{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T15:47:03Z","timestamp":1778255223838,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T00:00:00Z","timestamp":1547596800000},"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":["61675036"],"award-info":[{"award-number":["61675036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["CSTC2016JCYJA0193"],"award-info":[{"award-number":["CSTC2016JCYJA0193"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Chinese Academy of Sciences Key Laboratory of Beam Control Fund","award":["2017LBC006"],"award-info":[{"award-number":["2017LBC006"]}]},{"name":"Fundamental Research Funds for Central Universities","award":["2018CDGFTX0016"],"award-info":[{"award-number":["2018CDGFTX0016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Noise estimation for image sensor is a key technique in many image pre-processing applications such as blind de-noising. The existing noise estimation methods for additive white Gaussian noise (AWGN) and Poisson-Gaussian noise (PGN) may underestimate or overestimate the noise level in the situation of a heavy textured scene image. To cope with this problem, a novel homogenous block-based noise estimation method is proposed to calculate these noises in this paper. Initially, the noisy image is transformed into the map of local gray statistic entropy (LGSE), and the weakly textured image blocks can be selected with several biggest LGSE values in a descending order. Then, the Haar wavelet-based local median absolute deviation (HLMAD) is presented to compute the local variance of these selected homogenous blocks. After that, the noise parameters can be estimated accurately by applying the maximum likelihood estimation (MLE) to analyze the local mean and variance of selected blocks. Extensive experiments on synthesized noised images are induced and the experimental results show that the proposed method could not only more accurately estimate the noise of various scene images with different noise levels than the compared state-of-the-art methods, but also promote the performance of the blind de-noising algorithm.<\/jats:p>","DOI":"10.3390\/s19020339","type":"journal-article","created":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T11:30:27Z","timestamp":1547724627000},"page":"339","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Noise Estimation for Image Sensor Based on Local Entropy and Median Absolute Deviation"],"prefix":"10.3390","volume":"19","author":[{"given":"Yongsong","family":"Li","sequence":"first","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengzhou","family":"Li","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China"},{"name":"Key Laboratory of Beam Control, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiqi","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiangpeng","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Qi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Beam Control, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10339","DOI":"10.3390\/s120810339","article-title":"Grey level and noise evaluation of a Foveon X3 image sensor: A statistical and experimental approach","volume":"12","author":"Segui","year":"2012","journal-title":"Sensors"},{"key":"ref_2","first-page":"4172","article-title":"Estimation of Gaussian, Poissonian-Gaussian, and Processed Visual Noise and its level function","volume":"25","author":"Rakhshanfar","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1692","DOI":"10.3390\/s90301692","article-title":"Noise reduction for CFA image sensors exploiting HVS behaviour","volume":"9","author":"Bosco","year":"2009","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1051\/epjap:2002103","article-title":"CCD or CMOS camera noise characterisation","volume":"21","author":"Reibel","year":"2002","journal-title":"Eur. Phys. J. Appl. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1109\/TCSVT.2007.913972","article-title":"A technique for evaluation of CCD video-camera noise","volume":"18","author":"Irie","year":"2008","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"045207","DOI":"10.1088\/0957-0233\/19\/4\/045207","article-title":"A model for measurement of noise in CCD digital-video cameras","volume":"19","author":"Irie","year":"2008","journal-title":"Meas. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2676","DOI":"10.1109\/TIP.2006.877363","article-title":"CCD noise removal in digital images","volume":"15","author":"Faraji","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1109\/TPAMI.2007.1176","article-title":"Automatic estimation and removal of noise from a single image","volume":"30","author":"Liu","year":"2008","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1006\/cviu.1996.0060","article-title":"Fast noise variance estimation","volume":"64","year":"1996","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_10","unstructured":"Yang, S.-C., and Yang, S.M. (2008, January 12\u201314). A fast method for image noise estimation using Laplacian operator and adaptive edge detection. Proceedings of the 3rd International Symposium on Communications, Control and Signal Processing, St Julians, Malta."},{"key":"ref_11","first-page":"5158","article-title":"Noise estimation from digital step-model signal","volume":"22","author":"Laligant","year":"2013","journal-title":"IEEE Signal Process. Soc."},{"key":"ref_12","unstructured":"Zoran, D., and Weiss, Y. (October, January 29). Scale invariance and noise in natural images. Proceedings of the IEEE 12th International Conference on Computer Vision, Kyoto, Japan."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1007\/s11263-013-0688-y","article-title":"Exposing region splicing forgeries with blind local noise estimation","volume":"110","author":"Lyu","year":"2014","journal-title":"Int. J. Comput. Vis."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1109\/TIP.2016.2639447","article-title":"Noise level estimation for natural images based on scale-invariant kurtosis and piecewise stationarity","volume":"26","author":"Dong","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1093\/biomet\/81.3.425","article-title":"Ideal spatial adaptation by wavelet shrinkage","volume":"81","author":"Donoho","year":"1994","journal-title":"BIOMETRIKA"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/18.382009","article-title":"De-noising by soft-thresholding","volume":"41","author":"Donoho","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1109\/TIP.2012.2221728","article-title":"Image noise level estimation by principal component analysis","volume":"22","author":"Pyatykh","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5226","DOI":"10.1109\/TIP.2013.2283400","article-title":"Single-image noise level estimation for blind denoising","volume":"22","author":"Liu","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_19","unstructured":"Yang, J., Wu, Z., and Hou, C. (October, January 30). In estimation of signal-dependent sensor noise via sparse representation of noise level functions. Proceedings of the 19th IEEE International Conference on Image Processing."