Аннотация:The question of finding the optimal location and number of sensors is important when solving applied inverse problems of remote sensing. An incorrect answer to this question can significantly affect (1) the accuracy of reconstructing the unknown parameters of the object under study, and/or (2) the computational complexity of the inverse problem being solved. The work proposes an economical algorithm that allows among all equivalent (in the sense of the computational complexity of obtaining a solution to the inverse problem) sensor configurations, to select the one that will give a more accurate result when processing experimental data. This algorithm also allows to make a conclusion about whether it is really necessary to process all the experimental data obtained in the experiment, or whether it is possible to limit ourselves to only part of them without a significant loss of accuracy in the reconstructed solution. The algorithm is based on (1) the application of the mosaic-skeleton approximation method to the matrix of the system of equations to which the inverse problem being solved is reduced, and (2) the calculation of the compression rate of the approximating matrix relative to the original dense matrix for a given permissible relative approximation error. Thus, the algorithm is a priori, that is, it does not require a preliminary search for a solution to the inverse problem for the sensor configuration under study. Moreover, if the formulas that define the elements of the system matrix are known, then the algorithm requires the calculation of not all of these elements, but only part of them.
