{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T20:27:34Z","timestamp":1743020854285,"version":"3.40.3"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030173432"},{"type":"electronic","value":"9783030173449"}],"license":[{"start":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T00:00:00Z","timestamp":1555459200000},"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":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-17344-9_17","type":"book-chapter","created":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T16:14:16Z","timestamp":1555517656000},"page":"229-239","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Nonlocal Image Inpainting Problem Using the Linear Allen\u2013Cahn Equation"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0891-6246","authenticated-orcid":false,"given":"Antun Lovro","family":"Brki\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7828-4870","authenticated-orcid":false,"given":"Andrej","family":"Novak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,4,17]]},"reference":[{"issue":"6","key":"17_CR1","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1016\/0001-6160(79)90196-2","volume":"27","author":"SM Allen","year":"1979","unstructured":"Allen, S.M., Cahn, J.W.: A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metallurgica 27(6), 1085\u20131095 (1979)","journal-title":"Acta Metallurgica"},{"key":"17_CR2","doi-asserted-by":"crossref","unstructured":"Bertalmio, M., et al.: Image inpainting. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques. ACM Press\/Addison-Wesley Publishing Co. (2000)","DOI":"10.1145\/344779.344972"},{"key":"17_CR3","unstructured":"Bertalmio, M., Bertozzi, A.L., Sapiro, G.: Navier-stokes, fluid dynamics, and image and video inpainting. In: Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2001, vol. 1. IEEE (2001)"},{"key":"17_CR4","unstructured":"Feng, Z., Yin, J., Zhou, J.: Inpainting algorithm for jacquared image based on phase-field model. In: 3rd International Conference on Intelligent System and Knowledge Engineering, ISKE 2008, vol. 1. IEEE (2008)"},{"key":"17_CR5","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.dsp.2014.11.006","volume":"37","author":"Y Li","year":"2015","unstructured":"Li, Y., et al.: Fast local image inpainting based on the Allen-Cahn model. Digit. Sig. Process. 37, 65\u201374 (2015)","journal-title":"Digit. Sig. Process."},{"issue":"2","key":"17_CR6","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1137\/S0036139901390088","volume":"63","author":"J Shen","year":"2003","unstructured":"Shen, J., Kang, S.H., Chan, T.F.: Euler\u2019s elastica and curvature-based inpainting. SIAM J. Appl. Math. 63(2), 564\u2013592 (2003)","journal-title":"SIAM J. Appl. Math."},{"issue":"11","key":"17_CR7","doi-asserted-by":"publisher","first-page":"2421","DOI":"10.1016\/S0165-1684(03)00194-4","volume":"83","author":"B Mathieu","year":"2003","unstructured":"Mathieu, B., et al.: Fractional differentiation for edge detection. Sig. Process. 83(11), 2421\u20132432 (2003)","journal-title":"Sig. Process."},{"issue":"2","key":"17_CR8","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1109\/TIP.2009.2035980","volume":"19","author":"Y-F Pu","year":"2010","unstructured":"Pu, Y.-F., Zhou, J.-L., Yuan, X.: Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement. IEEE Trans. Image Process. 19(2), 491\u2013511 (2010)","journal-title":"IEEE Trans. Image Process."},{"issue":"10","key":"17_CR9","doi-asserted-by":"publisher","first-page":"2492","DOI":"10.1109\/TIP.2007.904971","volume":"16","author":"J Bai","year":"2007","unstructured":"Bai, J., Feng, X.-C.: Fractional-order anisotropic diffusion for image denoising. IEEE Trans. Image Process. 16(10), 2492\u20132502 (2007)","journal-title":"IEEE Trans. Image Process."},{"issue":"4","key":"17_CR10","doi-asserted-by":"publisher","first-page":"2487","DOI":"10.1137\/14097121X","volume":"8","author":"J Zhang","year":"2015","unstructured":"Zhang, J., Chen, K.: A total fractional-order variation model for image restoration with nonhomogeneous boundary conditions and its numerical solution. SIAM J. Imaging Sci. 8(4), 2487\u20132518 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"17_CR11","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1109\/TIP.2011.2160072","volume":"21","author":"M Zhou","year":"2012","unstructured":"Zhou, M., et al.: Nonparametric Bayesian dictionary learning for analysis of noisy and incomplete images. IEEE Trans. Image Process. 