Wavelet-Based Image Reconstruction for Hard-Field Tomography With Severely Limited Data

Abstract

We introduce a new wavelet-based hard-field image reconstruction method that is well suited for data inversion of limited path-integral data obtained from a geometrically sparse sensor array. It is applied to a chemical species tomography system based on near-IR spectroscopic absorption measurements along an irregular array of only 27 paths. This system can be classified as producing severely limited data, where both the number of viewing angles and the number of measurements are small. As shown in our previous work, the Landweber iteration method allows stable solution of this tomography problem by incorporating suitable a priori information. In the new method, a 2-D discrete wavelet transform has been used as a smoothing function. We present a method of designing the optimal waveletbased smoothing function, depending on a priori knowledge of the subject. The significance of the particular wavelet filter selected is considered in terms of the accuracy of reconstruction of the spatial location and shape of the gas distribution. Results are presented for simulated phantoms using different sensor arrays and for experiments with propane plumes, showing excellent spatial localization and quantification. The computational time of the iterative algorithm is significantly reduced by applying the wavelet transform method. Some of our conclusions are applicable to other hard-field tomographic modalities in applications where similar constraints may be encountered.

Tomographic imaging of the liquid and vapour fuel distributions in a single-cylinder direct-injection gasoline engine

“…Hence, extension of the present work to fired operation of single-cylinder optical engines is anticipated. Experimental validation of the in-cylinder fuel distributions obtained by tomography (in addition to reported laboratory validations, e.g., [6,23,24]) remains as a future objective, most probably by using PLIF. Subject to that proviso, the results obtained here promise that optical tomography and CST will provide, for some R&D studies, penetrating spatial and temporal information on in-cylinder fuel distributions, with the freedom to use a wide variety of fuels.…”

“…More limiting is that, by using individual fibres and collimators, optical mounting requirements around the engine cylinder dictate that only a few tens of distinct PCI measurements can be obtained, which is challenging in terms of image reconstruction. Extensive development of image reconstruction methods and robust laboratory tests of IMAGER [23,24] demonstrated its fundamental imaging capability, with spatial resolution about 4% of the subject cross-sectional area, which is clearly much poorer than PLIF.…”

Chemical species tomography

“…The resulting image reconstructions (Terzija et al, 2008;Wright et al, 2010), believed to be the first from data of this type, were obtained using an iterative median-filtered Landweber method. As noted in Section 5.4, ongoing research is focused on improving reconstruction algorithms by explicitly incorporating prior knowledge about the measurement subject into the reconstruction (Terzija et al, 2008;Daun et al, 2011;Twynstra et al, 2014;Terzija, 2011) and also on developing new techniques for optimizing beam layout (Twynstra & Daun, 2013). Measurements were made with the IMAGER system in one cylinder of a four-cylinder in-line Ford Duratec 2.0 L port fuel-injected engine operating at moderate speed and load conditions and running on retail gasoline (which is a mixture of many hydrocarbon species).…”

Constrained models for optical absorption tomography

“…Contrary to X-ray CT, data sets in CST tend to be limited due to instrumentation challenges [1], causing the image reconstruction approaches to depart from the typical Radon in-version framework [9]. 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.…”