## 1 Introduction
The Frost filter, in turn, uses an exponentially weighted value, with weights calculated using the local variance and mean. Order statistics filters are based on the analysis of a variational series and the application of linear or nonlinear averaging over the intensities selected according to some special ranking criteria [24]. This family of filters includes basic filters such as the median filter and minimum and maximum filters [20; 21; 22]. But the main representatives of this family are based on ranking intensities in a local window around a pixel to be processed based on their closeness to the intensity of a pixel of interest in terms of values or their ranks [23; 24; 25]. These latter filters provide a decent ability to suppress noise and better preserve image details. The widespread popularity of neural networks has led to their extensive adoption in various denoising methods, as well as other image processing tasks. A notable example is provided in [26], where machine learning techniques, and specifically neural networks, were employed for digital image restoration, noise removal, and object detection. A comprehensive overview of deep learning-based image denoising methods using feedforward and U-shaped neural network architectures was presented in [27]. The study analyzed the advantages and limitations of these architectures, as well as various learning strategies employed for efficient image denoising. Convolutional neural networks (CNNs) have captured the attention of researchers worldwide, including those working in the field of image filtering. Multiple CNN architectures were analyzed for filtering different types of noise in digital images in [28; 29; 30]. Among these, the Hybrid CNN [31] and the Pre-trained RLN [32] were specifically designed to address speckle noise and were reported to achieve performance comparable to, and in some cases surpassing, classical filters such as the Lee and Frost filters. The denoising convolutional neural network (DnCNN) was proposed in [33]. DnCNN employs a deep architecture with multiple convolutional layers of various types and does not include pooling layers. The network was trained to reduce Gaussian noise in grayscale and color images, achieving results that were comparable to, and in some cases better than, those of BM3D, WNNM, TNRD, and CSF. CNNs have also been adapted for specialized imaging domains. In [34], a deep CNN inspired by DnCNN was effectively utilized to filter a combination of additive Gaussian and Poisson noise in X-ray images obtained during the Multi-Shock (MShock) experiments conducted at the National Ignition Facility (NIF). According to the research, this approach achieved superior filtering results in terms of PSNR compared to filters such as the mean and Butterworth. In addition to CNNs, neural networks with different architectures have also been successfully applied to denoising tasks. In [35], a multilayer perceptron (MLP) with four hidden layers, each containing 2047 neurons, was proposed for filtering additive Gaussian noise. The network was trained on a dataset designed from image fragments in the spatial domain, comprising 362 million training samples. The MLP with this architecture slightly outperformed the BM3D algorithm or showed comparable results in Gaussian noise filtering for specific test images. Various types of neural networks, including those based on despeckling autoencoders, were evaluated for reducing speckle noise in ultrasound images in [36]. The study demonstrated that denoising solutions utilizing neural networks, such as Di-Conv-AE-Net, DGAN-Net [37; 38], and D-U-NET, based on U-Net [39], outperformed widely used filtering algorithms like BM3D. In [40], the stacked sparse denoising autoencoder (SSDA) architecture was proposed for denoising and inpainting grayscale images. This approach is based on sparse coding methods, which reconstruct images from a sparse linear combination of an overcomplete dictionary.