21(1), 130\u2013144 (2012)","journal-title":"IEEE Trans. Image Process."},{"key":"17_CR12","doi-asserted-by":"crossref","unstructured":"Larnier, S., Mecca, R.: Fractional-order diffusion for image reconstruction. In: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE (2012)","DOI":"10.1109\/ICASSP.2012.6288068"},{"issue":"1","key":"17_CR13","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/j.jcp.2005.05.017","volume":"211","author":"MM Meerschaert","year":"2006","unstructured":"Meerschaert, M.M., Scheffler, H.-P., Tadjeran, C.: Finite difference methods for two-dimensional fractional dispersion equation. J. Comput. Phys. 211(1), 249\u2013261 (2006)","journal-title":"J. Comput. Phys."},{"issue":"6\u20137","key":"17_CR14","doi-asserted-by":"publisher","first-page":"1222","DOI":"10.1080\/00207160.2017.1401707","volume":"95","author":"A Abirami","year":"2018","unstructured":"Abirami, A., Prakash, P., Thangavel, K.: Fractional diffusion equation-based image denoising model using CN-GL scheme. Int. J. Comput. Math. 95(6\u20137), 1222\u20131239 (2018)","journal-title":"Int. J. Comput. Math."},{"key":"17_CR15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511734304","volume-title":"Partial Differential Equation Methods for Image Inpainting","author":"C-B Sch\u00f6nlieb","year":"2015","unstructured":"Sch\u00f6nlieb, C.-B.: Partial Differential Equation Methods for Image Inpainting, vol. 29. Cambridge University Press, Cambridge (2015)"},{"issue":"1","key":"17_CR16","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1109\/MSP.2013.2273004","volume":"31","author":"C Guillemot","year":"2014","unstructured":"Guillemot, C., Le Meur, O.: Image inpainting: overview and recent advances. IEEE Sig. Process. Mag. 31(1), 127\u2013144 (2014)","journal-title":"IEEE Sig. Process. Mag."},{"issue":"1","key":"17_CR17","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.cam.2004.01.033","volume":"172","author":"MM Meerschaert","year":"2004","unstructured":"Meerschaert, M.M., Tadjeran, C.: Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 172(1), 65\u201377 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"17_CR18","doi-asserted-by":"publisher","first-page":"289","DOI":"10.3934\/cpaa.2006.5.289","volume":"5","author":"NJ Ford","year":"2006","unstructured":"Ford, N.J., Connolly, J.A.: Comparison of numerical methods for fractional differential equations. Commun. Pure Appl. Anal. 5, 289 (2006)","journal-title":"Commun. Pure Appl. Anal."},{"key":"17_CR19","doi-asserted-by":"crossref","DOI":"10.1142\/8180","volume-title":"Fractional Calculus: Models and Numerical Methods","author":"D Baleanu","year":"2012","unstructured":"Baleanu, D.: Fractional Calculus: Models and Numerical Methods, vol. 3. World Scientific, Singapore (2012)"},{"key":"17_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-09432-8","volume-title":"Classical Fourier Analysis, Graduate Text in Mathematics 249","author":"L Grafakos","year":"2008","unstructured":"Grafakos, L.: Classical Fourier Analysis, Graduate Text in Mathematics 249. Springer, Heidelberg (2008)"}],"container-title":["Lecture Notes in Electrical Engineering","Advances in Non-Integer Order Calculus and Its Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-17344-9_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T20:56:14Z","timestamp":1694811374000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-17344-9_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,17]]},"ISBN":["9783030173432","9783030173449"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-17344-9_17","relation":{},"ISSN":["1876-1100","1876-1119"],"issn-type":[{"type":"print","value":"1876-1100"},{"type":"electronic","value":"1876-1119"}],"subject":[],"published":{"date-parts":[[2019,4,17]]},"assertion":[{"value":"17 April 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"RRNR","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Conference on Non-integer Order Calculus and Its Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Bialystok","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 September 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 September 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"rrnr2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/rrnr2018.pb.edu.pl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}