## 2 Materials and Methods
All images were reduced to 150 \(\times\) 150 pixels just before being fed to the convolutional network. These sizes are 5 times the size of the MNIST images, so the size of the distortion regions ranged from 2 \(\times\) 2 pixels to 15 \(\times\) 15 pixels. Figure 6 shows examples of images with a cat (a) or a dog (b). Figure 5: Handwritten numbers from the MNIST dataset [47]. Figure 6: Examples of images in Kaggle dogs vs. cats dataset: (**a**) image with a cat [49] and (**b**) image with a dog [49]. Note that, the presented in Figure 6 color images of arbitrary sizes were converted to grayscale images of specified sizes. Since there are only 2 classes in such a database, and only one class is represented in each image, provided that the classes are balanced, we define the accuracy metric as the main one. Furthermore, it becomes obvious that the images are presented in such a way that each of them belongs to only one of the two classes. To analyze the effectiveness of the proposed algorithm, the following sets were obtained from the dogs vs. cats data:  
(1) DVC-1 set. Contains 18,000 distortion-free training images; 5000 images of the test sample without distortion, 500 images of the test sample with distortions by Attack No. 1, 500 images of the test sample with distortions by Attack No. 2, 500 images of the test sample with distortions by Attack No. 3, and 500 images of the test sample with distortions by Attack No. 4. (2) DVC-2 set. Contains 15,600 training images without distortion, 600 training images with distorted by Attack No. 1, 600 training images with distorted by Attack No. 2, 600 training images with distorted by Attack No. 3, and 600 training images with distorted by Attack No. 4; the test sample is similar to that described earlier. For both datasets, the signal-to-noise ratios are set in Attack No. 1 in the range of (0.2; 2). The proposed algorithm was tested both on well-known CNN architectures and on a network with a full learning process. In total, during the recognition process, characteristics were obtained for the following three architectures:  
(1) The VGG-16 network is a learning transfer-based architecture [50]. During the transfer, only the fully connected layer was trained to extract features that are important for the training data. Feature prefetching has always followed the VGG-16 architecture. The basic idea behind VGG architectures is to use more layers with smaller filters. In the VGG-16 version, the architecture consists of 16 layers. With small filters, you do not get many parameters, but you can handle them much more efficiently. Training is performed with a fully connected layer of 256 neurons. In the rest of the text, we will call this network \"VGG-16\". (2) The Inception-v3 network is a learning transfer-based architecture [51]. Learning takes place only for the fully connected layer, similar to the VGG-16 architecture. The main ideas of CNN Inception-v3 are as follows:  
* maximizing the flow of information in the network due to the careful balance between depth and width. Property maps are incremented before each pooling;
* with increasing depth, the number of properties, or the width of the layer, also systematically increases;
* the width of each layer is increased to increase the combination of properties before the next layer;
* only 3 \(\times\) 3 convolutions are used whenever possible. Considering 5 \(\times\) 5 and 7 \(\times\) 7 filters can be decomposed with multiple 3 \(\times\) 3 convolutions. Training is performed with a fully connected layer of 256 neurons. Further in the text we will call this network \"Inception-v3\". (3) The architecture of the simplest convolutional network has the following settings: 2 \(\times\) 2 kernel and 5 hidden layers, with 16, 32, 64, 128 and 256 inputs, respectively. A fully connected layer also consists of 256 elements. Since 5 layers of convolution are used, hereinafter we will call this network \"CNN-5\". The next section discusses the obtained results.