Tomographic reconstruction of stack plume based on sparse optimization

Abstract

In this paper, we present a novel method of computing tomography , i.e. the low third deviation total variation (LTD-TV) method to reconstruct the two-dimensional distribution of SO₂ of stack plume. The path-integral data of the plume are collected by only two imaging differential absorption spectrometers (IDOASs). However, due to the insufficient number of IDOASs, conventional reconstruction methods result in severe streaking artifacts. The traditional low third derivative method is widely used to reconstruct the gas distribution. It suggests a spatial distribution of gas concentrations, which has a low third spatial derivative in every direction and at every point. The derivatives are usually set to be zero. The method improves the reconstructed images by providing extra information which contains the gas concentration in line with the distribution of the second order polynomial, but it also gives rise to the extra artifacts. To address this issue, we further improve the traditional low third deviation (LTD) method by suggesting that the third derivative of gas concentration is sparse. We therefore adopt the compressed sensing (CS) based total variation (TV) optimization framework. In the LTD-TV method, a logarithmic barrier function with TV is used as an objective function. The objective function is then optimized by numerical optimization method, in which the gradient projection is used to determine its descent direction and a Barzilai-Borwein scheme to determine its step-size. The final results are obtained by iterative optimization. Numerical simulations are performed to simulate the reconstruction of gas distribution which is in line with Gaussian distribution. Compared with the conventional LTD method, the LTD-TV method enhances the proximity by 20%—80%, and greatly corrects the artifacts near the edges of images. The result of field campaign suggests that concordance correlation factor between the collected data and reconstructed image is 0.9023. It also shows that it has good noise immunity. In summary, it is the first time that we have introduced the CS theory into the field of gas plume reconstruction. Compared with the existing methods, the LTD-TV method can greatly reduce the artifacts and increase the credibility of the reconstruction.