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Regularization for improving the deconvolution in real-time near-field acoustic holography
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10.1121/1.3586790
/content/asa/journal/jasa/129/6/10.1121/1.3586790
http://aip.metastore.ingenta.com/content/asa/journal/jasa/129/6/10.1121/1.3586790

Figures

Image of FIG. 1.
FIG. 1.

Geometry of interest. Forward and backward propagation in real-time near-field acoustic holography. The distances between the measurement plane and the calculation plane in both configurations are the same.

Image of FIG. 2.
FIG. 2.

Impulse response .

Image of FIG. 3.
FIG. 3.

Modulus and phase of the theoretical Fourier transform of the inverse impulse response with , where fs is the sampling frequency.

Image of FIG. 4.
FIG. 4.

(Color online) Reconstructed time signals obtained by inverse filtering using singular value decomposition coupled with regularization (a)–(c), or Wiener approach (d)–(f), vs reference signals (dotted line) on locations R 2 [(a), (d)], R 3 [(b), (e)], and R 4 [(c), (f)] (see Fig. 1). The impulse response was processed using Chebyshev low-pass filtering.

Image of FIG. 5.
FIG. 5.

(Color online) Spatial maps for indicator T 1 in the case of regularization (a) and inverse filtering (b) with a contour line at the value 0.95. The locations of R 1(+), R 2(+), R 3(+), and R 4(*) are marked.

Image of FIG. 6.
FIG. 6.

Spatial maps for indicator T 2 in the case of regularization (a) and inverse filtering (b). The areas in gray correspond to values of T 2 below 0.05. The locations of R 1(+), R 2(+), R 3(+), and R 4(*) are marked.

Image of FIG. 7.
FIG. 7.

(Color online) Time-dependent spatial errors Ex , y [see Eq. (34)] and[see Eq. (35)] in the case of regularization (a), (c), and inverse filtering (b), (d) for three processing methods applied to the impulse response (direct sampling, Kaiser and Chebyshev filtering).

Image of FIG. 8.
FIG. 8.

(Color online) Comparison of the modulus in Pa of spatial sound pressure fields at time t = 6.2 ms: The back-propagated spatial sound pressure fields using regularization with (b) or without measurement noise (a), Wiener inverse filtering with (d) or without measurement noise (c), the reference field (e). Inversion is achieved from an impulse response preprocessed by Chebyshev low-pass filtering. In the case of measurement noise, the signal-to-noise ratio (SNR) is 3 dB.

Image of FIG. 9.
FIG. 9.

(Color online) Comparison between reference signals (dotted line) and back-propagated signals using regularization method (a)–(c), and inverse Wiener filtering method (d)–(f), associated with Chebyshev low-pass filtering on locations R 2, R 3, and R 4 with a signal to measurement noise ratio SNR = 3 dB.

Image of FIG. 10.
FIG. 10.

(Color online) Noise influence on the spatial errors Ex , y and in the case of regularization (a), (c) and inverse filtering (b), (d) when Chebyshev filtering is applied to the impulse response. The vertical line indicates the time chosen (t = 6.2 ms) for the spatial field representation in Fig. 8.

Tables

Generic image for table
TABLE I.

Indicator T 1 [see Eq. (30)] computed from reference signals and pressure signals back-propagated to the plane z = zc in locations R 1, R 2, R 3, and R 4 (see Fig. 1) using the inverse impulse responses obtained by Wiener filtering or regularization from preprocessed impulse responses by the direct method with fe  = 16 000 Hz, the average method, Chebyshev and Kaiser filtering.

Generic image for table
TABLE II.

Indicator T 2 [see Eq. (31)] computed from reference signals and pressure signals back-propagated to the plane z = zc in locations R 1, R 2, R 3, and R 4 (see Fig. 1) using the inverse impulse responses obtained by Wiener filtering or regularization from pre-processed impulse responses by the direct method with fe  = 16 000 Hz, the average method, Chebyshev and Kaiser filtering.

Generic image for table
TABLE III.

Indicators T 1 and T 2 [see Eqs. (30) and (31)] computed from reference signals and pressure signals back-propagated to the plane z = zc in locations R 1, R 2, R 3, and R 4 (see Fig. 1) using the inverse impulse responses obtained by Wiener filtering or regularization in the case of measurement noise with a signal to noise ratio SNR = 3 dB.

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/content/asa/journal/jasa/129/6/10.1121/1.3586790
2011-06-14
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Regularization for improving the deconvolution in real-time near-field acoustic holography
http://aip.metastore.ingenta.com/content/asa/journal/jasa/129/6/10.1121/1.3586790
10.1121/1.3586790
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