The main tasks of Remote Sensing (RS) are the tasks of pattern recognition and classification of objects in multispectral satellite images. An urgent problem in solving these problems is the construction of a flexible classifier, adaptable to specific conditions. The conducted studies have shown that the most promising classifier, in terms of flexibility and adaptation for solving remote sensing problems, is a classifier based on artificial neural networks (ANN). We have studied two main ways of optimizing the processes of constructing and training ANN classifiers. The first way is to optimize the selection of training samples for training and the selection of a minimum informative set of features or input neurons. The number of neurons in the initial layer largely predetermines the complexity of the neural network architecture, and the number of samples and the complexity of the ANN architecture determine the amount of computations when training the classifier. The second way of optimization is the use of number-theoretic methods when performing the linear part of the transformations associated with the procedure of weighted summation of neurons. The number of neurons in the input layer largely predetermines the complexity of the neural network architecture, and the number of samples and the complexity of the ANN architecture determine the amount of computations during classifier training. The use of orthogonal bases for transformations in the feature space contributes to solving the problem of finding the generalization threshold when compiling the initial set of training examples. The second way of optimization is the use of number-theoretic methods when performing the linear part of the transformations associated with the procedure of weighted summation of neurons. These transformations are repeated over many iterations and require a huge number of floating point calculations.