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1561","DOI":"10.1109\/TIP.2015.2405417","article-title":"Estimation of signal-dependent noise level function in transform domain via a sparse recovery model","volume":"24","author":"Yang","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1186\/s13640-015-0093-2","article-title":"Superpixel-based image noise variance estimation with local statistical assessment","volume":"2015","author":"Wu","year":"2015","journal-title":"EURASIP J. Image Video Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1016\/j.neucom.2017.05.057","article-title":"A spatially cohesive superpixel model for image noise level estimation","volume":"266","author":"Fu","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1162\/neco.1997.9.8.1627","article-title":"Minimax entropy principle and its application to texture modeling","volume":"9","author":"Zhu","year":"1997","journal-title":"Neural Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.patcog.2015.12.012","article-title":"The Kolmogorov\u2013Sinai entropy in the setting of fuzzy sets for image texture analysis and classification","volume":"53","author":"Pham","year":"2016","journal-title":"Pattern Recognit."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.patcog.2017.03.012","article-title":"Unsupervised hierarchical image segmentation through fuzzy entropy maximization","volume":"68","author":"Yin","year":"2017","journal-title":"Pattern Recognit."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"8031","DOI":"10.1007\/s11042-016-3455-6","article-title":"Noise robust and rotation invariant entropy features for texture classification","volume":"76","author":"Shakoor","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.dsp.2018.03.005","article-title":"Signal enumeration in Gaussian and non-Gaussian noise using entropy estimation of eigenvalues","volume":"78","author":"Asadi","year":"2018","journal-title":"Digit. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1109\/TIP.2008.2001399","article-title":"Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data","volume":"17","author":"Foi","year":"2008","journal-title":"IEEE Trans. Image Process."},{"key":"ref_29","unstructured":"Zabrodina, V., Abramov, S.K., Lukin, V.V., Astola, J., Vozel, B., and Chehdi, K. (September, January 29). Blind estimation of mixed noise parameters in images using robust regression curve fitting. Proceedings of the 19th European Signal Processing Conference, Barcelona, Spain."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.3390\/s18041019","article-title":"Poisson-Gaussian noise analysis and estimation for low-dose X-ray images in the NSCT domain","volume":"18","author":"Lee","year":"2018","journal-title":"Sensors"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lee, M.S., Park, S.W., and Kang, M.G. (2017). Denoising algorithm for CFA image sensors considering inter-channel correlation. Sensors, 17.","DOI":"10.3390\/s17061236"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3656","DOI":"10.1109\/JSEN.2017.2696562","article-title":"Noise Model of a Multispectral TDI CCD imaging system and its parameter estimation of piecewise weighted least square fitting","volume":"17","author":"Zheng","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2715","DOI":"10.1109\/TIP.2018.2812083","article-title":"Effective and fast estimation for image sensor noise via constrained weighted least squares","volume":"27","author":"Dong","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3459","DOI":"10.1109\/TIP.2014.2321504","article-title":"Indirect estimation of signal-dependent noise with nonadaptive heterogeneous samples","volume":"23","author":"Azzari","year":"2014","journal-title":"IEEE Trans. Image Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4361","DOI":"10.1109\/TIP.2014.2347204","article-title":"Practical signal-dependent noise parameter estimation from a single noisy image","volume":"23","author":"Liu","year":"2014","journal-title":"IEEE Trans. Image Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1097\/00000542-200107000-00010","article-title":"Shannon entropy applied to the measurement of the electroencephalographic effects of desflurane","volume":"95","author":"Bruhn","year":"2001","journal-title":"Am. Soc. Anesthesiol."},{"key":"ref_37","unstructured":"(2018, March 06). Standard Kodak PCD0992 Test Images. Available online: http:\/\/r0k.us\/graphics\/kodak\/."},{"key":"ref_38","unstructured":"Martin, D.R., Fowlkes, C., Tal, D., and Malik, J. (2001, January 7\u201314). A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. Proceedings of the 9th International Conference on Computer Vision, Vancouver, BC, Canada."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Khalil, H.H., Rahmat, R.O.K., and Mahmoud, W.A. (2008, January 9\u201311). Estimation of noise in gray-scale and colored images using median absolute deviation (MAD). Proceedings of the 3rd International Conference on Geometric Modeling and Imaging, London, UK.","DOI":"10.1109\/GMAI.2008.7"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1016\/j.imavis.2008.08.002","article-title":"Automatic noise estimation in images using local statistics. Additive and multiplicative cases","volume":"27","year":"2009","journal-title":"Image Vis. Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.sigpro.2013.10.002","article-title":"Simplified noise model parameter estimation for signal-dependent noise","volume":"96","author":"Jeong","year":"2014","journal-title":"Signal Process."},{"key":"ref_42","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_43","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1109\/TIP.2012.2202675","article-title":"Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise","volume":"22","author":"Makitalo","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_44","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."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/2\/339\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:26:25Z","timestamp":1760185585000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/2\/339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,16]]},"references-count":44,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["s19020339"],"URL":"https:\/\/doi.org\/10.3390\/s19020339","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,16]]}}}