{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T17:51:39Z","timestamp":1774893099344,"version":"3.50.1"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,5,12]],"date-time":"2015-05-12T00:00:00Z","timestamp":1431388800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Pattern Anal Applic"],"published-print":{"date-parts":[[2016,5]]},"DOI":"10.1007\/s10044-015-0477-z","type":"journal-article","created":{"date-parts":[[2015,5,11]],"date-time":"2015-05-11T05:44:02Z","timestamp":1431323042000},"page":"427-445","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A texture image denoising approach based on fractional developmental mathematics"],"prefix":"10.1007","volume":"19","author":[{"given":"Yi-Fei","family":"Pu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ni","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ji-Liu","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,5,12]]},"reference":[{"key":"477_CR1","unstructured":"T. Chan, S. Esedoglu, F. Park, et al. (2005) Recent Developments in Total Variation Image Restoration, in Mathematical Models of Computer Vision, Springer Verlag"},{"issue":"2","key":"477_CR2","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1137\/040616024","volume":"4","author":"A Buades","year":"2005","unstructured":"Buades A, Coll B, Morel JM (2005) A review of image denoising algorithms, with a new one. Multiscale Model. Simul 4(2):490\u2013530","journal-title":"Multiscale Model. Simul"},{"key":"477_CR3","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/978-0-387-44588-5","volume-title":"Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, Applied Mathematical Sciences","author":"G Aubert","year":"2006","unstructured":"Aubert G, Kornprobst P (2006) Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, Applied Mathematical Sciences. Springer-Verlag, New York, p 147"},{"issue":"7","key":"477_CR4","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/34.56205","volume":"12","author":"P Perona","year":"1990","unstructured":"Perona P, Malik J (1990) Scale-space and edges detecting using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629\u2013639","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"477_CR5","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L Rudin","year":"1992","unstructured":"Rudin L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phys D 60:259\u2013268","journal-title":"Phys D"},{"issue":"11","key":"477_CR6","doi-asserted-by":"crossref","first-page":"1582","DOI":"10.1109\/83.541429","volume":"5","author":"G Sapiro","year":"1996","unstructured":"Sapiro G, Ringach D (1996) Anisotropic diffusion of multivalued images with applications to color filtering. IEEE Trans Image Process 5(11):1582\u20131586","journal-title":"IEEE Trans Image Process"},{"issue":"3","key":"477_CR7","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1109\/83.661180","volume":"7","author":"P Blomgren","year":"1998","unstructured":"Blomgren P, Chan T (1998) Color TV: total variation methods for restoration of vector-valued images. IEEE Trans Image Process 7(3):304\u2013309","journal-title":"IEEE Trans Image Process"},{"issue":"9","key":"477_CR8","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1109\/34.713359","volume":"20","author":"SZ Li","year":"1998","unstructured":"Li SZ (1998) Clost-form solution and parameter selection for convex minimization-based edges-preserving smoothing. IEEE Trans Pattern Anal Mach Intell 20(9):916\u2013932","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"9","key":"477_CR9","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1109\/83.941854","volume":"10","author":"N Nguyen","year":"2001","unstructured":"Nguyen N, Milanfar P, Golub G (2001) Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement. IEEE Trans Image Process 10(9):1299\u20131308","journal-title":"IEEE Trans Image Process"},{"issue":"1","key":"477_CR10","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1137\/040621624","volume":"5","author":"DM Strong","year":"2006","unstructured":"Strong DM, Aujol JF, Chan TF (2006) Scale recognition, regularization parameter selection, and meyer\u2019s g norm in total variation regularization. Multiscale Model. Simul. 5(1):273\u2013303","journal-title":"Multiscale Model. Simul."