## 1 Introduction  
Practical experience and the results of scientific and technical publications [1; 2; 3] unequivocally indicate that under the current circumstances, one of the most important scientific and practical tasks in the field of protecting critical infrastructure facilities (CIFs) is the task of increasing the effectiveness of personnel authentication systems at the specified facilities. At the same time, one of the high-priority directions for improving efficiency is the improvement of biometric authentication (BA) tools, which today are among the key components of such systems. This is due to the fact that the human factor plays a key role in ensuring the stability and security of critical processes, and an insufficiently effective authentication system leads to a high probability of attackers gaining unauthorized access to confidential information, critical resources, or management systems, which can lead a disruption in the functioning of the CIF, the emergence of man-made incidents, or even threats to national security. In this context, one of the priority areas for increasing the effectiveness of the authentication system is the improvement of biometric authentication (BA) tools, which are key components of such a system.  
Although CIF personnel authentication systems use tools that perform BA based on the analysis of a fairly wide range of biometric parameters, tools based on facial image (FI) analysis have become the most widespread. This is explained by the availability and testing of both the FI registration means (video cameras) and the technology of their use, which ensures the possibility of authentication not only during the verification of the identity of a personnel representative during their entrance to the CIF but also during the performance of official duties. At the same time, many scientific and practical works point to the imperfection of modern BA tools based on the analysis of biometric data, associated with insufficient effectiveness in countering attacks using dummies; high resource intensity and insufficient accuracy of neural network models (NNMs), which in the vast majority of cases are used to analyze biometric parameters; lack of ability to recognize the psycho-emotional state of a personnel representative; and insufficiently complete integration with authentication tools based on the analysis of biometric parameters, which can be registered using modern video cameras simultaneously with the registration of a facial image. Thus, a generalization of the results of studies [4; 5; 6] allows us to state that the probability of success in implementing modern types of spoofing attacks using volumetric masks exceeds 0.1, and the accuracy indicators of the FAR (false acceptance rate) and FRR (false rejection rate) of the NNM, although they are within the permissible limits of 0.1-1% and 1-5%, respectively, under reference video recording conditions, deteriorate significantly in cases of insufficient or overly bright lighting, the presence of interference in the FI, etc. At the same time, the development of an NNM used as the basis of BA tools requires large FI databases, and the actual process of training the NNM is quite lengthy and usually requires the use of high-performance software and hardware. In addition, works [7; 8] indicate the expediency of the integration of BA by means of FI with means that perform authentication by the iris of the eye (IE), which is explained by the possibility of the simultaneous registration of specified biometric parameters using distributed video cameras. This explains the relevance of research aimed at increasing the effectiveness of neural network tools for BA of CIF personnel by FI, taking into account the need to ensure sufficient recognition accuracy in the expected operating conditions, considering the possibility of the implementation of spoofing attacks and taking into account resource limitations in the creation and application of the system.