2013.2277813","article-title":"Nonlocal hierarchical dictionary learning using wavelets for image denoising","volume":"22","author":"Yan","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_40","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_41","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1109\/TIP.2015.2499698","article-title":"Multi-scale patch-based image restoration","volume":"25","author":"Papyan","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2014). Bayesian Data Analysis, Chapman & Hall\/CRC.","DOI":"10.1201\/b16018"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Rasmussen, C., and Williams, C. (2006). Gaussian Processes for Machine Learning, MIT Press.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5349","DOI":"10.1109\/TIP.2014.2363735","article-title":"Noise parameter mismatch in variance stabilization, with an application to Poisson-Gaussian noise estimation","volume":"23","author":"Makitalo","year":"2014","journal-title":"IEEE Trans. Image Process."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1080\/00031305.1992.10475878","article-title":"Explaining the Gibbs sampler","volume":"46","author":"Casella","year":"1992","journal-title":"Am. Stat."},{"key":"ref_46","unstructured":"Rodriguez, Y.G., Davis, R., and Scharf, L. (2004). Efficient Gibbs Sampling of Truncated Multivariate Normal with Application to Constrained Linear Regression, Columbia University."},{"key":"ref_47","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_48","doi-asserted-by":"crossref","first-page":"2370","DOI":"10.1109\/JSTARS.2015.2434997","article-title":"Spectral\u2013Spatial Classification of Hyperspectral Image Based on Low-Rank Decomposition","volume":"8","author":"Xu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/10\/1718\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:33:12Z","timestamp":1760211192000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/10\/1718"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,17]]},"references-count":48,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2016,10]]}},"alternative-id":["s16101718"],"URL":"https:\/\/doi.org\/10.3390\/s16101718","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,10,17]]}}}