Constrained models for optical absorption tomography

Nick Polydorides , Alex Tsekenis, Edward Fisher, Andrea Chigine, Hugh McCann, Luca Dimiccoli, Paul Wright, Michael Lengden, Thomas Benoy, David Wilson, Gordon Humphries, Walter Johnstone

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider the inverse problem of concentration imaging in optical absorption tomography with limited data sets. The measurement setup involves simultaneous acquisition of near infrared wavelength modulated spectroscopic measurements from a small number of pencil beams equally distributed among six projection angles surrounding the plume. We develop an approach for image reconstruction that involves constraining the value of the image to the conventional concentration bounds and a projection into low-dimensional subspaces to reduce the degrees of freedom in the inverse problem. Effectively, by reparameterising the forward model we impose simultaneously spatial smoothness and a choice between three types of inequality constraints, namely positivity, boundedness and logarithmic boundedness in a simple way that yields an unconstrained optimisation problem in a new set of surrogate parameters. Testing this numerical scheme with simulated and experimental phantom data indicates that the combination of affine inequality constraints and subspace projection leads to images that are qualitatively and quantitatively superior to unconstrained regularised reconstructions. This improvement is more profound in targeting concentration profiles of small spatial variation. We present images and convergence graphs from solving these inverse problems using Gauss-Newton's algorithm to demonstrate the performance and convergence of our method.
LanguageEnglish
PagesB1-B9
Number of pages9
JournalApplied Optics
Volume57
Issue number7
DOIs
Publication statusPublished - 23 Oct 2017

Fingerprint

optical absorption
tomography
projection
pencil beams
image reconstruction
newton
plumes
acquisition
degrees of freedom
optimization
profiles
wavelengths

Keywords

  • computational imaging
  • tomography
  • combustion diagnostics

Cite this

Polydorides , N., Tsekenis, A., Fisher, E., Chigine, A., McCann, H., Dimiccoli, L., ... Johnstone, W. (2017). Constrained models for optical absorption tomography. Applied Optics, 57(7), B1-B9. https://doi.org/10.1364/AO.57.0000B1
Polydorides , Nick ; Tsekenis, Alex ; Fisher, Edward ; Chigine, Andrea ; McCann, Hugh ; Dimiccoli, Luca ; Wright, Paul ; Lengden, Michael ; Benoy, Thomas ; Wilson, David ; Humphries, Gordon ; Johnstone, Walter. / Constrained models for optical absorption tomography. In: Applied Optics. 2017 ; Vol. 57, No. 7. pp. B1-B9.
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Polydorides , N, Tsekenis, A, Fisher, E, Chigine, A, McCann, H, Dimiccoli, L, Wright, P, Lengden, M, Benoy, T, Wilson, D, Humphries, G & Johnstone, W 2017, 'Constrained models for optical absorption tomography' Applied Optics, vol. 57, no. 7, pp. B1-B9. https://doi.org/10.1364/AO.57.0000B1

Constrained models for optical absorption tomography. / Polydorides , Nick ; Tsekenis, Alex; Fisher, Edward; Chigine, Andrea; McCann, Hugh; Dimiccoli, Luca; Wright, Paul; Lengden, Michael; Benoy, Thomas; Wilson, David; Humphries, Gordon; Johnstone, Walter.

In: Applied Optics, Vol. 57, No. 7, 23.10.2017, p. B1-B9.

Research output: Contribution to journalArticle

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T1 - Constrained models for optical absorption tomography

AU - Polydorides , Nick

AU - Tsekenis, Alex

AU - Fisher, Edward

AU - Chigine, Andrea

AU - McCann, Hugh

AU - Dimiccoli, Luca

AU - Wright, Paul

AU - Lengden, Michael

AU - Benoy, Thomas

AU - Wilson, David

AU - Humphries, Gordon

AU - Johnstone, Walter

N1 - © 2017 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.

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Y1 - 2017/10/23

N2 - We consider the inverse problem of concentration imaging in optical absorption tomography with limited data sets. The measurement setup involves simultaneous acquisition of near infrared wavelength modulated spectroscopic measurements from a small number of pencil beams equally distributed among six projection angles surrounding the plume. We develop an approach for image reconstruction that involves constraining the value of the image to the conventional concentration bounds and a projection into low-dimensional subspaces to reduce the degrees of freedom in the inverse problem. Effectively, by reparameterising the forward model we impose simultaneously spatial smoothness and a choice between three types of inequality constraints, namely positivity, boundedness and logarithmic boundedness in a simple way that yields an unconstrained optimisation problem in a new set of surrogate parameters. Testing this numerical scheme with simulated and experimental phantom data indicates that the combination of affine inequality constraints and subspace projection leads to images that are qualitatively and quantitatively superior to unconstrained regularised reconstructions. This improvement is more profound in targeting concentration profiles of small spatial variation. We present images and convergence graphs from solving these inverse problems using Gauss-Newton's algorithm to demonstrate the performance and convergence of our method.

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KW - combustion diagnostics

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T2 - Applied Optics

JF - Applied Optics

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Polydorides N, Tsekenis A, Fisher E, Chigine A, McCann H, Dimiccoli L et al. Constrained models for optical absorption tomography. Applied Optics. 2017 Oct 23;57(7):B1-B9. https://doi.org/10.1364/AO.57.0000B1