Abstract

In the study of optical testing, the computed tomogaphy technique has been widely adopted to reconstruct three-dimensional distributions of physical parameters of various kinds of fluid fields, such as flame, plasma, etc. In most cases, projection data are often stained by noise due to environmental disturbance, instrumental inaccuracy, and other random interruptions. To improve the reconstruction performance in noisy cases, an algorithm that combines a self-adaptive prefiltering denoising approach (SPDA) with a multicriterion iterative reconstruction (MCIR) is proposed and studied. First, the level of noise is approximately estimated with a frequency domain statistical method. Then the cutoff frequency of a Butterworth low-pass filter was established based on the evaluated noise energy. After the SPDA processing, the MCIR algorithm was adopted for limited-view optical computed tomography reconstruction. Simulated reconstruction of two test phantoms and a flame emission spectral tomography experiment were employed to evaluate the performance of SPDA-MCIR in noisy cases. Comparison with some traditional methods and experiment results showed that the SPDA-MCIR combination had obvious improvement in the case of noisy data reconstructions.

© 2007 Optical Society of America

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References

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    [CrossRef]

2005

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

2004

X. Wan, S. Yu, Y. Gao, and Q. Zhu, "Self-adaptive reconstruction algorithm for emission spectral volume tomography," Opt. Eng. 43, 1244-1250 (2004).
[CrossRef]

X. Wan, S. Yu, G. Cai, Y. Gao, and J. Yi, "Three-dimensional plasma field reconstruction with multiobjective optimization emission spectral tomography," J. Opt. Soc. Am. A 21, 1161-1171 (2004).
[CrossRef]

2003

X. Wan, Y. Gao, and Y. Wang, "3-D flame temperature field reconstruction with multiobjective neural network," Chin. Opt. Lett. 1, 78-81 (2003).

X. Wan, Y. Gao, Q. Wang, S. Lee, and S. Yu, "Limited-angle computed tomography algorithms for the physical sciences," Opt. Eng. 42, 2659-2669 (2003).
[CrossRef]

2002

X. Wan, Y. Gao, and S. Yu, "Study of limited-view tomography algorithms for plasma diagnostics," Plast. Eng. (Brookfield, Conn.) 4927, 625-632 (2002).

2001

S. Sardy, P. Tseng, and A. Bruce, "Robust wavelet denoising," IEEE Trans. Signal Process. 49, 1146-1152 (2001).
[CrossRef]

1994

D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
[CrossRef]

L. I. Poplevina, I. M. Tokmulin, and G. N. Vishnyakov, "Emission spectral tomography of multijet plasma flow," in Inverse Optics III, M. A. Fiddy, ed., Proc. SPIE 2241, 90-98 (1994).

1993

1991

1988

1987

1983

Abbiss, J. B.

Aono, T.

Bahl, S.

Bruce, A.

S. Sardy, P. Tseng, and A. Bruce, "Robust wavelet denoising," IEEE Trans. Signal Process. 49, 1146-1152 (2001).
[CrossRef]

Cai, G.

Chen, X.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

Cheng, X.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

De Mol, C.

Defrise, M.

Dhadwal, H. S.

Donoho, D. L.

D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
[CrossRef]

Gao, Y.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

X. Wan, S. Yu, Y. Gao, and Q. Zhu, "Self-adaptive reconstruction algorithm for emission spectral volume tomography," Opt. Eng. 43, 1244-1250 (2004).
[CrossRef]

X. Wan, S. Yu, G. Cai, Y. Gao, and J. Yi, "Three-dimensional plasma field reconstruction with multiobjective optimization emission spectral tomography," J. Opt. Soc. Am. A 21, 1161-1171 (2004).
[CrossRef]

X. Wan, Y. Gao, Q. Wang, S. Lee, and S. Yu, "Limited-angle computed tomography algorithms for the physical sciences," Opt. Eng. 42, 2659-2669 (2003).
[CrossRef]

X. Wan, Y. Gao, and Y. Wang, "3-D flame temperature field reconstruction with multiobjective neural network," Chin. Opt. Lett. 1, 78-81 (2003).

X. Wan, Y. Gao, and S. Yu, "Study of limited-view tomography algorithms for plasma diagnostics," Plast. Eng. (Brookfield, Conn.) 4927, 625-632 (2002).

He, X.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

Hino, M.

Johnstone, I. M.

D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
[CrossRef]

Kawata, S.

Lee, S.

X. Wan, Y. Gao, Q. Wang, S. Lee, and S. Yu, "Limited-angle computed tomography algorithms for the physical sciences," Opt. Eng. 42, 2659-2669 (2003).
[CrossRef]

Liburdy, J. A.

Minami, S.

Nakajima, M.

Nakamura, O.

Poplevina, L. I.

L. I. Poplevina, I. M. Tokmulin, and G. N. Vishnyakov, "Emission spectral tomography of multijet plasma flow," in Inverse Optics III, M. A. Fiddy, ed., Proc. SPIE 2241, 90-98 (1994).

Sardy, S.

