Inverse source problem for discrete Helmholtz equation

被引：2

作者：

Novikov, Roman ^{[1
,2
]}

Sharma, Basant Lal ^{[3
]}

机构：

[1] Inst Polytech Paris, Ecole Polytech, CMAP, CNRS, F-91128 Palaiseau, France

[2] IEPT RAS, Moscow 117997, Russia

[3] Indian Inst Technol Kanpur, Dept Mech Engn, Kanpur, Uttar Pradesh, India

来源：

INVERSE PROBLEMS | 2024年 / 40卷 / 10期

关键词：

discrete Helmholtz operators; multi-frequency inverse source problem; phase retrieval; monochromatic inverse scattering in the Born approximation; LATTICE GREENS-FUNCTION; SQUARE LATTICE; SCHRODINGER-OPERATORS; SCATTERING; DIFFRACTION; NONUNIQUENESS; STABILITY; WAVES;

D O I：

10.1088/1361-6420/ad7054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice Zd, d >= 1. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schr & ouml;dinger operators in the Born approximation are also provided.

引用

页数：17

共 50 条

[1] LATTICE GREENS FUNCTION FOR SIMPLE CUBIC AND TETRAGONAL LATTICES AT ARBITRARY POINTS [J].

ABE, Y ;

KATSURA, S .

ANNALS OF PHYSICS, 1973, 75 (02) :348-380

[2] Inverse problem on the line without phase information [J].

Aktosun, T ;

Sacks, PE .

INVERSE PROBLEMS, 1998, 14 (02) :211-224

[3] Spectral Properties of Schrodinger Operators on Perturbed Lattices [J].

Ando, Kazunori ;

Isozaki, Hiroshi ;

Morioka, Hisashi .

ANNALES HENRI POINCARE, 2016, 17 (08) :2103-2171

[4] Inverse Scattering Theory for Discrete Schrodinger Operators on the Hexagonal Lattice [J].

Ando, Kazunori .

ANNALES HENRI POINCARE, 2013, 14 (02) :347-383

[5]

[Anonymous], 1989, Electronic Structure and the Properties of Solids-The Physics of the Chemical Bond

[6] Recovering point sources for the inhomogeneous Helmholtz equation * [J].

Bao, Gang ;

Liu, Yuantong ;

Triki, Faouzi .

INVERSE PROBLEMS, 2021, 37 (09)

[7] A multi-frequency inverse source problem [J].

Bao, Gang ;

Lin, Junshan ;

Triki, Faouzi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (12) :3443-3465

[8] Geometry of the phase retrieval problem [J].

Barnett, Alexander H. ;

Epstein, Charles L. ;

Greengard, Leslie F. ;

Magland, Jeremy F. .

INVERSE PROBLEMS, 2020, 36 (09)

[9]

Bloch F., 1929, Z. Phys., V52, P555, DOI DOI 10.1007/BF01339455

[10] A remark on Lipschitz stability for inverse problems [J].

Bourgeois, Laurent .

COMPTES RENDUS MATHEMATIQUE, 2013, 351 (5-6) :187-190

← 1 2 3 4 5 →