New Results on Inverse Photon Transport∗

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 application are the re-trieval of the vertical profile of the atmospheric tem-perature from satellite data, and the estimation of the absortion and scattering coefficients of natural waters type-2. The estimation of the vertical atmospheric tem-perature from radiaces at infrared wavelenth is com-puted using a new methodology employing artificial neural networks. The radiative transfer equation is known as Schwarchild’s equation citeLiou:1980, 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 off-shore ocean waters is also presented, using in-situ radiance measurements in several depths and sin-gle wavelength. The inverse problem is formu-lated as an optimization problem and iteratively solved using the radiative transfer equation as di-rect model. Bio-optical models are employed to correlate the chlorophyll concentration to these co-efficients [4]. The radiative transfer equation is solved using the Laplace transform discrete ordi-nate (LTSN) method. The objective function is minimized by an Ant Colony System (ACS) code. A regularization scheme pre-selects candidate solu-tions based on their smoothness [1], computed from the Tikhonov’s norm. Multi-spectral estimation of chlorophyll concentration are shown too [5]