S. Sardy, P. Tseng, and A. Bruce, "Robust wavelet denoising," IEEE Trans. Signal Process. 49, 1146-1152 (2001).
[CrossRef]

Tokmulin, I. M.

L. I. Poplevina, I. M. Tokmulin, and G. N. Vishnyakov, "Emission spectral tomography of multijet plasma flow," in Inverse Optics III, M. A. Fiddy, ed., Proc. SPIE 2241, 90-98 (1994).

Tseng, P.

S. Sardy, P. Tseng, and A. Bruce, "Robust wavelet denoising," IEEE Trans. Signal Process. 49, 1146-1152 (2001).
[CrossRef]

Verhoeven, D.

Vishnyakov, G. N.

L. I. Poplevina, I. M. Tokmulin, and G. N. Vishnyakov, "Emission spectral tomography of multijet plasma flow," in Inverse Optics III, M. A. Fiddy, ed., Proc. SPIE 2241, 90-98 (1994).

Wan, X.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

X. Wan, S. Yu, Y. Gao, and Q. Zhu, "Self-adaptive reconstruction algorithm for emission spectral volume tomography," Opt. Eng. 43, 1244-1250 (2004).
[CrossRef]

X. Wan, S. Yu, G. Cai, Y. Gao, and J. Yi, "Three-dimensional plasma field reconstruction with multiobjective optimization emission spectral tomography," J. Opt. Soc. Am. A 21, 1161-1171 (2004).
[CrossRef]

X. Wan, Y. Gao, Q. Wang, S. Lee, and S. Yu, "Limited-angle computed tomography algorithms for the physical sciences," Opt. Eng. 42, 2659-2669 (2003).
[CrossRef]

X. Wan, Y. Gao, and Y. Wang, "3-D flame temperature field reconstruction with multiobjective neural network," Chin. Opt. Lett. 1, 78-81 (2003).

X. Wan, Y. Gao, and S. Yu, "Study of limited-view tomography algorithms for plasma diagnostics," Plast. Eng. (Brookfield, Conn.) 4927, 625-632 (2002).

Wang, Q.

X. Wan, Y. Gao, Q. Wang, S. Lee, and S. Yu, "Limited-angle computed tomography algorithms for the physical sciences," Opt. Eng. 42, 2659-2669 (2003).
[CrossRef]

Wang, Y.

Yi, J.

Yin, A.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

Yu, S.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

X. Wan, S. Yu, Y. Gao, and Q. Zhu, "Self-adaptive reconstruction algorithm for emission spectral volume tomography," Opt. Eng. 43, 1244-1250 (2004).
[CrossRef]

X. Wan, S. Yu, G. Cai, Y. Gao, and J. Yi, "Three-dimensional plasma field reconstruction with multiobjective optimization emission spectral tomography," J. Opt. Soc. Am. A 21, 1161-1171 (2004).
[CrossRef]

X. Wan, Y. Gao, Q. Wang, S. Lee, and S. Yu, "Limited-angle computed tomography algorithms for the physical sciences," Opt. Eng. 42, 2659-2669 (2003).
[CrossRef]

X. Wan, Y. Gao, and S. Yu, "Study of limited-view tomography algorithms for plasma diagnostics," Plast. Eng. (Brookfield, Conn.) 4927, 625-632 (2002).

Yuta, S.

Zhu, Q.

X. Wan, S. Yu, Y. Gao, and Q. Zhu, "Self-adaptive reconstruction algorithm for emission spectral volume tomography," Opt. Eng. 43, 1244-1250 (2004).
[CrossRef]

Zou, W.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

Appl. Opt.

Biometrika

D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika 81, 425-455 (1994).
[CrossRef]

Chin. Opt. Lett.

IEEE Trans. Signal Process.

S. Sardy, P. Tseng, and A. Bruce, "Robust wavelet denoising," IEEE Trans. Signal Process. 49, 1146-1152 (2001).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

X. Wan, A. Yin, Y. Gao, X. He, X. Chen, X. Cheng, W. Zou, and S. Yu, "Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects," Opt. Eng. 44, 118001 (2005).
[CrossRef]

X. Wan, Y. Gao, Q. Wang, S. Lee, and S. Yu, "Limited-angle computed tomography algorithms for the physical sciences," Opt. Eng. 42, 2659-2669 (2003).
[CrossRef]

X. Wan, S. Yu, Y. Gao, and Q. Zhu, "Self-adaptive reconstruction algorithm for emission spectral volume tomography," Opt. Eng. 43, 1244-1250 (2004).
[CrossRef]

Plast. Eng.

X. Wan, Y. Gao, and S. Yu, "Study of limited-view tomography algorithms for plasma diagnostics," Plast. Eng. (Brookfield, Conn.) 4927, 625-632 (2002).

Other

L. I. Poplevina, I. M. Tokmulin, and G. N. Vishnyakov, "Emission spectral tomography of multijet plasma flow," in Inverse Optics III, M. A. Fiddy, ed., Proc. SPIE 2241, 90-98 (1994).

