Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the emitted wavelength. In this work we propose a method based on physically informed neural-networks for solving the source refocusing problem, constructing a novel loss term which promotes super-resolving capabilities of the network and is based on the physics of wave propagation. We demonstrate the approach in the setup of imaging an a priori unknown number of point sources in a two-dimensional rectangular waveguide from measurements of wavefield recordings along a vertical cross section. The results show the ability of the method to approximate the locations of sources with high accuracy, even when placed close to each other.
REFERENCES
1.
U.
Albocher
,
A. A.
Oberai
,
P. E.
Barbone
, and
I.
Harari
, “
Adjoint-weighted equation for inverse problems of incompressible plane-stress elasticity
,” Comput. Methods Appl. Mech. Eng.
198
(30-32
), 2412
–2420
(2009
).2.
P. E.
Barbone
,
A. A.
Oberai
, and
I.
Harari
, “
Adjoint-weighted variational formulation for a direct computational solution of an inverse heat conduction problem
,” Inv. Problems
23
(6
), 2325
–2342
(2007
).3.
D.
Colton
and
R.
Kress
, “
Inverse acoustic and electromagnetic scattering theory
,” in Applied Mathematical Sciences
(
Springer
,
New York
, 2013
), Vol. 93.4.
V.
Isakov
, “
Inverse problems for partial differential equations
,” in Applied Mathematical Sciences
(
Springer
,
New York
, 1998
), Vol. 127.5.
A.
Tarantola
, Inverse Problem Theory and Methods for Model Parameter Estimation
(
SIAM
,
Philadelphia
, 2005
).6.
C. R.
Vogel
, Computational Methods for Inverse Problems
(
SIAM
,
Philadelphia
, 2002
).7.
R. V.
Allen
, “
Automatic earthquake recognition and timing from single traces
,” Bull. Seismol. Soc. Am.
68
(5
), 1521
–1532
(1978
).8.
M.
Baer
and
U.
Kradolfer
, “
An automatic phase picker for local and teleseismic events
,” Bull. Seismol. Soc. Am.
77
(4
), 1437
–1445
(1987
).9.
L.
Küperkoch
,
T.
Meier
,
J.
Lee
,
W.
Friederich
, and
E. W.
Group
, “
Automated determination of p-phase arrival times at regional and local distances using higher order statistics
,” Geophys. J. Int.
181
(2
), 1159
–1170
(2010
).10.
R.
Sleeman
and
T.
Van Eck
, “
Robust automatic P-phase picking: An on-line implementation in the analysis of broadband seismogram recordings
,” Phys. Earth Planet. Int.
113
(1-4
), 265
–275
(1999
).11.
H.
Niu
,
E.
Reeves
, and
P.
Gerstoft
, “
Source localization in an ocean waveguide using supervised machine learning
,” J. Acoust. Soc. Am.
142
(3
), 1176
–1188
(2017
).12.
H.
Niu
,
Z.
Gong
,
E.
Ozanich
,
P.
Gerstoft
,
H.
Wang
, and
Z.
Li
, “
Deep-learning source localization using multi-frequency magnitude-only data
,” J. Acoust. Soc. Am.
146
(1
), 211
–222
(2019
).13.
M.
Raissi
,
P.
Perdikaris
, and
G. E.
Karniadakis
, “
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
,” J. Comput. Phys.
378
, 686
–707
(2019
).14.
W.
Zhu
and
G. C.
Beroza
, “
Phasenet: A deep-neural-network-based seismic arrival-time picking method
,” Geophys. J. Int.
216
(1
), 261
–273
(2018
).15.
S.
Arridge
,
P.
Maass
,
O.
Öktem
, and
C.-B.
Schönlieb
, “
Solving inverse problems using data-driven models
,” Acta Numerica
28
, 1
–174
(2019
).16.
Y.
Wang
and
H.
Peng
, “
Underwater acoustic source localization using generalized regression neural network
,” J. Acoust. Soc. Am.