},{"issue":"8","key":"477_CR11","doi-asserted-by":"crossref","first-page":"2269","DOI":"10.1109\/TIP.2006.875248","volume":"15","author":"G Gilboa","year":"2006","unstructured":"Gilboa G, Sochen N, Zeevi YY (2006) Estimation of optimal PDE-based denoising in the SNR sense. IEEE Trans Image Process 15(8):2269\u20132280","journal-title":"IEEE Trans Image Process"},{"issue":"1","key":"477_CR12","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1137\/0917016","volume":"17","author":"CR Vogel","year":"1996","unstructured":"Vogel CR, Oman ME (1996) Iterative methods for total variation denoising. SIAM J Sci Comput 17(1):227\u2013238","journal-title":"SIAM J Sci Comput"},{"issue":"5","key":"477_CR13","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1137\/S003614299528701X","volume":"34","author":"DC Dobson","year":"1997","unstructured":"Dobson DC, Vogel CR (1997) Convergence of an iterative method for total variation denoising. SIAM J Number Anal 34(5):1779\u20131791","journal-title":"SIAM J Number Anal"},{"issue":"1\u20132","key":"477_CR14","first-page":"89","volume":"20","author":"A Chambolle","year":"2004","unstructured":"Chambolle A (2004) An algorithm for total variation minimization and applications. J Math Imaging Vis 20(1\u20132):89\u201397","journal-title":"J Math Imaging Vis"},{"issue":"3","key":"477_CR15","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s10851-006-8803-0","volume":"26","author":"J Darbon","year":"2006","unstructured":"Darbon J, Sigelle M (2006) Image restoration with discrete constrained total variation part i: fast and exact optimization. J Math Imaging Vis 26(3):261\u2013276","journal-title":"J Math Imaging Vis"},{"issue":"3","key":"477_CR16","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s10851-006-0644-3","volume":"26","author":"J Darbon","year":"2006","unstructured":"Darbon J, Sigelle M (2006) Image restoration with discrete constrained total variation part ii: levelable functions, convex priors and non-convex cases. J Math Imaging Vis 26(3):277\u2013291","journal-title":"J Math Imaging Vis"},{"issue":"1","key":"477_CR17","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1137\/0729012","volume":"29","author":"F Catte","year":"1992","unstructured":"Catte F, Lions PL, Morel JM et al (1992) Image selective smoothing and edges detection by nonlinear diffusion. SIAM J Number Anal 29(1):182\u2013193","journal-title":"SIAM J Number Anal"},{"key":"477_CR18","doi-asserted-by":"crossref","unstructured":"Meyer Y (2001) Oscillating patterns in image processing and in some nonlinear evolution equations. American Mathematical Society, Providence, RI","DOI":"10.1090\/ulect\/022"},{"issue":"12","key":"477_CR19","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1023\/B:JMIV.0000011920.58935.9c","volume":"20","author":"M Nikolova","year":"2004","unstructured":"Nikolova M (2004) A variational approach to remove outliers and impulse noise. J Math Imaging Vis 20(12):99\u2013120","journal-title":"J Math Imaging Vis"},{"issue":"3","key":"477_CR20","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1137\/S0036142901389165","volume":"40","author":"M Nikolova","year":"2002","unstructured":"Nikolova M (2002) Minimizers of cost-functions involving nonsmooth data-fidelity terms. SIAM J Number Anal 40(3):965\u2013994","journal-title":"SIAM J Number Anal"},{"issue":"2","key":"477_CR21","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1137\/040605412","volume":"4","author":"S Osher","year":"2005","unstructured":"Osher S, Burger M, Goldfarb D et al (2005) An iterative regularization method for total variation based on image restoration. Multiscale Model. Simul 4(2):460\u2013489","journal-title":"Multiscale Model. Simul"},{"key":"477_CR22","unstructured":"Gilboa G, Zeevi YY, Sochen N (2003) Texture preserving variational denoising using an adaptive fidelity term. In: Proc. VLSM, Nice, France, pp 137\u2013144"},{"issue":"12","key":"477_CR23","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1002\/cpa.20045","volume":"57","author":"S Esedoglu","year":"2004","unstructured":"Esedoglu S, Osher S (2004) Decomposition of images by the anisotropic rudin-osher-fatemi model. Comm Pure Appl Math 57(12):1609\u20131626","journal-title":"Comm Pure Appl Math"},{"key":"477_CR24","doi-asserted-by":"crossref","unstructured":"Plomgren P, Mulet P, Chan T et al (1997) Total variation image restoration: numerical methods and extensions. In: ICIP, Santa Barbara, pp 384\u2013387","DOI":"10.1109\/ICIP.1997.632128"},{"issue":"3","key":"477_CR25","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1109\/TSMCB.2012.2222375","volume":"43","author":"H Zhang","year":"2013","unstructured":"Zhang H, Yang J, Zhang Y, Huang T (2013) Image and video restorations via nonlocal kernel regression. IEEE Trans Cybernetics 43(3):1035\u20131046","journal-title":"IEEE Trans Cybernetics"},{"issue":"7","key":"477_CR26","doi-asserted-by":"crossref","first-page":"1838","DOI":"10.1109\/TIP.2011.2108306","volume":"20","author":"W Dong","year":"2011","unstructured":"Dong W, Zhang L, Shi G, Wu X (2011) Image deblurring and superresolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans Image Process 20(7):1838\u20131857","journal-title":"IEEE Trans Image