Tomographic reconstruction of flowing gases using sparse training

Abstract

Tunable Diode Laser Absorption Spectroscopy (TDLAS) is an emerging technique for simultaneous sensing of temperature and concentration of gaseous media. However, simultaneous reconstruction of temperature and concentration using TDLAS measurements is a nonlinear inverse problem and unlike other forms of computed tomography (CT), it is typically not possible to take a large number of projection measurements; so reconstructions are often computed using simplistic assumptions that limit the usability of the results.In this paper, we present a fast algorithm for model-based iterative reconstruction (MBIR) of TDLAS data. Our TDLAS-MBIR method uses a nonlinear forward model based on the physics of light absorption and incorporates a holistic prior model that can be learned from very sparse training data. Reconstructions performed on computational fluid dynamics (CFD) phantoms show that our proposed reconstruction algorithm is fast; works well when the number of pixels, p, far exceeds the number of measurements, M ; is robust against noise; and produces good reconstructions using few training examples for the prior model.

Gaussian mixture prior models for imaging of flow cross sections from sparse hyperspectral measurements

“…We compare the reconstruction results of proposed prior model with the results of two different prior models; Gaussian model (GM) [7] and Gaussian Markov random field (GMRF) model [23] and also with the reconstruction results of another approach i.e., proper orthogonal decomposition (POD) as in [42] 1 . To compare the reconstructions objectively, we use the metric of normalized RMSE (NRMSE) which is obtained by normalizing the RMSE by the range of the ground truth.…”

“…These CFD simulated images can improve the reconstruction quality by providing training examples for the prior model [7]. However, CFD simulations are computationally expensive and therefore usually very few of them are available for training.…”

“…DATA MODEL In TDLAT imaging [33]- [35], projection measurements corresponding to a particular target molecule, in our case water, are made along a few projection paths and few discrete frequencies [7], [22]. The different discrete frequencies correspond to different absorption transitions [36].…”

“…However, such assumptions limit the scope of possible applications. An alternate approach to improve the accuracy of reconstructions is model-based iterative reconstruction (MBIR) framework [7], [21]. In MBIR, a model is specified for both the measurement process (forward model) and the unknown image (prior model) and typically a maximum a posteriori (MAP) estimate of the unknown image is computed.…”

“…where f ∈ R Kp 2 is a nonlinear function of unknown x that models the physics of measurements [7], w∼ N (0, Iσ 2 ) ∈ R JK is additive white Gaussian noise vector and H ∈ R JK× Kp 2 is the line integral matrix. Combining this together, the log likelihood of the measurements y given the unknown x is given by…”