To overcome the contradiction between the resolution and the measurement cost, various algorithms for reconstructing the sound field with sparse measurement have been developed. However, limited attention is paid to the computation efficiency. In this study, a fast sparse reconstruction method is proposed based on the Bayesian compressive sensing. First, the reconstruction problem is modeled by a sparse decomposition of the sound field via singular value decomposition. Then, the Bayesian compressive sensing is adapted to reconstruct the sound field with sparse measurement of sound pressure. Numerical results demonstrate that the proposed method is applicable to either the spatially sparse distributed sound sources or the spatially extended sound sources. And comparisons with other two sparse reconstruction methods show that the proposed one has the advantages in terms of reconstruction accuracy and computational efficiency. In addition, as it is developed in the framework of multitask compressive sensing, the method can use multiple snapshots to perform reconstruction, which greatly enhances the robustness to noise. The validity and the advantage of the proposed method are further proved by experimental results.

References

References
1.
Ning
,
C.
,
Mohammad-Djafari
,
A.
, and
Picheral
,
J.
,
2013
, “
Robust Bayesian Super-Resolution Approach Via Sparsity Enforcing a Priori for Near-Field Aeroacoustic Source Imaging
,”
J. Sound Vib.
,
332
(
18
), pp.
4369
4389
.
2.
Wu
,
S. F.
, and
Natarajan
,
L. K.
,
2013
, “
Panel Acoustic Contribution Analysis
,”
J. Acoust. Soc. Am.
,
133
(
2
), pp.
799
809
.
3.
Bissinger
,
G.
,
Williams
,
E. G.
, and
Valdivia
,
N.
,
2007
, “
Violin f-Hole Contribution to Far-Field Radiation Via Patch Near-Field Acoustical Holography
,”
J. Acoust. Soc. Am.
,
121
(
6
), pp.
3899
3906
.
4.
Zhang
,
Y.
,
Zhang
,
X. Z.
,
Bi
,
C. X.
, and
Zhang
,
Y. B.
,
2017
, “
An Inverse Direct Time Domain Boundary Element Method for the Reconstruction of Transient Acoustic Field
,”
ASME J. Vib. Acoust.
,
139
(
3
), p.
021013
.
5.
Williams
,
E. G.
,
Houston
,
B. H.
,
Herdic
,
P. C.
,
Raveendra
,
S. T.
, and
Gardner
,
B.
,
2000
, “
Interior Near-Field Acoustical Holography in Flight
,”
J. Acoust. Soc. Am.
,
108
(
4
), pp.
1451
1463
.
6.
Maynard
,
J. D.
,
Williams
,
E. G.
, and
Lee
,
Y.
,
1985
, “
Nearfield Acoustic Holography: I. Theory of Generalized Holography and the Development of NAH
,”
J. Acoust. Soc. Am.
,
78
(
4
), pp.
1395
1413
.
7.
Jacobsen
,
F.
,
Chen
,
X.
, and
Jaud
,
V.
,
2008
, “
A Comparison of Statistically Optimized Near Field Acoustic Holography Using Single Layer Pressure–Velocity Measurements and Using Double Layer Pressure Measurements
,”
J. Acoust. Soc. Am.
,
123
(
4
), pp.
1842
1845
.
8.
Bai
,
M. R.
,
1992
, “
Application of BEM (Boundary Element Method)-Based Acoustic Holography to Radiation Analysis of Sound Sources With Arbitrarily Shaped Geometries
,”
J. Acoust. Soc. Am.
,
92
(
1
), pp.
533
549
.
9.
Bi
,
C. X.
,
Chen
,
X. Z.
,
Chen
,
J.
, and
Zhou
,
R.
,
2005
, “
Nearfield Acoustic Holography Based on the Equivalent Source Method
,”
Sci. China Ser. E: Technol. Sci.
,
48
(
3
), pp.
338
354
.
10.
Lee
,
M.
