{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:24:43Z","timestamp":1753881883294,"version":"3.41.2"},"reference-count":43,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","award":["340-2013-5342"],"award-info":[{"award-number":["340-2013-5342"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LQ21A010003"],"award-info":[{"award-number":["LQ21A010003"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:p> Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. An unknown signal with block structure can be accurately recovered from under-determined linear measurements provided that it is sufficiently block sparse. However, in practice, the block sparsity level is typically unknown. In this paper, we propose a soft measure of block sparsity [Formula: see text] with [Formula: see text], and present a procedure to estimate it by using multivariate centered isotropic symmetric [Formula: see text]-stable random projections. The limiting distribution of the estimator is given. Simulations are conducted to illustrate our theoretical results. <\/jats:p>","DOI":"10.1142\/s0219691322500345","type":"journal-article","created":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T07:45:31Z","timestamp":1659080731000},"source":"Crossref","is-referenced-by-count":0,"title":["Estimation of block sparsity in compressive sensing"],"prefix":"10.1142","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9861-6134","authenticated-orcid":false,"given":"Zhiyong","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, Institute of Digital Finance, Zhejiang University City College, Hangzhou 310015, P. R. China"}]},{"given":"Jun","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Mathematical Statistics, Ume\u00e5 University, Ume\u00e5, 901 87, Sweden"}]}],"member":"219","published-online":{"date-parts":[[2022,8,20]]},"reference":[{"doi-asserted-by":"publisher","key":"S0219691322500345BIB001","DOI":"10.1109\/TIT.2010.2040894"},{"key":"S0219691322500345BIB002","volume-title":"Thermodynamics of Chaotic Systems: An Introduction","volume":"4","author":"Beck C.","year":"1995"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB003","DOI":"10.1016\/j.acha.2009.04.002"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB004","DOI":"10.1109\/TIT.2009.2013003"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB005","DOI":"10.1002\/cpa.20124"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB006","DOI":"10.1109\/TIT.2005.858979"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB007","DOI":"10.1109\/TIT.2006.885507"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB008","DOI":"10.1109\/TSP.2006.881263"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB009","DOI":"10.1137\/S1064827596304010"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB010","DOI":"10.1109\/TSP.2005.849172"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB011","DOI":"10.1109\/TIT.2006.871582"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB012","DOI":"10.1109\/TSP.2011.2161982"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB013","DOI":"10.1017\/CBO9780511665622"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB014","DOI":"10.1109\/ICASSP.2009.4960226"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB015","DOI":"10.1109\/TSP.2010.2044837"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB016","DOI":"10.1017\/CBO9780511794308"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB017","DOI":"10.1109\/TIT.2009.2030471"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB018","DOI":"10.1109\/TSP.2012.2196694"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB019","DOI":"10.1007\/978-0-8176-4948-7"},{"issue":"3","key":"S0219691322500345BIB020","first-page":"217","volume-title":"Proc. 30th International Conf. Machine Learning","volume":"28","author":"Lopes M.","year":"2013"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB021","DOI":"10.1109\/TIT.2016.2587772"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB022","DOI":"10.1109\/TSP.2011.2105478"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB023","DOI":"10.1016\/j.sigpro.2010.05.016"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB024","DOI":"10.2307\/3315381"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB025","DOI":"10.1016\/0167-7152(94)00221-S"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB026","DOI":"10.1109\/TSP.2008.927802"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB027","DOI":"10.1109\/TSP.2009.2012791"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB028","DOI":"10.1016\/j.acha.2008.07.002"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB029","DOI":"10.1007\/s00180-013-0396-7"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB030","DOI":"10.1109\/JSTSP.2008.924384"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB031","DOI":"10.1002\/cpa.21442"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB032","DOI":"10.1016\/0047-259X(72)90038-3"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB033","DOI":"10.1109\/TSP.2009.2020754"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB034","DOI":"10.1109\/TIT.2007.909108"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB035","DOI":"10.1007\/978-3-319-19749-4_1"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB036","DOI":"10.1186\/s13634-019-0653-1"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB037","DOI":"10.1049\/iet-spr.2019.0200"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB038","DOI":"10.1111\/j.1467-9868.2005.00532.x"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB039","DOI":"10.1109\/TSP.2015.2441032"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB041","DOI":"10.1016\/j.sigpro.2019.07.003"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB042","DOI":"10.1016\/j.cam.2018.11.031"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB043","DOI":"10.1016\/j.sigpro.2018.10.002"},{"doi-asserted-by":"publisher","key":"S0219691322500345BIB044","DOI":"10.1090\/mmono\/065"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691322500345","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T01:59:19Z","timestamp":1664157559000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691322500345"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,20]]},"references-count":43,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["10.1142\/S0219691322500345"],"URL":"https:\/\/doi.org\/10.1142\/s0219691322500345","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2022,8,20]]},"article-number":"2250034"}}