Evaluation of Algorithms for Tomographic Reconstruction of Chemical Concentrations in Indoor Air

Abstract

Numerical studies were performed to evaluate and compare four different algorithms for tomographically reconstructing pollutant concentrations in indoor air measured with an optical remote sensing system. With a remote sensing/computed tomography system, two-dimensional maps of air concentrations can be created for an entire room with good spatial and temporal resolution. The success of such a system for characterizing the flow of contaminants in air, exposure assessment, and leak detection depends on the choice of tomographic reconstruction algorithm. A systematic method was developed to evaluate the performance of four algorithms: ART, ART3, SIRT, and SART. One hundred and twenty test maps were reconstructed by each algorithm under ideal and nonideal sampling conditions, and image quality was evaluated using four criteria. The nonideal sampling conditions included simulation of measurement noise and reduction in the number density of rays. Performance of the algorithms was found to be intimately related to the number of peaks in the test maps. The importance of using multiple measures of image quality was underscored by the fact that for some sampling conditions simulated, performance of the algorithms was judged differently depending on the evaluation criteria. Results indicated that using numerical studies is successful for evaluating such algorithms.

Computed tomography and optical remote sensing: Development for the study of indoor air pollutant transport and dispersion

“…In fact, the value of oray can be made to be as low as desired problems with indeterminacy were to be expected. Previous simulation work (Todd and k i t h , 1990;Todd and Ramachandran, 1994) has shown that, under favorable conditions, good reconstructions can be obtained for an underdetermined system with the ratio of the number of pixels to the number of rays being as large as 6.7. In those reported cases, the reconstructed pixel concentrations matched the true distribution well.…”

“…Todd simulated concentration profiles composed of a superposition of bivariate Gaussians with rotational symmetry. She generated path-integral concentration data based on these profiles for a variety of iterative computed tomography algorithms (Todd and Ramachandran, 1994a) and scanning geometries (Todd and Ramachandran, 1994b). All calculations were based on a discretized plane of measurement.…”

“…By necessity, the ray geometry differed substantially from that employed in the previous chapter. This new ray geometry, though permitting us to largely overcome the problem of temporal variability, created false spatial variability in the reconstructed concentration profiles when used in conjunction with the standard algebraic reconstruction technique (ART) suggested by and Todd and Ramachandran (1994). Because the rays in the new geometry were less "independent" than would be an equal number of rays in parallel projections, they produced a more underdetermined system of equations when using the number of pixels necessary to accurately capture spatial variability in the concentration profiles.…”

2-D reconstruction of atmospheric concentration peaks from horizontal long path DOAS tomographic measurements: parametrisation and geometry within a discrete approach

“…The a priori x a is provided by the iteration start x (0) . The order of the algorithms according to (Todd and Ramachandran, 1994a) and (Laepple et al, 2004) is ART>SART>SIRT, reversing to SIRT>SART>ART with noise in both studies. Here, we do not go into the details of the iteration procedures themselves but refer the reader to the two studies mentioned and references therein and in the following will only consider ART and SIRT.…”

“…This study used a discrete approach by approximating the NO 2 concentration field by a finite sum over local piecewise constant (so called box) and piecewise linear basis functions, respectively. The state vector of discrete concentration values was fitted to the measurement data by a least squares minimum norm principle, comparing three iterative projection algorithms originally developed to solve large systems of equations in image reconstruction: The Algebraic Reconstruction Technique (ART), the Simultaneous ART (SART) and the Simultaneous Iterative Reconstruction Technique (SIRT), which were already studied in Todd and Ramachandran (1994a) for 2-D reconstruction of Gaussian shaped indoor gas concentrations. Both studies find that ART performs best, if measurement errors are negligible, whereas SIRT is preferred for noisy data.…”