Broadband chemical species tomography: Measurement theory and a proof-of-concept emission detection experiment

Constrained models for optical absorption tomography

“…Moreover, its analytic formulation allows for a direct application to a default constrained optimisation solver, such as those included in Matlab, from where we compute images for comparison. Thirdly, the Tikhonov problem bares an evocative resemblance to the maximum a posteriori estimator in the Bayesian inverse problem, subject to a suitably smooth prior density [8], [15], and lastly upon the appropriate choice of the regularization matrix and parameter it can impose the required smoothness in the unknown image profile, which makes is compatible to our method. Note however that our scheme enforces smoothness explicitly by selecting a (particular) basis for the projection in Eq.…”

“…CST was initially inspired by the success of X-ray computed tomography, and has since been developed into an optical imaging modality for gas tomography suitable to the cases where photon transmission and absorption phenomena dominate those of scattering and diffusion. Over the recent years, collimated pencil, fan or ad hoc beam arrangements have been proposed [4], and rapid developments have seen CST evolve from the monochromatic to the hyperspectral setting exploiting advances in calibration-free 2f/1f wavelength modulation spectroscopy technique (TDLS-WMS), see for example [5], [6], [7] and [8]. While measurement models involve invariably computation of line integrals under some assumptions based on the experimental conditions, the acquisition of spectral measurements has paved the way for more ambitious imaging ventures that seek to recover aside the species concentration, the gas temperature and pressure profiles [7], [6], [2].…”

“…Existing algorithms are predominantly algebraic using inverse problem regularization tools, see for example the early work [10] and the more recent [11], [12], [13]. The use of statistical imaging methods is less by comparison, and some notable examples include the simulated annealing algorithm in [14] and the Bayesian estimation in [15], [8] and [12], who have developed algorithms for maximum a posteriori estimation assuming Gaussian priors and measurement likelihood probability density functions. As a detailed review of CST is beyond the scope of this paper, we mention that historical milestones and recent advances of the method are succinctly summarised in the recent review [16] and the book chapter [1].…”

“…sparsity promoting, total variation or levelset regularisation [18], [19]. Unfortunately, these advantages come at the cost of loosing the original model's linearity and thus a direct analytical inverse solution is no longer feasible, while the Bayesian setting results in a non-Gaussian posterior for the surrogate parameters, which complicates the inference calculations [8]. Moreover, the use of global basis functions as we advocated in [13] in reducing the dimensionality of the problem poses limitations to the statistical approaches that rely on computing image covariances and constructing prior densities from uncorrelated samples [15].…”

Methane Emission Estimation of Oil and Gas Sector: A Review of Measurement Technologies, Data Analysis Methods and Uncertainty Estimation

“…Combined with instrument parameters, CRDS can give out high sensitivity results of the point density of methane and is rather easy to operate. However, when conducting multipoint measurements, CRDS has to be facilitated with mobile vehicles, which increases the use cost [27]. CRDS is also limited by the unavailability of lasers in all spectral regions and a small wavelength range over which the high reflective mirrors can maintain their reflectivity [28].…”