Multiresolution subspace-based optimization method for inverse scattering problems

Giacomo Oliveri; Yu Zhong; Xudong Chen; Andrea Massa

doi:10.1364/JOSAA.28.002057

Journal of the Optical Society of America A
Vol. 28,
Issue 10,
pp. 2057-2069
(2011)
•https://doi.org/10.1364/JOSAA.28.002057

Multiresolution subspace-based optimization method for inverse scattering problems

Giacomo Oliveri, Yu Zhong, Xudong Chen, and Andrea Massa

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Giacomo Oliveri, Yu Zhong, Xudong Chen, and Andrea Massa, "Multiresolution subspace-based optimization method for inverse scattering problems," J. Opt. Soc. Am. A 28, 2057-2069 (2011)

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- Image Processing
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About this Article
History
- Original Manuscript: June 6, 2011
- Manuscript Accepted: July 20, 2011
- Published: September 13, 2011
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 6, Iss. 11

Abstract

This paper investigates an approach to inverse scattering problems based on the integration of the subspace-based optimization method (SOM) within a multifocusing scheme in the framework of the contrast source formulation. The scattering equations are solved by a nested three-step procedure composed of (a) an outer multiresolution loop dealing with the identification of the regions of interest within the investigation domain through an iterative information-acquisition process, (b) a spectrum analysis step devoted to the reconstruction of the deterministic components of the contrast sources, and (c) an inner optimization loop aimed at retrieving the ambiguous components of the contrast sources through a conjugate gradient minimization of a suitable objective function. A set of representative reconstruction results is discussed to provide numerical evidence of the effectiveness of the proposed algorithmic approach as well as to assess the features and potentialities of the multifocusing integration in comparison with the state-of-the-art SOM implementation.

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		SOM				IMSA-SOM
Actual Object	SNR (dB)	$Ψ_{tot}$	$Ψ_{int}$	$Ψ_{ext}$	$Δ t$ (s)	$Ψ_{tot}$	$Ψ_{int}$	$Ψ_{ext}$	$Δ t$ (s)
Figure 7a	∞	$9.06 \times 10^{- 3}$	$8.92 \times 10^{- 2}$	$3.71 \times 10^{- 3}$	$3.48 \times 10^{2}$	$6.83 \times 10^{- 3}$	$1.09 \times 10^{- 1}$	0.0	51.9
( $τ_{in} = 1.2$ )	30	$9.39 \times 10^{- 3}$	$8.88 \times 10^{- 2}$	$4.02 \times 10^{- 3}$	$3.59 \times 10^{2}$	$8.28 \times 10^{- 3}$	$1.32 \times 10^{- 1}$	0.0	50.8
	10	$1.20 \times 10^{- 2}$	$8.60 \times 10^{- 2}$	$7.10 \times 10^{- 3}$	$3.52 \times 10^{2}$	$8.58 \times 10^{- 3}$	$1.37 \times 10^{- 1}$	0.0	51.0
Figure 7a	∞	$4.53 \times 10^{- 3}$	$3.24 \times 10^{- 2}$	$2.88 \times 10^{- 3}$	$3.51 \times 10^{2}$	$3.81 \times 10^{- 3}$	$4.20 \times 10^{- 2}$	$1.56 \times 10^{- 3}$	51.1
( $τ_{in} = 0.0$ )	30	$4.80 \times 10^{- 3}$	$3.28 \times 10^{- 2}$	$3.15 \times 10^{- 3}$	$3.47 \times 10^{2}$	$3.81 \times 10^{- 3}$	$4.18 \times 10^{- 2}$	$1.57 \times 10^{- 3}$	52.0
	10	$7.87 \times 10^{- 3}$	$4.92 \times 10^{- 2}$	$5.96 \times 10^{- 3}$	$3.50 \times 10^{2}$	$7.39 \times 10^{- 3}$	$1.09 \times 10^{- 1}$	$1.37 \times 10^{- 3}$	51.9
Figure 7a	∞	$4.77 \times 10^{- 3}$	$3.70 \times 10^{- 2}$	$2.62 \times 10^{- 3}$	$3.51 \times 10^{2}$	$1.18 \times 10^{- 3}$	$1.89 \times 10^{- 2}$	0.0	52.3
( $τ_{in} = 0.6$ )	30	$5.04 \times 10^{- 3}$	$3.70 \times 10^{- 2}$	$2.91 \times 10^{- 3}$	$3.54 \times 10^{2}$	$1.19 \times 10^{- 3}$	$1.88 \times 10^{- 2}$	0.0	52.1
	10	$8.16 \times 10^{- 3}$	$4.18 \times 10^{- 2}$	$5.92 \times 10^{- 3}$	$3.41 \times 10^{2}$	$4.02 \times 10^{- 3}$	$6.44 \times 10^{- 2}$	0.0	51.6
Figure 14a	∞	$1.15 \times 10^{- 2}$	$6.70 \times 10^{- 2}$	$8.80 \times 10^{- 3}$	$3.63 \times 10^{2}$	$1.01 \times 10^{- 2}$	$1.13 \times 10^{- 1}$	$5.36 \times 10^{- 3}$	51.2
	30	$1.17 \times 10^{- 2}$	$6.64 \times 10^{- 2}$	$9.02 \times 10^{- 3}$	$3.29 \times 10^{2}$	$1.09 \times 10^{- 2}$	$1.67 \times 10^{- 1}$	$3.28 \times 10^{- 3}$	51.5
	10	$1.17 \times 10^{- 2}$	$6.25 \times 10^{- 2}$	$9.24 \times 10^{- 3}$	$3.48 \times 10^{2}$	$1.10 \times 10^{- 2}$	$1.68 \times 10^{- 1}$	$3.28 \times 10^{- 3}$	50.8