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Figures (15)

Fig. 1
Fig. 1

Typical no-noise projection data and frequency property.

Fig. 2
Fig. 2

Typical noisy projection data and frequency property.

Fig. 3
Fig. 3

Choice of the cutoff frequency of low-pass filters.

Fig. 4
Fig. 4

(a) Cosine phantom, (b) cos-Gauss phantom.

Fig. 5
Fig. 5

Comparison of projection data of noise level 2 (a) before SPDA and (b) after SPDA.

Fig. 6
Fig. 6

Cosine reconstruction results of four algorithms without SPDA preprocessing in the case of noise level 2. (a) SIRT, (b) ART, (c) MART, (d) MCIR.

Fig. 7
Fig. 7

Cosine reconstruction results of four algorithms with SPDA preprocessing in the case of noise level 2. (a) SIRT, (b) ART, (c) MART, (d) MCIR.

Fig. 8
Fig. 8

Cos-Gauss reconstruction results of four algorithms without SPDA preprocessing in the case of noise level 2. (a) SIRT, (b) ART, (c) MART, (d) MCIR.

Fig. 9
Fig. 9

Cos-Gauss reconstruction results of four algorithms with SPDA preprocessing in the case of noise level 2. (a) SIRT, (b) ART, (c) MART, (d) MCIR.

Fig. 10
Fig. 10

EST system used to test the emission coefficients field of a candle flame.

Fig. 11
Fig. 11

Four-channel spectral intensity images without disturbance (650 nm). (a) 0°, (b) 45°, (c) 90°, (d) 135°.

Fig. 12
Fig. 12

Four-channel spectral intensity images with disturbance (650 nm). (a) 0°, (b) 45°, (c) 90°, (d) 135°.

Fig. 13
Fig. 13

Certain line spectral intensity data from A2 before SPDA processing. (a) Without disturbance, (b) with disturbance.

Fig. 14
Fig. 14

Certain line spectral intensity data from A2 after SPDA processing. (a) Without disturbance, (b) with disturbance.

Fig. 15
Fig. 15

Reconstruction images of the emission coefficients using the data in (a) Fig. 13(a), (b) Fig. 13(b), (c) Fig. 14(a), (d) Fig. 14(b).

Tables (4)

Tables Icon

Table 1 Range of the Proportion Coefficient and Choice of Cutoff Frequency

Tables Icon

Table 2 Reconstruction Errors of the Four Algorithms without SPDA in Noisy Cases a

Tables Icon

Table 3 Reconstruction Errors of the Four Algorithms with SPDA in Noisy Cases a

Tables Icon

Table 4 Proportion Coefficient Prop of Tested Data

Equations (40)

Equations on this page are rendered with MathJax. Learn more.

prop=k=0RPV/4|i=0RPV1p(i+1)exp(j2πRPVik)|2k=(RPV/4)+1RPV/2|i=0RPV1p(i+1)exp(j2πRPVik)|2,
π/2
π/2
p(i)
ωc
Calculate  prop,Make   certain  r,TOE=k=0RPV/2|i=0RPV1p(i+1)exp(j2πRPVik)|2,
TE0=|i=0RPV1p(i+1)|2,
TEk=TEk1+|i=0RPV1p(i+1)exp(j2πRPVik)|2,k=1  to  (RPV/2),
ωc=kRPV/2π, if  TEkr×TOE,
H(jω)=11+(ωωc)2N,
p=IDFT[DFT(p)H(jω)].
TOE
k/(RPV/2)π
P=WF+E,
F^
Φ(F^)=l=13λlΦl(F^),
λl
 dΦ(F^)dF^=2λ11σ2WT(IWF^)+2λ2BF^+λ3(ln  F^+1)=0.
F(0)=1,F(j)(k+1)=R(j)k·F(j)k,j=1,2,,  MN,
R(j)(k)=1+γ[2λ1(k)1σ2wij(IiWiF(k))2λ2(k)BijF(j)(k)λ3(k)(ln  F(j)(k)+1)],i=k(mod  I)+1,
σ2
λ1(1)
λ2(1)
λ3(1)
1/3
ΔΦl(k+1)=|Φl(k+1)Φl(k)|,l=1,2,3.
λ1+λ2+λ3=1,
λ1ΔΦ1=λ2ΔΦ2=λ3ΔΦ3.
λl(k+1)=τlΔΦτ(k+1)l=13[τlΔΦτ(k+1)],l,τ=1,2,3.
|F(k+1)F(k)|<ε1.
Cosine(x,y)={0.25{1cos[2π(x+0.5)4/5]} ×{1cos[2π(y+0.5)2/3]},|x,y|<0.50,otherwise.
x1=0.20
y1=0.10
(x2=0.20,y2=0.35)
cos - Gauss(x,y)=1.09{0.075{1cos[2π(x+0.5)4/5]}×{1cos[2π(y+0.5)2/3]}+0.8{exp{[9(xx1)]2[6(yy1)]2}+exp{[8(xx2)]2[30(yy2)]2}}}.
A1
A2
A2
A2
A2

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