Dimension reduction of satellite observations for remote sensing. Part 1: A comparison of compression, channel selection and bottleneck channel approaches

With the increasing volume of satellite observations, dimension reduction techniques are more and more important for storage or transmission. Furthermore, they are essential for inversion schemes that, in practice, cannot handle the huge amount of information provided by modern instruments for near‐real‐time inversion. In this article, we compare the theoretical advantages and limitations of the two general strategies: compression (i.e. feature extraction) and channel selection (i.e. feature selection). The statistical ‘input variable selection’ framework is adopted to revisit the basis of these remote‐sensing techniques. The flexibility of these methods to specific applications is demonstrated. Special emphasis is put on the optimization of observation dimension reduction for the simultaneous retrieval of several variables (e.g. temperature and humidity). In addition to considering the signal‐to‐noise ratio for the variable to retrieve, we propose to account for contamination by other unknown variables. We also introduce a new approach named ‘bottleneck channels’ (BC), which combines compression and channel selection techniques and can therefore benefit from the advantages of both strategies. Various configurations of the BC approach can be considered: strict, linearly or nonlinearly projected, each with advantages and drawbacks. In the companion article, experiments will be conducted on microwave data to illustrate the practical advantages of each approach. BC are able to compress and suppress noise in a similar way to principal component analysis (PCA) and they can be interpreted as channels, as in channel selection.