{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:31:20Z","timestamp":1760243480867,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2013,6,18]],"date-time":"2013-06-18T00:00:00Z","timestamp":1371513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Wavelet analysis is known to be a good option for change detection in many contexts. Detecting changes in solution volumes that are measured with both additive and relative error is an important aspect of safeguards for facilities that process special nuclear material. This paper qualitatively compares wavelet-based change detection to a lag-one differencing option using realistic simulated solution volume data for which the true change points are known. We then show quantitatively that Haar wavelet-based change detection is effective for finding the approximate location of each change point, and that a simple piecewise linear optimization step is effective to refine the initial wavelet-based change point estimate.<\/jats:p>","DOI":"10.3390\/axioms2020271","type":"journal-article","created":{"date-parts":[[2013,6,18]],"date-time":"2013-06-18T11:40:45Z","timestamp":1371555645000},"page":"271-285","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Change Detection Using Wavelets in Solution Monitoring Data for Nuclear Safeguards"],"prefix":"10.3390","volume":"2","author":[{"given":"Claire","family":"Longo","sequence":"first","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tom","family":"Burr","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kary","family":"Myers","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"44","DOI":"10.3390\/axioms2010044","article-title":"Gibbs phenomenon in wavelet analysis of solution monitoring data for nuclear safeguards","volume":"2","author":"Burr","year":"2013","journal-title":"Axioms"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1093\/biomet\/82.2.385","article-title":"Jump and sharp cusp detection by wavelets","volume":"82","author":"Wang","year":"1995","journal-title":"Biometrika"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tang, Y. (2000). Wavelet Theory and Its Application to Pattern Recognition, World Scientific.","DOI":"10.1142\/9789812385529"},{"key":"ref_4","first-page":"6","article-title":"Pattern recognition options to combine process monitoring and material accounting data in nuclear safeguards","volume":"1","author":"Burr","year":"2012","journal-title":"Stat. Res. Lett."},{"key":"ref_5","unstructured":"Burr, T., Howell, J., Suzuki, M., Crawford, J., and Williams, T. (2009, January 5\u20139). Evaluation of Loss Detection Methods in Solution Monitoring for Nuclear Safeguards. Proceedings of American Nuclear Society Conference on Human-Machine Interfaces, Knoxville, TN, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1080\/18811248.2007.9711520","article-title":"A study on loss detection algorithms using tank monitoring data","volume":"46","author":"Suzuki","year":"2009","journal-title":"J. Nucl. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.nima.2011.02.078","article-title":"Signal estimation and change detection in tank data for nuclear safeguards","volume":"640","author":"Burr","year":"2011","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1080\/00223131.2011.649076","article-title":"Loss detection results on simulated tank data modified by realistic effects","volume":"49","author":"Burr","year":"2012","journal-title":"J. Nucl. Sci. Technol."},{"key":"ref_9","unstructured":"Aigner, H., Binner, R., and Kuhn, E. International target values 2000 for measurement uncertainties in safeguarding nuclear materials. Available online: http:\/\/www.inmm.org\/topics\/publications."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1021\/ie061615t","article-title":"Practical issues relating to tank volume determination","volume":"47","author":"Binner","year":"2008","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1177\/0142331207086813","article-title":"Towards the re-verification of process tank calibrations","volume":"31","author":"Howell","year":"2009","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1080\/01621459.1995.10476626","article-title":"Adapting to unknown smoothing via wavelet shrinkage","volume":"90","author":"Donoho","year":"1995","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1002\/(SICI)1099-128X(199905\/08)13:3\/4<415::AID-CEM544>3.0.CO;2-8","article-title":"Multiscale analysis and modeling using wavelets","volume":"13","author":"Bakshi","year":"1999","journal-title":"J. Chem."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Nason, G.P. (2008). Wavelet Methods in Statistics with R, Springer.","DOI":"10.1007\/978-0-387-75961-6"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1109\/97.803428","article-title":"Low-complexity image denoising based on statistical modeling of wavelet coefficients","volume":"6","author":"Mihcak","year":"1999","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_16","unstructured":"Medeiros, C.B., Egenhofer, M.J., and Bertino, E. (2005, January 22\u201324). Change detection in time series data using wavelet footprints. Proceedings of Symposium on Large Spatial Databases, Angra dos Reis, Brazil."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1109\/18.119727","article-title":"Singularity detection and processing with wavelets","volume":"38","author":"Mallat","year":"1992","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Mallat, S.G. (1999). A Wavelet Tour of Signal Processing, Elsevier. [2nd ed.].","DOI":"10.1016\/B978-012466606-1\/50008-8"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1049\/ip-vis:20040398","article-title":"Statistical modelling of the wavelet coefficients with different bases and decomposition levels","volume":"151","author":"Lam","year":"2004","journal-title":"IEEE Image Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1080\/10485250211396","article-title":"Detecting abrupt changes by wavelet methods","volume":"14","author":"Antoniadis","year":"1997","journal-title":"J. Nonparametr. Stat."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/jae.659","article-title":"Computation and analysis of multiple structural change models","volume":"18","author":"Bai","year":"2003","journal-title":"J. Appl. Econom."},{"key":"ref_22","first-page":"395","article-title":"A peaks over threshold model for change-point detection by wavelets","volume":"14","author":"Raimondo","year":"2004","journal-title":"Stat. Sin."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1109\/TPAMI.1986.4767851","article-title":"A computational approach to edge detection","volume":"8","author":"Canny","year":"1986","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Daubechies, I. (1992). Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611970104"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2549","DOI":"10.1109\/78.709544","article-title":"On time-dependent wavelet denoising","volume":"46","author":"Vidakovic","year":"1998","journal-title":"IEEE Signal Process."},{"key":"ref_26","unstructured":"Available online: www.r-project.org."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1093\/biomet\/81.3.425","article-title":"Ideal spatial adaption by wavelet shrinkage","volume":"81","author":"Donoho","year":"1994","journal-title":"Biometrika"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1111\/1467-9868.00071","article-title":"Wavelet threshold estimators for data with correlated noise","volume":"59","author":"Johnstone","year":"1997","journal-title":"J. R Stat. Soc. B"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xiaohong, G., and Jinhui, C. (2008, January 25\u201327). Study of the Gibbs phenomenon in de-noising by wavelets. Proceedings of the 7th World Congress on Intelligent Control and Automation, Chongqing, China.","DOI":"10.1109\/WCICA.2008.4594585"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/2\/2\/271\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:47:24Z","timestamp":1760219244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/2\/2\/271"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,18]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,6]]}},"alternative-id":["axioms2020271"],"URL":"https:\/\/doi.org\/10.3390\/axioms2020271","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2013,6,18]]}}}