# Neural Network System for Recognizing Images Affected by Random-Valued Impulse Noise
## 1 Introduction
### Research Motivation  
Thus, it is very important to completely clean up noisy images with a high noise density at the pre-processing stage [19]. However, this is not always possible, and the pre-processing for image restoration itself is an expensive and time-consuming process, which leads to low efficiency of training and validation of the neural network [24]. One of the ways to eliminate distortions is to use mathematical (and computer) processing of measurement results in order to eliminate distorting factors, and increase the resolution of instruments and the quality of image visualization. After obtaining a clearer image, the accuracy of identification (classification, recognition, diagnostics) of the object increases. Researchers [18] were among the first to implement Principal Component Analysis for filter generation in a convolutional neural network, which helped combine the neural network's image classification capabilities with PCA's reduction in computational overhead. In their research [19], [PERSON] et al. proposed to use a two-channel convolutional neural network model containing additional image features with enhanced contours. Thus, using the original and enhanced image, the accuracy of the dataset did not decrease. Some researches proved that training a neural network on mixed data (noisy and clean images) increases its resistance to these noises and improves classification accuracy [34]. To do this, special resizing layers must be used, as well as an adaptive union operator, to reduce noise interference [24]. For noise reduction reconstructed using positron emission tomography, a convolutional neural network can also be used. The classification of reconstructed images, compared to conventional noise smoothing, showed better results [35]. The DeQCANet quaternion convolutional neural network can remove color random-valued impulse noise using a new scheme for constructing a quaternion map and obtaining color characteristics by channels [36]. [PERSON] et al. showed in their work that DNNs are susceptible to spatially uncorrelated white noise, and by introducing a noise learning procedure, it is possible to provide a better qualitative match to human performance [37]. In [38], a controlled random quantum neural network was proposed that used hybrid classical quantum algorithms with superposition and amplitude state coding functions, which improved not only the classification accuracy on MNIST, FashionMNIST, and KMNIST data, but also stability under conditions of increased noise. Also, a complex valued multilayer neural network with multivalued neurons (MLMVN) was adapted and successfully applied to filter impulse noise [39]. Despite a fairly large knowledge base and ongoing research in the field of image recognition using neural networks, none of the works offer a complex of a preprocessing filter and a recognizer. The pre-processing stage is necessary for a more accurate recognition result that is not spoiled by noise and impulses. In general, the researchers either recognized noisy images or cleaned the image of impulse or other noise. There were no works that would combine the search and elimination of noisy pixels and their further recognition. We have combined these important steps and created a system that denoises images efficiently and recognizes pre-processed images with high accuracy. In this paper, we propose a neural network complex for recognizing images exposed to random-valued impulse noise. The presented system for the recognition of noisy images consists of a preprocessing stage, which includes a detector of distorted pixels, a system for their cleaning, and a neural network complex for recognizing cleaned images. The proposed method, in comparison with the existing ones, allows obtaining a gain in the accuracy of image recognition, which is confirmed by the experimental results of recognition of the same image, cleared of noise by different methods.