	SOM				IMSA-SOM
Actual Object	$Ψ_{tot}$	$Ψ_{int}$	$Ψ_{ext}$	$Δ t$ (s)	$Ψ_{tot}$	$Ψ_{int}$	$Ψ_{ext}$	$Δ t$ (s)
Figure 12	$4.56 \times 10^{- 3}$	$6.78 \times 10^{- 1}$	$6.22 \times 10^{- 3}$	$4.31 \times 10^{5}$	$1.23 \times 10^{- 3}$	$1.21 \times 10^{- 1}$	$3.46 \times 10^{- 4}$	$1.94 \times 10^{3}$
Figure 13	$2.34 \times 10^{- 3}$	$1.07 \times 10^{- 1}$	$1.32 \times 10^{- 3}$	$4.29 \times 10^{5}$	$1.48 \times 10^{- 3}$	$1.48 \times 10^{- 1}$	0.0	$1.98 \times 10^{3}$
Figure 15	$6.53 \times 10^{- 3}$	$8.96 \times 10^{- 2}$	$4.37 \times 10^{- 3}$	$4.25 \times 10^{5}$	$2.24 \times 10^{- 3}$	$5.33 \times 10^{- 2}$	$2.31 \times 10^{- 3}$	$1.95 \times 10^{3}$

