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

Tunable diode laser absorption tomography (TD-LAT) has emerged as a popular non-intrusive technique for simultaneous sensing of gas concentration and temperature. Major challenges of TDLAT include availability of limited projection measurements and limited training data. Conventional tomographic techniques are therefore not directly applicable. Usually approximations are made which are limited in scope. In this paper, we propose a novel model-based iterative reconstruction (MBIR) framework for TDLAT imaging of gas concentration and temperature. First, we propose a novel prior model that captures non-homogeneous and non-Gaussian characteristics of the images by modeling their distribution as a Gaussian mixture and impose constraints on the mixture parameters to avoid overfitting of the sparse training set. Next, we present the nonlinear forward model of TDLAT. We formulate the inversion problem into a MAP estimation problem and propose a multigrid optimization algorithm that solves the resulting optimization problem in eigenimage basis using surrogate functions for the non-convex prior. We demonstrate the efficacy of our approach by performing reconstructions of simulated TDLAT data.