143
(4
), 2321
–2331
(2018
).17.
P.-A.
Grumiaux
,
S.
Kitić
,
L.
Girin
, and
A.
Guérin
, “
A survey of sound source localization with deep learning methods
,” J. Acoust. Soc. Am.
152
(1
), 107
–151
(2022
).18.
Y.
Huang
,
X.
Wu
, and
T.
Qu
, “
Dnn-based sound source localization method with microphone array
,” in International Conference on Information, Electronic and Communication Engineering
(2018
), pp. 191
–197
.19.
D.
Suvorov
,
G.
Dong
, and
R.
Zhukov
, “
Deep residual network for sound source localization in the time domain
,” J. Eng. Appl. Sci.
13
(13
), 5096
–5104
(2018
), available at https://scholar.google.com/scholar?cluster=16621617040146518240&hl=en&as_sdt=0,40&as_vis=1.20.
G.
Bologni
,
R.
Heusdens
, and
J.
Martinez
, “
Acoustic reflectors localization from stereo recordings using neural networks
,” in ICASSP 2021–2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(
IEEE
,
Piscataway, NJ
, 2021
), pp. 1
–5
.21.
M.
Li
,
L.
Demanet
, and
L.
Zepeda-Núñez
, “
Accurate and robust deep learning framework for solving wave-based inverse problems in the super-resolution regime
,” arXiv:2106.01143 (2021
).22.
A. G.
Baydin
,
B. A.
Pearlmutter
,
A. A.
Radul
, and
J. M.
Siskind
, “
Automatic differentiation in machine learning: A survey
,” J. Machine Learn. Res.
18
, 1
–43
(2018
).23.
G. E.
Karniadakis
,
I. G.
Kevrekidis
,
L.
Lu
,
P.
Perdikaris
,
S.
Wang
, and
L.
Yang
, “
Physics-informed machine learning
,” Nat. Rev. Phys.
3
(6
), 422
–440
(2021
).24.
H.
Sundar
,
W.
Wang
,
M.
Sun
, and
C.
Wang
, “
Raw waveform based end-to-end deep convolutional network for spatial localization of multiple acoustic sources
,” in ICASSP 2020–2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(2020
).25.
N.
Bleistein
, Mathematical Methods for Wave Phenomena
(
Academic Press
,
New York
, 2012
).26.
D.
Batenkov
,
L.
Demanet
, and
H. N.
Mhaskar
, “
Stable soft extrapolation of entire functions
,” Inv. Probl.
35
(1
), 015011
(2019
).27.
M.
Bertero
and
C.
de Mol
, “
III Super-resolution by data inversion
,” Prog. Opt.
36
, 129
–178
(1996
).28.
G.
De Villiers
and
E. R.
Pike
, The Limits of Resolution
(
CRC Press
,
Boca Raton, FL
, 2016
).29.
J.
Lindberg
, “
Mathematical concepts of optical superresolution
,” J. Opt.
14
(8
), 083001
(2012
).30.
I.
Daubechies
,
M.
Defrise
, and
C. D.
Mol
, “
Sparsity-enforcing regularisation and ISTA revisited
,” Inv. Probl.
32
(10
), 104001
(2016
).31.
E. J.
Candès
and
C.
Fernandez-Granda
, “
Towards a mathematical theory of super-resolution
,” Commun. Pure Appl. Math.
67
(6
), 906
–956
(2014
).32.
D.
Batenkov
,
G.
Goldman
, and
Y.
Yomdin
, “
Super-resolution of near-colliding point sources
,” Inf. Inference: J. IMA
10
(2
), 515
–572
(2021
).33.
34.
L.
Borcea
,
G.
Papanicolaou
, and
F. G.
Vasquez
, “
Edge illumination and imaging of extended reflectors
,” SIAM J. Imaging Sci.
1
(1
), 75
–114
(2008
).© 2023 Acoustical Society of America.
2023
Acoustical Society of America
You do not currently have access to this content.