		SOM				IMSA-SOM
Actual Object	SNR (dB)	$Ψ_{tot}$	$Ψ_{int}$	$Ψ_{ext}$	$Δ t$ (s)	$Ψ_{tot}$	$Ψ_{int}$	$Ψ_{ext}$	$Δ t$ (s)
Figure 7a	∞	$9.06 \times 10^{- 3}$	$8.92 \times 10^{- 2}$	$3.71 \times 10^{- 3}$	$3.48 \times 10^{2}$	$6.83 \times 10^{- 3}$	$1.09 \times 10^{- 1}$	0.0	51.9
( $τ_{in} = 1.2$ )	30	$9.39 \times 10^{- 3}$	$8.88 \times 10^{- 2}$	$4.02 \times 10^{- 3}$	$3.59 \times 10^{2}$	$8.28 \times 10^{- 3}$	$1.32 \times 10^{- 1}$	0.0	50.8
	10	$1.20 \times 10^{- 2}$	$8.60 \times 10^{- 2}$	$7.10 \times 10^{- 3}$	$3.52 \times 10^{2}$	$8.58 \times 10^{- 3}$	$1.37 \times 10^{- 1}$	0.0	51.0
Figure 7a	∞	$4.53 \times 10^{- 3}$	$3.24 \times 10^{- 2}$	$2.88 \times 10^{- 3}$	$3.51 \times 10^{2}$	$3.81 \times 10^{- 3}$	$4.20 \times 10^{- 2}$	$1.56 \times 10^{- 3}$	51.1
( $τ_{in} = 0.0$ )	30	$4.80 \times 10^{- 3}$	$3.28 \times 10^{- 2}$	$3.15 \times 10^{- 3}$	$3.47 \times 10^{2}$	$3.81 \times 10^{- 3}$	$4.18 \times 10^{- 2}$	$1.57 \times 10^{- 3}$	52.0
	10	$7.87 \times 10^{- 3}$	$4.92 \times 10^{- 2}$	$5.96 \times 10^{- 3}$	$3.50 \times 10^{2}$	$7.39 \times 10^{- 3}$	$1.09 \times 10^{- 1}$	$1.37 \times 10^{- 3}$	51.9
Figure 7a	∞	$4.77 \times 10^{- 3}$	$3.70 \times 10^{- 2}$	$2.62 \times 10^{- 3}$	$3.51 \times 10^{2}$	$1.18 \times 10^{- 3}$	$1.89 \times 10^{- 2}$	0.0	52.3
( $τ_{in} = 0.6$ )	30	$5.04 \times 10^{- 3}$	$3.70 \times 10^{- 2}$	$2.91 \times 10^{- 3}$	$3.54 \times 10^{2}$	$1.19 \times 10^{- 3}$	$1.88 \times 10^{- 2}$	0.0	52.1
	10	$8.16 \times 10^{- 3}$	$4.18 \times 10^{- 2}$	$5.92 \times 10^{- 3}$	$3.41 \times 10^{2}$	$4.02 \times 10^{- 3}$	$6.44 \times 10^{- 2}$	0.0	51.6
Figure 14a	∞	$1.15 \times 10^{- 2}$	$6.70 \times 10^{- 2}$	$8.80 \times 10^{- 3}$	$3.63 \times 10^{2}$	$1.01 \times 10^{- 2}$	$1.13 \times 10^{- 1}$	$5.36 \times 10^{- 3}$	51.2
	30	$1.17 \times 10^{- 2}$	$6.64 \times 10^{- 2}$	$9.02 \times 10^{- 3}$	$3.29 \times 10^{2}$	$1.09 \times 10^{- 2}$	$1.67 \times 10^{- 1}$	$3.28 \times 10^{- 3}$	51.5
	10	$1.17 \times 10^{- 2}$	$6.25 \times 10^{- 2}$	$9.24 \times 10^{- 3}$	$3.48 \times 10^{2}$	$1.10 \times 10^{- 2}$	$1.68 \times 10^{- 1}$	$3.28 \times 10^{- 3}$	50.8

	SOM				IMSA-SOM
Actual Object	$Ψ_{tot}$	$Ψ_{int}$	$Ψ_{ext}$	$Δ t$ (s)	$Ψ_{tot}$	$Ψ_{int}$	$Ψ_{ext}$	$Δ t$ (s)
Figure 12	$4.56 \times 10^{- 3}$	$6.78 \times 10^{- 1}$	$6.22 \times 10^{- 3}$	$4.31 \times 10^{5}$	$1.23 \times 10^{- 3}$	$1.21 \times 10^{- 1}$	$3.46 \times 10^{- 4}$	$1.94 \times 10^{3}$
Figure 13	$2.34 \times 10^{- 3}$	$1.07 \times 10^{- 1}$	$1.32 \times 10^{- 3}$	$4.29 \times 10^{5}$	$1.48 \times 10^{- 3}$	$1.48 \times 10^{- 1}$	0.0	$1.98 \times 10^{3}$
Figure 15	$6.53 \times 10^{- 3}$	$8.96 \times 10^{- 2}$	$4.37 \times 10^{- 3}$	$4.25 \times 10^{5}$	$2.24 \times 10^{- 3}$	$5.33 \times 10^{- 2}$	$2.31 \times 10^{- 3}$	$1.95 \times 10^{3}$

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Journal of the Optical Society of America A