, and
Bolton
,
J. S.
,
2007
, “
Reconstruction of Source Distributions From Sound Pressures Measured Over Discontinuous Regions: Multipatch Holography and Interpolation
,”
J. Acoust. Soc. Am.
,
121
(
4
), pp.
2086
2096
.
11.
Xu
,
L.
,
Bi
,
C.
,
Chen
,
X.
, and
Chen
,
J.
,
2008
, “
Resolution Enhancement of Nearfield Acoustic Holography by Interpolation Using Band-Limited Signal Restoration Method
,”
Chin. Sci. Bull.
,
53
(
20
), pp.
3142
3150
.
12.
Harris
,
M. C.
,
Blotter
,
J. D.
, and
Sommerfeldt
,
S. D.
,
2006
, “
Obtaining the Complex Pressure Field at the Hologram Surface for Use in Near-Field Acoustical Holography When Pressure and In-Plane Velocities Are Measured
,”
J. Acoust. Soc. Am.
,
119
(
3
), pp.
192
195
.
13.
Wang
,
R.
,
Chen
,
J.
, and
Dong
,
G.
,
2012
, “
Data Interpolation Method Based on the Wave Superposition Algorithm
,”
J. Vib. Control
,
20
(
3
), pp.
421
435
.
14.
Leclère
,
Q.
,
2009
, “
Acoustic Imaging Using Under-Determined Inverse Approaches: Frequency Limitations and Optimal Regularization
,”
J. Sound Vib.
,
321
(
3
), pp.
605
619
.
15.
Chardon
,
G.
,
Daudet
,
L.
,
Peillot
,
A.
,
Ollivier
,
F.
,
Bertin
,
N.
, and
Gribonval
,
R.
,
2012
, “
Near-Field Acoustic Holography Using Sparse Regularization and Compressive Sampling Principles
,”
J. Acoust. Soc. Am.
,
132
(
3
), pp.
1521
1534
.
16.
Donoho
,
D. L.
,
2004
, “
Compressed Sensing
,”
IEEE Trans. Inf. Theory
,
52
(
4
), pp.
1289
1306
.
17.
Ji
,
S.
,
Xue
,
Y.
, and
Carin
,
L.
,
2008
, “
Bayesian Compressive Sensing
,”
IEEE Trans. Signal Process.
,
56
(
6
), pp.
2346
2356
.
18.
Fernandez-Grande
,
E.
,
Xenaki
,
A.
, and
Gerstoft
,
P.
,
2017
, “
A Sparse Equivalent Source Method for Near-Field Acoustic Holography
,”
J. Acoust. Soc. Am.
,
141
(
1
), pp.
532
542
.
19.
Hald
,
J.
,
2018
, “
A Comparison of Iterative Sparse Equivalent Source Methods for Near-Field Acoustical Holography
,”
J. Acoust. Soc. Am.
,
143
(
6
), pp.
3758
3769
.
20.
Bi
,
C. X.
,
Liu
,
Y.
,
Xu
,
L.
, and
Zhang
,
Y. B.
,
2017
, “
Sound Field Reconstruction Using Compressed Modal Equivalent Point Source Method
,”
J. Acoust. Soc. Am.
,
141
(
1
), pp.
73
79
.
21.
Hu
,
D. Y.
,
Li
,
H. B.
,
Hu
,
Y.
, and
Fang
,
Y.
,
2018
, “
Sound Field Reconstruction With Sparse Sampling and the Equivalent Source Method
,”
Mech. Syst. Signal Process.
,
108
(
9
), pp.
317
325
.
22.
Hald
,
J.
,
2016
, “
Fast Wideband Acoustical Holography
,”
J. Acoust. Soc. Am.
,
139
(
4
), pp.
1508
1517
.
23.
Pereira
,
A.
,
Antoni
,
J.
, and
Leclère
,
Q.
,
2015
, “
Empirical Bayesian Regularization of the Inverse Acoustic Problem
,”
Appl. Acoust.
,
97
, pp.