Process"},{"issue":"12","key":"477_CR27","doi-asserted-by":"crossref","first-page":"3736","DOI":"10.1109\/TIP.2006.881969","volume":"15","author":"M Elad","year":"2006","unstructured":"Elad M, Aharon M (2006) Image denoising via Sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736\u20133745","journal-title":"IEEE Trans Image Process"},{"issue":"8","key":"477_CR28","doi-asserted-by":"crossref","first-page":"2080","DOI":"10.1109\/TIP.2007.901238","volume":"16","author":"K Dabov","year":"2007","unstructured":"Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. on Image Processing 16(8):2080\u20132095","journal-title":"IEEE Trans. on Image Processing"},{"issue":"4","key":"477_CR29","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.1109\/TIP.2012.2235847","volume":"22","author":"W Dong","year":"2013","unstructured":"Dong W, Zhang L, Shi G, Li X (2013) Nonlocally centralized sparse representation for image restoration. IEEE Trans Image Processing 22(4):1620\u20131630","journal-title":"IEEE Trans Image Processing"},{"key":"477_CR30","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1112\/jlms\/s2-3.2.241","volume":"3","author":"ER Love","year":"1971","unstructured":"Love ER (1971) Fractional Derivatives of Imaginary Order. J. London Math Soc 3:241\u2013259","journal-title":"J. London Math Soc"},{"key":"477_CR31","volume-title":"The fractional calculus: integrations and differentiations of arbitrary order","author":"KB Oldham","year":"1974","unstructured":"Oldham KB, Spanier. (1974) The fractional calculus: integrations and differentiations of arbitrary order. Academic Press, New York"},{"key":"477_CR32","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1023\/A:1016566017098","volume":"29","author":"S Manabe","year":"2002","unstructured":"Manabe S (2002) A suggestion of fractional-order controller for flexible spacecraft attitude control. Nonlinear Dyn 29:251\u2013268","journal-title":"Nonlinear Dyn"},{"issue":"4","key":"477_CR33","doi-asserted-by":"crossref","first-page":"1424","DOI":"10.1121\/1.1646399","volume":"115","author":"W Chen","year":"2004","unstructured":"Chen W, Holm S (2004) fractional laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency dependency. J Acoustic Soc Am 115(4):1424\u20131430","journal-title":"J Acoustic Soc Am"},{"issue":"5","key":"477_CR34","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1109\/78.917808","volume":"49","author":"E Perrin","year":"2001","unstructured":"Perrin E, Harba R, Berzin-Joseph C, Iribarren I, Bonami A (2001) Nth-order fractional brownian motion and fractional gaussian noises. IEEE Trans Signal Processing 49(5):1049\u20131059","journal-title":"IEEE Trans Signal Processing"},{"issue":"3","key":"477_CR35","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1109\/97.905945","volume":"8","author":"CC Tseng","year":"2001","unstructured":"Tseng CC (2001) Design of fractional-order digital FIR differentiators. IEEE Signal Process Lett 8(3):77\u201379","journal-title":"IEEE Signal Process Lett"},{"key":"477_CR36","doi-asserted-by":"crossref","unstructured":"Chen YQ, Vinagre BM (2003) A New IIR-Type digital fractional-order differentiator, Elsevier Science, pp 1\u201312","DOI":"10.1016\/S0165-1684(03)00188-9"},{"key":"477_CR37","unstructured":"Pu YF. (2006) Research on application of fractional calculus to latest signal analysis and processing. Ph.D. Dissertation, Sichuan University, Chengdu China"},{"issue":"5","key":"477_CR38","first-page":"118","volume":"37","author":"YF Pu","year":"2005","unstructured":"Pu YF, Yuan X, Liao K et al (2005) Five numerical algorithms of fractional calculus applied in modern signal analyzing and processing. J. Sichuan University Engi Sci Edition 37(5):118\u2013124","journal-title":"J. Sichuan University Engi Sci Edition"},{"key":"477_CR39","unstructured":"Pu YF, Yuan X, Liao K et al (2005) Structuring analog fractance circuit for 1\/2 order fractional calculus. In: IEEE Proceedings of 6th International Conference on ASIC, pp 1039\u20131042"},{"issue":"1","key":"477_CR40","first-page":"128","volume":"38","author":"YF Pu","year":"2006","unstructured":"Pu YF, Yuan X, Liao K et al (2006) Implement any fractional-order neural-type pulse oscillator with net-grid type analog fractance circuit. J. Sichuan University Eng Sci Edition 38(1):128\u2013132","journal-title":"J. Sichuan University Eng Sci Edition"},{"key":"477_CR41","first-page":"13","volume":"3459","author":"S Didas","year":"2005","unstructured":"Didas S, Burgeth B, Imiya A et al (2005) Regularity and Scale space properties of fractional high order linear filtering, scale spaces PDE Meth. Comput Vis 3459:13\u201325","journal-title":"Comput Vis"},{"key":"477_CR42","unstructured":"Pu YF, Zhou JL, Zhang Y, Zhang N, Huang G, Siarry P (2013) Fractional extreme value adaptive training method: fractional