Information approach to optimal selection of spectral channels

In this paper we examine methods for the selection of measurement subsets using information theory. These methods are applied to an overdetermined inverse problem typical to high‐resolution spectrometry. The optimal selection of spectral channels becomes especially important with the recent introduction of high spectral resolution satellite instruments for monitoring the atmosphere. The vast amount of data these instruments provide in a continuous fashion makes it necessary to carefully consider which channels are really needed in the retrieval of geophysical quantities. Two optimization problems in channel selection, both taking the information content of the measurements as a criterion, are defined and discussed. The concept of the information content of each individual measurement is introduced, and basic analytical relations are derived. A sequential deselecting procedure is developed, and a fast algorithm for channel selection is proposed. These provide approximations to solutions of the optimization problem. The efficiencies of these selection procedures and a sequential selection procedure [ Rodgers, 1996 ] are compared by means of a Monte Carlo generation of the forward model in a low‐dimensional case. As a real application, the selection of the most informative spectral channels for GOMOS measurements is considered.