11
29
.
24.
Fernandez-Grande
,
E.
, and
Daudet
,
L.
,
2016
, “
Near-Field Acoustic Imaging Based on Laplacian Sparsity
,”
22nd International Congress on Acoustics
,
Buenos Aires, Argentina
,
Sept. 5–9
, pp.
1
9
.
25.
Fernandez-Grande
,
E.
, and
Xenaki
,
A.
,
2016
, “
Compressive Sensing With a Spherical Microphone Array
,”
J. Acoust. Soc. Am.
,
139
(
2
), pp.
EL45
EL49
.
26.
Abusag
,
N. M.
, and
Chappell
,
D. J.
,
2016
, “
On Sparse Reconstructions in Near-Field Acoustic Holography Using the Method of Superposition
,”
J. Comput. Acoust.
,
24
(
3
), pp.
554
930
.
27.
Fernandez-Grande
,
E.
, and
Xenaki
,
A.
,
2015
, “
Sparse Acoustic Imaging With a Spherical Array
,”
EuroNoise 2015
,
Maastricht, Netherlands
,
May 31–June 3
, pp.
1
6
.
28.
He
,
Y. S.
,
Liu
,
C.
,
Xu
,
Z. M.
, and
Li
,
S.
,
2018
, “
Application of Inverse Patch Transfer Functions Method With Wideband Holography Algorithm to Sparsely Distributed Sources Identification
,”
ASME J. Vib. Acoust.
,
140
(
1
), p.
011008
.
29.
Xu
,
Z. M.
,
Wang
,
Q. H.
,
He
,
Y. S.
,
Zhang
,
Z. F.
,
Li
,
S.
, and
Li
,
M. R.
,
2018
, “
A Monotonic Two-Step Iterative Shrinkage/Thresholding Algorithm for Sound Source Identification Based on Equivalent Source Method
,”
Appl. Acoust.
,
129
, pp.
386
396
.
30.
Tipping
,
M. E.
,
2001
, “
Sparse Bayesian Learning and the Relevance Vector Machine
,” ,
1
(
3
), pp.
211
244
.
31.
Borgiotti
,
L. S. G. V.
, and
Williams
,
E. G.
,
1990
, “
Conformal Generalized Near-Field Acoustic Holography for Axisymmetric Geometries
,”
J. Acoust. Soc. Am.
,
88
(
1
), pp.
199
209
.
32.
Pereira
,
A.
,
Leclere
,
Q.
, and
Antoni
,
J. A.
,
2012
, “
A Theoretical and Experimental Comparison of the Equivalent Source Method and a Bayesian Approach to Noise Source Identification
,”
4th Berlin Beamforming Conference
,
Berlin, Germany
,
Feb. 22–23
, pp.
1
12
.
33.
Leclere
,
Q.
, and
Laulagnet
,
B.
,
2005
, “
An Alternative Acoustic Imaging Technique to Improve Capabilities of Microphone Array Measurements
,”
Saint Raphael
,
France
,
Apr. 18–21
, pp.
1
8
.
34.
Cotter
,
S. F.
,
Rao
,
B. D.
, and
Kreutz-Delgado
,
K.
,
2005
, “
Sparse Solutions to Linear Inverse Problems With Multiple Measurement Vectors
,”
IEEE Trans. Signal Process.
,
53
(
7
), pp.
2477
2488
.
35.
Tivive
,
F. H. C.
, and
Bouzerdoum
,
A.
,
2013
, “
A Compressed Sensing Method for Complex-Valued Signals With Application to Through-the-Wall Radar Imaging
,”
IEEE International Conference on Acoustics, Speech and Signal Processing
,
Vancouver, BC
,
May 26–30
, pp.
2144
2148
.
36.
Ji
,
S.
,
Dunson
,
D.
, and
Carin
,
L.
,
2009
, “
Multitask Compressive Sensing
,”
IEEE Trans. Signal Process.
,
57
(
1
), pp.
92
106
.
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