Constrained models for optical absorption tomography

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 reparameterizing the forward model, we impose, simultaneously, spatial smoothness and a choice among three types of inequality constraints, namely, positivity, boundedness, and logarithmic boundedness in a simple way that yields an unconstrained optimization 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 regularized 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.

A Custom, High-Channel Count Data Acquisition System for Chemical Species Tomography of Aero-Jet Engine Exhaust Plumes

“…CO2 concentrations and air temperatures [8], while tomographic methods have also been developed [10]. The detail of the mechanical structure, and the setup for imaging tests is shown in Fig.…”

“…The detail of the mechanical structure, and the setup for imaging tests is shown in Fig. 2, while experimental validation of gas concentration imaging and a preliminary investigation as to constrained algorithms are provided in Fig.3 [8,10]. The reconstruction results show that, while under-determined due to costs, tomographic imaging can be performed with reconstruction artefacts of low-severity [10].…”

“…By obtaining video-rate images and showing scalability towards >200 fps, the dynamics of gas mixing within the plume [5] can start to be observed and will complement existing, intrusive testing. While optical and mechanical challenges have been addressed [7,8] and issues surrounding tomographic reconstruction with a small number of beams and angular views have been targeted algorithmically [9,10], the increase in size and complexity of this setup has presented issues for electrical designs [7,8] and data acquisition [11]. Some of these have been covered in a 2018 I2MTC prelude to this paper [12].…”

“…While the specifics of the mechanical setup are discussed elsewhere [7,8,10,11], the harsh environment raises numerous data acquisition challenges. The specifics are covered below using a top-down discussion of system requirements, however high-throughput, hard real-time, fully-synchronized DAQs are well researched with many solutions now becoming standard in tomographic systems [13,14,15,16,17], many of which use fieldprogrammable gate arrays (FPGAs).…”

Two-Dimensional Temperature Measurement in a High-Temperature and High-Pressure Combustor Using Computed Tomography Tunable Diode Laser Absorption Spectroscopy (CT-TDLAS) with a Wide-Scanning Laser at 1335–1375 nm

“…The measurement errors depend on the factors such as laser beams number, view angles, CT-algorithm, uncertainty of spectral database, and so on. 17–20 There are various CT reconstruction methods, 33–36 such as the algebraic reconstruction technique (ART), the multiplicative algebraic reconstruction technique (MART), Gauss–Newton's algorithm, and so on. Usually, the reconstruction of 2D spatial scale distribution is determined according to the rectangular coordinate.…”