Analysis & PDE Vol. 14, No. 3, 2021 (original) (raw)

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Volume 19, 3 issues Volume 19 Issue 3, 413–626 Issue 2, 203–411 Issue 1, 1–202 Volume 18, 10 issues Volume 18 Issue 10, 2325–2550 Issue 9, 2081–2323 Issue 8, 1835–2080 Issue 7, 1567–1834 Issue 6, 1309–1566 Issue 5, 1065–1308 Issue 4, 805–1064 Issue 3, 549–803 Issue 2, 279–548 Issue 1, 1–278 Volume 17, 10 issues Volume 17 Issue 10, 3371–3670 Issue 9, 2997–3369 Issue 8, 2619–2996 Issue 7, 2247–2618 Issue 6, 1871–2245 Issue 5, 1501–1870 Issue 4, 1127–1500 Issue 3, 757–1126 Issue 2, 379–756 Issue 1, 1–377 Volume 16, 10 issues Volume 16 Issue 10, 2241–2494 Issue 9, 1989–2240 Issue 8, 1745–1988 Issue 7, 1485–1744 Issue 6, 1289–1483 Issue 5, 1089–1288 Issue 4, 891–1088 Issue 3, 613–890 Issue 2, 309–612 Issue 1, 1–308 Volume 15, 8 issues Volume 15 Issue 8, 1861–2108 Issue 7, 1617–1859 Issue 6, 1375–1616 Issue 5, 1131–1373 Issue 4, 891–1130 Issue 3, 567–890 Issue 2, 273–566 Issue 1, 1–272 Volume 14, 8 issues Volume 14 Issue 8, 2327–2651 Issue 7, 1977–2326 Issue 6, 1671–1976 Issue 5, 1333–1669 Issue 4, 985–1332 Issue 3, 667–984 Issue 2, 323–666 Issue 1, 1–322 Volume 13, 8 issues Volume 13 Issue 8, 2259–2480 Issue 7, 1955–2257 Issue 6, 1605–1954 Issue 5, 1269–1603 Issue 4, 945–1268 Issue 3, 627–944 Issue 2, 317–625 Issue 1, 1–316 Volume 12, 8 issues Volume 12 Issue 8, 1891–2146 Issue 7, 1643–1890 Issue 7, 1397–1644 Issue 6, 1397–1642 Issue 5, 1149–1396 Issue 4, 867–1148 Issue 3, 605–866 Issue 2, 259–604 Issue 1, 1–258 Volume 11, 8 issues Volume 11 Issue 8, 1841–2148 Issue 7, 1587–1839 Issue 6, 1343–1586 Issue 5, 1083–1342 Issue 4, 813–1081 Issue 3, 555–812 Issue 2, 263–553 Issue 1, 1–261 Volume 10, 8 issues Volume 10 Issue 8, 1793–2041 Issue 7, 1539–1791 Issue 6, 1285–1538 Issue 5, 1017–1284 Issue 4, 757–1015 Issue 3, 513–756 Issue 2, 253–512 Issue 1, 1–252 Volume 9, 8 issues Volume 9 Issue 8, 1772–2050 Issue 7, 1523–1772 Issue 6, 1285–1522 Issue 5, 1019–1283 Issue 4, 773–1018 Issue 3, 515–772 Issue 2, 259–514 Issue 1, 1–257 Volume 8, 8 issues Volume 8 Issue 8, 1807–2055 Issue 7, 1541–1805 Issue 6, 1289–1539 Issue 5, 1025–1288 Issue 4, 765–1023 Issue 3, 513–764 Issue 2, 257–511 Issue 1, 1–255 Volume 7, 8 issues Volume 7 Issue 8, 1713–2027 Issue 7, 1464–1712 Issue 6, 1237–1464 Issue 5, 1027–1236 Issue 4, 771–1026 Issue 3, 529–770 Issue 2, 267–527 Issue 1, 1–266 Volume 6, 8 issues Volume 6 Issue 8, 1793–2048 Issue 7, 1535–1791 Issue 6, 1243–1533 Issue 5, 1001–1242 Issue 4, 751–1000 Issue 3, 515–750 Issue 2, 257–514 Issue 1, 1–256 Volume 5, 5 issues Volume 5 Issue 5, 887–1173 Issue 4, 705–885 Issue 3, 423–703 Issue 2, 219–422 Issue 1, 1–218 Volume 4, 5 issues Volume 4 Issue 5, 639–795 Issue 4, 499–638 Issue 3, 369–497 Issue 2, 191–367 Issue 1, 1–190 Volume 3, 4 issues Volume 3 Issue 4, 359–489 Issue 3, 227–358 Issue 2, 109–225 Issue 1, 1–108 Volume 2, 3 issues Volume 2 Issue 3, 261–366 Issue 2, 119–259 Issue 1, 1–81 Volume 1, 3 issues Volume 1 Issue 3, 267–379 Issue 2, 127–266 Issue 1, 1–126

Abstract
We consider the problem of locating and reconstructing the geometry of a penetrable obstacle from time-domain measurements of causal waves. More precisely, we assume that we are given the scattered field due to point sources placed on a surface enclosing the obstacle and that the scattered field is measured on the same surface. From these multistatic scattering data we wish to determine the position and shape of the target. To deal with this inverse problem, we propose and analyze the time-domain linear sampling method (TDLSM) by means of localizing the interior transmission eigenvalues in the Fourier–Laplace domain. We also prove new time-domain estimates for the forward problem and the interior transmission problem, as well as analyze several time-domain operators arising in the inversion scheme.

Abstract

We consider the problem of locating and reconstructing the geometry of a penetrable obstacle from time-domain measurements of causal waves. More precisely, we assume that we are given the scattered field due to point sources placed on a surface enclosing the obstacle and that the scattered field is measured on the same surface. From these multistatic scattering data we wish to determine the position and shape of the target. To deal with this inverse problem, we propose and analyze the time-domain linear sampling method (TDLSM) by means of localizing the interior transmission eigenvalues in the Fourier–Laplace domain. We also prove new time-domain estimates for the forward problem and the interior transmission problem, as well as analyze several time-domain operators arising in the inversion scheme.

Keywords

time-dependent linear sampling method, inverse scattering, penetrable scatterer

Mathematical Subject Classification 2010

Primary: 35R30, 65M32

Milestones

Received: 8 July 2018

Revised: 7 May 2019

Accepted: 2 December 2019

Published: 18 May 2021

Authors

Department of Mathematics Rutgers University New Brunswick, NJ United States
Peter Monk
Department of Mathematical Sciences University of Delaware Newark, DE United States
Virginia Selgas
Departamento de Matemáticas Escuela Politécnica de Ingeniería de Gijón University of Oviedo Gijón Spain