steepest descent approach. In: IEEE Trans. Neural Networks and Learning Systems, to be published. Available: http:\/\/www.ieeexplore.ieee.org\/xpl\/login.jsp?tp=&arnumber=6650068&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D6650068"},{"key":"477_CR43","doi-asserted-by":"crossref","first-page":"2421","DOI":"10.1016\/S0165-1684(03)00194-4","volume":"83","author":"B Mathieu","year":"2003","unstructured":"Mathieu B, Melchior P, Oustaloup A et al (2003) Fractional differentiation for edges detection. Sig Process 83:2421\u20132432","journal-title":"Sig Process"},{"issue":"8","key":"477_CR44","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1109\/83.605414","volume":"6","author":"SC Liu","year":"1997","unstructured":"Liu SC, Chang S (1997) Dimension estimation of discrete-time fractional brownian motion with applications to image texture classification. IEEE Trans on Image Processing 6(8):1176\u20131184","journal-title":"IEEE Trans on Image Processing"},{"key":"477_CR45","doi-asserted-by":"crossref","unstructured":"Pu YF (2006) Fractional calculus approach to texture of digital image. In: IEEE Proceedings of 8th International Conference on Signal Processing, pp 1002\u20131006","DOI":"10.1109\/ICOSP.2006.345713"},{"issue":"12","key":"477_CR46","first-page":"2252","volume":"38","author":"YF Pu","year":"2008","unstructured":"Pu YF, Wang WX, ZHOU JL et al (2008) Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation. Sci China Ser F Inform Sci 38(12):2252\u20132272","journal-title":"Sci China Ser F Inform Sci"},{"issue":"1","key":"477_CR47","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1080\/00207160903134263","volume":"88","author":"YF Pu","year":"2011","unstructured":"Pu YF, Zhou JL (2011) A novel approach for multi-scale texture segmentation based on fractional differential. Int J Comp Math 88(1):58\u201378","journal-title":"Int J Comp Math"},{"issue":"2","key":"477_CR48","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/TIP.2009.2035980","volume":"19","author":"YF Pu","year":"2010","unstructured":"Pu YF, Zhou JL, Yuan X (2010) Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement. IEEE Trans Image Process 19(2):491\u2013511","journal-title":"IEEE Trans Image Process"},{"issue":"10","key":"477_CR49","doi-asserted-by":"crossref","first-page":"2492","DOI":"10.1109\/TIP.2007.904971","volume":"16","author":"J Bai","year":"2007","unstructured":"Bai J, Feng XC (2007) Fractional-Order anisotropic diffusion for image denoising. IEEE Trans Image Process 16(10):2492\u20132502","journal-title":"IEEE Trans Image Process"},{"issue":"7","key":"477_CR50","first-page":"1","volume":"57","author":"YF Pu","year":"2014","unstructured":"Pu YF, Siarry P, Zhou JL, Liu YG, Zhang N, Huang G et al (2014) Fractional partial differential equation denoising models for texture image. Sci China Ser F Inform Sci 57(7):1\u201319","journal-title":"Sci China Ser F Inform Sci"},{"issue":"12","key":"477_CR51","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.1002\/mma.2935","volume":"37","author":"YF Pu","year":"2014","unstructured":"Pu YF, Siarry P, Zhou JL, Zhang N (2014) A fractional partial differential equation based multi-scale denoising model for texture image. Math Methods Appl Sci 37(12):1784\u20131806","journal-title":"Math Methods Appl Sci"},{"issue":"11","key":"477_CR52","doi-asserted-by":"crossref","first-page":"2756","DOI":"10.1016\/j.aop.2008.04.005","volume":"323","author":"VE Tarasov","year":"2008","unstructured":"Tarasov VE (2008) Fractional vector calculus and fractional Maxwell\u2019s equations. Ann Phys 323(11):2756\u20132778","journal-title":"Ann Phys"},{"issue":"4","key":"477_CR53","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","volume":"13","author":"Z Wang","year":"2004","unstructured":"Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error measurement to structural similarity. IEEE Trans Image Process 13(4):600\u2013612","journal-title":"IEEE Trans Image Process"}],"container-title":["Pattern Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-015-0477-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10044-015-0477-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-015-0477-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,24]],"date-time":"2019-08-24T22:05:08Z","timestamp":1566684308000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10044-015-0477-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,12]]},"references-count":53,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,5]]}},"alternative-id":["477"],"URL":"https:\/\/doi.org\/10.1007\/s10044-015-0477-z","relation":{},"ISSN":["1433-7541","1433-755X"],"issn-type":[{"value":"1433-7541","type":"print"},{"value":"1433-755X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,12]]}}}