A Model Based Iterative Reconstruction Approach to Tunable Diode Laser Absorption Tomography
Tunable diode laser absorption tomography (TDLAT) has emerged as a popular nonintrusive technique for simultaneous sensing of gas concentration and temperature. The gas concentration and temperature is computed by making light absorbance measurements using tunable diode lasers. Major challenges of TDLAT imaging include a highly nonlinear measurement process and availability of only a few light absorbance measurements. Therefore, TDLAT imaging of concentration and temperature is an ill-posed, nonlinear inverse problem. Conventional approaches to TDLAT primarily consist of making restrictive assumptions about the gas flow to simplify the problem. In this thesis, we study the problem of reconstruction of TDLAT measurements into images representing 2D flow fields. We first propose a novel model-based iterative reconstruction (MBIR) framework for TDLAT imaging. To do this, we formulate a nonlinear measurement model for TDLAT that incorporates the physics of light absorbance through the gaseous media. In model based inference, apart from the measurement model, there also exists a model for the unknown signals to be reconstructed, called the prior model. We develop a non-Gaussian prior model based on a Gaussian mixture distribution that can be trained using a sparse training set. We set up an optimization problem using maximum a posteriori (MAP) estimation. In order to speed up the computation of the reconstruction algorithm, we propose a multigrid algorithm along with a majorization minimization framework to solve this optimization problem. The inclusion of prior models can introduce bias in the reconstructions which is part of the well known bias variance trade off. This is particularly problematic if the training data used to tune the parameters of the prior model is not sufficient and representative. So, for the scenarios where there is limited training data available for training the prior model, we propose a novel hybrid Gaussian prior model by combining a conventional Gaussian distribution with a Gaussian Markov random field. We combine the two distributions using a mixing parameter γ ∈ [0, 1]. The hybrid prior produces reconstructions without overfitting the sparse training set. Finally, we propose a systematic framework to indicate inaccuracies in the posterior distribution/model. This is extremely important when there is no ground truth available for the reconstructions. Inaccuracies in models can reflect in the form of errors in the reconstruction which can be hard to identify due to the lack of availability of the ground truth. We analyze the residual error between the absorbance measurements and the predicted absorbance values to identify unlikely patterns in the error. The existence of non-random structures or unexpected dynamic range of the residual error is an indication of possible modeling errors that may result in an inaccurate posterior distribution. Inaccuracy in the posterior distribution can arise either due to an inaccurate forward model, or an inaccurate prior model typically caused by insufficient or poor quality training data that is not representative of the true prior distribution. We look for inaccuracy in the posterior distribution by developing a metric based on hypothesis testing theory, and we demonstrate that we can detect when the posterior distribution is inaccurate by using the methods we propose.
Bouman, Purdue University.
Computer Engineering|Engineering|Electrical engineering
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