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Imaging Sci."],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we introduce a frequency-domain approach to extract information on the trajectory of a moving point source. The method hinges on the analysis of multifrequency near-field data recorded at one and sparse observation points in three dimensions. The radiating period of the moving point source is supposed to be supported on the real axis and a priori known. In contrast to inverse stationary source problems, one needs to classify observable and non-observable measurement positions. The analogues of these concepts in the far-field regime were first proposed in the authors\u2019 previous paper [ SIAM J. Imaging\u00a0Sci., 16 (2023),\u00a0pp. 1535\u20131571]. In this paper we shall derive the observable and non-observable measurement positions for straight and circular motions in [Formula: see text]. In the near-field case, we verify that the smallest annular region centered at an observable position that contains the trajectory can be imaged for an admissible class of orbit functions. Using the data from sparse observable positions, it is possible to reconstruct the [Formula: see text]-convex domain of the trajectory. Intensive 3D numerical tests with synthetic data are performed to show effectiveness and feasibility of this new algorithm.<\/jats:p>","DOI":"10.1137\/23m162260x","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T12:47:29Z","timestamp":1720010849000},"page":"1377-1414","source":"Crossref","is-referenced-by-count":2,"title":["Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Points (Part II): Near-Field Case in 3D"],"prefix":"10.1137","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5159-0715","authenticated-orcid":true,"given":"Guanqiu","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6361-1982","authenticated-orcid":true,"given":"Hongxia","family":"Guo","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guanghui","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab8f85"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/3\/035005"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00248724"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(82)90105-7"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/17M112364X"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2014.11.005"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/17M111290X"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1137\/23M1572696"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/23M1545045"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab1496"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s10255-020-0917-4"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-15-1592-7_5"},{"key":"ref13","volume-title":"Inverse Source Problems","author":"Isakov V.","year":"1989"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ac9999"},{"key":"ref15","volume-title":"The Factorization Method for Inverse Problems","author":"Kirsch A.","year":"2008"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/abf813"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ac0c20"},{"key":"ref18","first-page":"73","volume":"2174","author":"Liu Y.","year":"2021","journal-title":"RIMS Kokyuroku"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/28\/6\/065018"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/27\/11\/115011"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02571402"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1080\/17415977.2019.1696787"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/22M1500691"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/23M162260X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:55:45Z","timestamp":1787320545000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M162260X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,3]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9,30]]}},"alternative-id":["10.1137\/23M162260X"],"URL":"https:\/\/doi.org\/10.1137\/23m162260x","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,3]]}}}