Abstract: Solutions for inverse problems appearing in space applications are described. The work is focused on recent results obtained from the LAC-INPE group on Inverse Problems. These applications are the retrieval of the vertical profile of the atmospheric temperature from satellite data, and the estimation of the absortion and scattering coefficients of natural waters type-2. The estimation of the vertical atmospheric temperature from radiaces at infrared wavelenth is computed using a new methodology employing artificial neural networks. The radiative transfer equation is known as Schwarchild's equation [2], in the absence of clouds, where there is no scattering, and the atmosphere is considered as a black body. Good results have been obtained using multi-layer perceptron [3], and Hopfield neural network [6]. A methodology to reconstruct vertical profiles of the absorption and scattering coefficients in offshore ocean waters is also presented, using in-situ radiance measurements in several depths and single wavelength. The inverse problem is formulated as an optimization problem and iteratively solved using the radiative transfer equation as direct model. Bio-optical models are employed to correlate the chlorophyll concentration to these coefficients [4]. The radiative transfer equation is solved using the Laplace transform discrete ordinate (LTSN) method. The objective function is minimized by an Ant Colony System (ACS) code. A regularization scheme pre-selects candidate solutions based on their smoothness [1], computed from the Tikhonov's norm. Multi-spectral estimation of chlorophyll concentration are shown too [5].
References:
[1] A.J. Preto, H.F. Campos Velho, J.C. Becceneri, N.N. Arai, R.P. Souto, S. Stephany (2004): A New Regularization Technique for an Ant-colony Based Inverse Solver Applied to a Crystal Growth Problem, 13th Inverse Problem in Engineering Seminar (IPES-2004), 14-15 June 2004, University of Cincinnati, Ohio, USA.
[2] K.-N. Liou (1980): An Introduction to the Atmospheric Radiation, Academic Press.
[3] E.H. Shiguemiri, J.D.S. da Silva, H.F. de Campos Velho, J.C. Carvalho (2004): Neural Network based Models in the Inversion of Temperature Vertical Profiles from Satellite Data, Inverse Problems, Design and Optimization Symposium (IPDO), 17-19 March, Rio de Janeiro (RJ), Brazil - Proc. in CD-Rom: paper code IPDO-077.
[4] R.P. Souto, H.F. de Campos Velho, S. Stephany (2004): Reconstruction of Chlorophyll Concentration Profile in Offshore Ocean Water using an Ant Colony Code, 16th European Conference on Artificial Intelligence (ECAI-2004): Hybrid Metaheuristics (HM-2004), 22-24 August, Valencia, Spain, pp. 19-24.
[5] R.P. Souto, S. Stephany, H.F. de Campos Velho (2004): Reconstruction Vertical Profiles of Absorption and Scattering Coefficients from Up-welling Water Radiances, Pan-American Workshop on Applied and Computational Mathematics, 21-25 June, Tegucigalpa, Honduras.
[6] V.C. de Viterbo, J.P. Braga, E.H. Shiguemiri, J.D.S. da Silva, H.F. de Campos Velho (2004): Atmospheric Temperature Retrieval using Non-linear Hopfield Neural Network, Inverse Problems, Design and Optimization Symposium (IPDO), 17-19 March, Rio de Janeiro (RJ), Brazil -- Proc. in CD-Rom: paper code IPDO-119.