{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:27:39Z","timestamp":1772296059645,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1998,3,1]],"date-time":"1998-03-01T00:00:00Z","timestamp":888710400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1998,3]]},"DOI":"10.1007\/bf02684327","type":"journal-article","created":{"date-parts":[[2007,8,22]],"date-time":"2007-08-22T03:51:56Z","timestamp":1187754716000},"page":"1-27","source":"Crossref","is-referenced-by-count":72,"title":["Denoising with higher order derivatives of bounded variation and an application to parameter estimation"],"prefix":"10.1007","volume":"60","author":[{"given":"O.","family":"Scherzer","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02684327_CR1","unstructured":"Barrett, R., Berry, M., Chan, T., Demmel, J., Donato, J., Dongarra, J., Eijkhoui, V., Pozo, R., Romine, Ch., van der Vorst, H.: TEMPLATES for the solution of linear systems: building blocks for iterative methods. Software Package for the solution of linear systems."},{"key":"BF02684327_CR2","volume-title":"Nonlinear functional analysis","author":"K. Deimling","year":"1980","unstructured":"Deimling, K.: Nonlinear functional analysis. Berlin, Heidelberg, New York: Springer 1980."},{"key":"BF02684327_CR3","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1088\/0266-5611\/10\/2\/008","volume":"10","author":"D. Dobson","year":"1994","unstructured":"Dobson, D., Santosa, F.: An image enhancement technique for electrical impedance tomography. Inverse Problems10, 317\u2013334 (1994).","journal-title":"Inverse Problems"},{"key":"BF02684327_CR4","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1088\/0266-5611\/12\/5\/005","volume":"12","author":"D. Dobson","year":"1996","unstructured":"Dobson, D., Scherzer, O.: Analysis of regularized total variation penalty methods for denoising. Inverse Problems12, 601\u2013617 (1996).","journal-title":"Inverse Problems"},{"key":"BF02684327_CR5","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1137\/S003614299528701X","volume":"34","author":"D. Dobson","year":"1997","unstructured":"Dobson, D., Vogel, C. R.: Convergence of an iterative method for total variation denoising. SIAM J. Numer. Anal.34, 1779\u20131791 (1997).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02684327_CR6","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1088\/0266-5611\/5\/4\/007","volume":"5","author":"H. W. Engl","year":"1989","unstructured":"Engl, H. W., Kunisch, K., Neubauer, A.: Convergence rates for Tikhonov regularization of non-linear ill-posed problems. Inverse Problems5, 523\u2013540 (1989).","journal-title":"Inverse Problems"},{"key":"BF02684327_CR7","volume-title":"Measure theory and fine properties of functions","author":"L. C. Evans","year":"1995","unstructured":"Evans, L. C., Gariepy, R. F.: Measure theory and fine properties of functions. Ann Arbor: CRC Press 1995."},{"key":"BF02684327_CR8","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/0021-9045(92)90053-Q","volume":"70","author":"C. W. Groetsch","year":"1992","unstructured":"Groetsch, C. W.: Spectral methods for linear inverse problems with unbounded operators. J. Approx. Theory70, 16\u201328 (1992).","journal-title":"J. Approx. Theory"},{"key":"BF02684327_CR9","doi-asserted-by":"crossref","DOI":"10.1090\/surv\/034","volume-title":"Inverse source problems","author":"V. Isakov","year":"1990","unstructured":"Isakov, V.: Inverse source problems. Rhode Island: AMS 1990."},{"key":"BF02684327_CR10","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1051\/m2an\/1988220101191","volume":"22","author":"R. V. Kohn","year":"1988","unstructured":"Kohn, R. V., Lowe, B. D.: A variational method for parameter identification. RAIRO. Math. Modell. Numer. Anal.22, 119\u2013158 (1988).","journal-title":"RAIRO. Math. Modell. Numer. Anal."},{"key":"BF02684327_CR11","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/0022-247X(88)90074-1","volume":"132","author":"K. Kunisch","year":"1988","unstructured":"Kunisch, K.: Inherent identifiability of parameters in elliptic differential equations. J. Math. Anal. Appl.132, 453\u2013472 (1988).","journal-title":"J. Math. Anal. Appl."},{"key":"BF02684327_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0567-5","volume-title":"Variational Methods in Image Segmentation","author":"J.-M. Morel","year":"1995","unstructured":"Morel, J.-M., Solimini, S.: Variational Methods in Image Segmentation. Basel: Birkh\u00e4user 1995."},{"key":"BF02684327_CR13","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1088\/0266-5611\/5\/4\/008","volume":"5","author":"A. Neubauer","year":"1989","unstructured":"Neubauer, A.: Tikhonov regularisation for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation. Inverse Problems5, 541\u2013557 (1989).","journal-title":"Inverse Problems"},{"key":"BF02684327_CR14","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1137\/0727053","volume":"27","author":"S. Osher","year":"1990","unstructured":"Osher, S., Rudin, L.: Feature oriented image enhancement using shock filters. SIAM J. Numer. Anal.27, 919\u2013940 (1990).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02684327_CR15","doi-asserted-by":"crossref","first-page":"1796","DOI":"10.1137\/0730091","volume":"30","author":"O. Scherzer","year":"1993","unstructured":"Scherzer, O., Engl, H. W., Kunisch, K.: Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems. SIAM J. Numer. Anal.30, 1796\u20131838 (1993).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02684327_CR16","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1080\/01630569208816485","volume":"13","author":"G. Vainikko","year":"1992","unstructured":"Vainikko, G.: On the discretization and regularization of ill-posed problems with noncompact operators. Num. Funct. Anal. Opt.13, 381\u2013396 (1992).","journal-title":"Num. Funct. Anal. Opt."},{"key":"BF02684327_CR17","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1137\/0917016","volume":"17","author":"C. Vogel","year":"1996","unstructured":"Vogel, C., Oman, M.: Iterative methods for total variation denoising. SIAM J. Sci. Comput.17, 227\u2013238 (1996).","journal-title":"SIAM J. Sci. Comput."},{"key":"BF02684327_CR18","volume-title":"Linear operators in Hilbert spaces","author":"J. Weidmann","year":"1990","unstructured":"Weidmann, J.: Linear operators in Hilbert spaces. Berlin, Heidelberg, New York, Tokyo: Springer 1990."},{"key":"BF02684327_CR19","volume-title":"Weakly Differentiable functions","author":"W. P. Ziemer","year":"1980","unstructured":"Ziemer, W. P.: Weakly Differentiable functions. Berlin, Heidelberg, New York, Tokyo: Springer 1980."}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02684327.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02684327\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02684327","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T18:22:37Z","timestamp":1558203757000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02684327"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,3]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,3]]}},"alternative-id":["BF02684327"],"URL":"https:\/\/doi.org\/10.1007\/bf02684327","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,3]]}}}