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

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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.
Original languageEnglish
Pages (from-to)B1-B9
Number of pages9
JournalApplied Optics
Volume57
Issue number7
DOIs
Publication statusPublished - 23 Oct 2017

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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