A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing

<p>Optical remote sensing (ORS) combined with the computerized tomography (CT) technique is a powerful tool to retrieve a two-dimensional concentration map over an area under investigation. Whereas medical CT usually uses a beam number of hundreds of thousands, ORS-CT usually uses a beam numbe...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	S. Li, K. Du
Formato:	article
Lenguaje:	EN
Publicado:	Copernicus Publications 2021
Materias:	Environmental engineering TA170-171 Earthwork. Foundations TA715-787
Acceso en línea:	https://doaj.org/article/5724dfcc736c422fa291e9a1cf0ad71e
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:5724dfcc736c422fa291e9a1cf0ad71e
record_format	dspace
spelling	oai:doaj.org-article:5724dfcc736c422fa291e9a1cf0ad71e2021-11-25T08:33:14ZA minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing10.5194/amt-14-7355-20211867-13811867-8548https://doaj.org/article/5724dfcc736c422fa291e9a1cf0ad71e2021-11-01T00:00:00Zhttps://amt.copernicus.org/articles/14/7355/2021/amt-14-7355-2021.pdfhttps://doaj.org/toc/1867-1381https://doaj.org/toc/1867-8548<p>Optical remote sensing (ORS) combined with the computerized tomography (CT) technique is a powerful tool to retrieve a two-dimensional concentration map over an area under investigation. Whereas medical CT usually uses a beam number of hundreds of thousands, ORS-CT usually uses a beam number of dozens, thus severely limiting the spatial resolution and the quality of the reconstructed map. The smoothness a priori information is, therefore, crucial for ORS-CT. Algorithms that produce smooth reconstructions include smooth basis function minimization, grid translation and multiple grid (GT-MG), and low third derivative (LTD), among which the LTD algorithm is promising because of the fast speed. However, its theoretical basis must be clarified to better understand the characteristics of its smoothness constraints. Moreover, the computational efficiency and reconstruction quality need to be improved for practical applications. This paper first treated the LTD algorithm as a special case of the Tikhonov regularization that uses the approximation of the third-order derivative as the regularization term. Then, to seek more flexible smoothness constraints, we successfully incorporated the smoothness seminorm used in variational interpolation theory into the reconstruction problem. Thus, the smoothing effects can be well understood according to the close relationship between the variational approach and the spline functions. Furthermore, other algorithms can be formulated by using different seminorms. On the basis of this idea, we propose a new minimum curvature (MC) algorithm by using a seminorm approximating the sum of the squares of the curvature, which reduces the number of linear equations to half that in the LTD algorithm. The MC algorithm was compared with the non-negative least square (NNLS), GT-MG, and LTD algorithms by using multiple test maps. The MC algorithm, compared with the LTD algorithm, shows similar performance in terms of reconstruction quality but requires only approximately 65 <span class="inline-formula">%</span> the computation time. It is also simpler to implement than the GT-MG algorithm because it directly uses high-resolution grids during the reconstruction process. Compared with the traditional NNLS algorithm, it shows better performance in the following three aspects: (1) the nearness of reconstructed maps is improved by more than 50 <span class="inline-formula">%</span>, (2) the peak location accuracy is improved by 1–2 <span class="inline-formula">m</span>, and (3) the exposure error is improved by 2 to 5 times. Testing results indicated the effectiveness of the new algorithm according to the variational approach. More specific algorithms could be similarly further formulated and evaluated. This study promotes the practical application of ORS-CT mapping of atmospheric chemicals.</p>S. LiK. DuCopernicus PublicationsarticleEnvironmental engineeringTA170-171Earthwork. FoundationsTA715-787ENAtmospheric Measurement Techniques, Vol 14, Pp 7355-7368 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Environmental engineering TA170-171 Earthwork. Foundations TA715-787
spellingShingle	Environmental engineering TA170-171 Earthwork. Foundations TA715-787 S. Li K. Du A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing
description	<p>Optical remote sensing (ORS) combined with the computerized tomography (CT) technique is a powerful tool to retrieve a two-dimensional concentration map over an area under investigation. Whereas medical CT usually uses a beam number of hundreds of thousands, ORS-CT usually uses a beam number of dozens, thus severely limiting the spatial resolution and the quality of the reconstructed map. The smoothness a priori information is, therefore, crucial for ORS-CT. Algorithms that produce smooth reconstructions include smooth basis function minimization, grid translation and multiple grid (GT-MG), and low third derivative (LTD), among which the LTD algorithm is promising because of the fast speed. However, its theoretical basis must be clarified to better understand the characteristics of its smoothness constraints. Moreover, the computational efficiency and reconstruction quality need to be improved for practical applications. This paper first treated the LTD algorithm as a special case of the Tikhonov regularization that uses the approximation of the third-order derivative as the regularization term. Then, to seek more flexible smoothness constraints, we successfully incorporated the smoothness seminorm used in variational interpolation theory into the reconstruction problem. Thus, the smoothing effects can be well understood according to the close relationship between the variational approach and the spline functions. Furthermore, other algorithms can be formulated by using different seminorms. On the basis of this idea, we propose a new minimum curvature (MC) algorithm by using a seminorm approximating the sum of the squares of the curvature, which reduces the number of linear equations to half that in the LTD algorithm. The MC algorithm was compared with the non-negative least square (NNLS), GT-MG, and LTD algorithms by using multiple test maps. The MC algorithm, compared with the LTD algorithm, shows similar performance in terms of reconstruction quality but requires only approximately 65 <span class="inline-formula">%</span> the computation time. It is also simpler to implement than the GT-MG algorithm because it directly uses high-resolution grids during the reconstruction process. Compared with the traditional NNLS algorithm, it shows better performance in the following three aspects: (1) the nearness of reconstructed maps is improved by more than 50 <span class="inline-formula">%</span>, (2) the peak location accuracy is improved by 1–2 <span class="inline-formula">m</span>, and (3) the exposure error is improved by 2 to 5 times. Testing results indicated the effectiveness of the new algorithm according to the variational approach. More specific algorithms could be similarly further formulated and evaluated. This study promotes the practical application of ORS-CT mapping of atmospheric chemicals.</p>
format	article
author	S. Li K. Du
author_facet	S. Li K. Du
author_sort	S. Li
title	A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing
title_short	A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing
title_full	A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing
title_fullStr	A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing
title_full_unstemmed	A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing
title_sort	minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing
publisher	Copernicus Publications
publishDate	2021
url	https://doaj.org/article/5724dfcc736c422fa291e9a1cf0ad71e
work_keys_str_mv	AT sli aminimumcurvaturealgorithmfortomographicreconstructionofatmosphericchemicalsbasedonopticalremotesensing AT kdu aminimumcurvaturealgorithmfortomographicreconstructionofatmosphericchemicalsbasedonopticalremotesensing AT sli minimumcurvaturealgorithmfortomographicreconstructionofatmosphericchemicalsbasedonopticalremotesensing AT kdu minimumcurvaturealgorithmfortomographicreconstructionofatmosphericchemicalsbasedonopticalremotesensing
_version_	1718413556709326848

A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing

Ejemplares similares