## 1 Introduction  
The primary challenge in effective image and signal processing is the presence of noise. Noise refers to random deviations of a signal from its true value, caused by various external or internal factors within an image. As a result, a significant portion of image processing research and techniques focuses on noise reduction and removal. In this article, we consider intelligent filtering of two common types of noise: additive Gaussian noise and speckle noise. Additive Gaussian noise with the Gaussian probability distribution function is usually caused by the following factors [1, 2]:  
* Discrete nature of light (photons), resulting in the fluctuation in the number of photons detected by an image sensor in a given period of time;
* Imperfections in electronic circuits, including amplifiers and analog-to-digital converters;
* Distribution of microscopic grains of metallic silver or dye particles in film emulsions while working with photographic film. Speckle noise is a multiplicative noise, which may also contain an additive component. Speckle noise can be observed in images that are acquired using a coherent source (for example, laser, radar, and ultrasound). The cause of speckles is the microscopic variations in the surface roughness within one pixel, so when coherent radiation strikes the surface and becomes reflected, a received signal is subjected to random variations in phase and amplitude [3]. Noise filtering in images is a long-standing problem. However, it remains highly relevant today. Since the advent of digital imaging, numerous noise filtering methods have been developed. These range from a variety of spatial and frequency domain linear and nonlinear filters to filtering methods based on the use of neural networks and fuzzy logic. One of the most efficient filters to deal with additive and speckle noise in images is the BM3D filter [4]. It is an efficient noise reduction method that operates in the frequency domain, utilizing the 3D Fourier transform on blocks constructed from statistically similar image patches. The BM3D filter has demonstrated high efficiency in reducing both Gaussian and speckle noise. A variety of image denoising methods, including anisotropic diffusion, total variation minimization, weighted nuclear norm minimization (WNNM), trainable nonlinear reaction diffusion (TNRD), and shrinkage fields, have been explored in [5; 6]. Techniques based on anisotropic diffusion, detailed in [7; 8; 9; 10; 11; 12], employ a partial differential equation to iteratively smooth pixel intensities in low-gradient regions while preserving edges in high-gradient areas, effectively reducing noise while maintaining critical image features. Similarly, TNRD, introduced in [13; 14], was demonstrated to be effective for filtering additive Gaussian noise in [5]. Total variation minimization, described in [15], reduces noise by minimizing the integral of the signal gradient, producing a denoised image that retains essential features. Other interesting noise filtering techniques are based on the use of shrinkage fields and nuclear norm minimization. The former one utilizes a structure called cascade of shrinkage fields (CSF) [16], offering computationally efficient denoising for high-resolution images. In turn, WNNM [17] constructs a low-rank matrix from similar image patches to estimate denoised patches, demonstrating high effectiveness in filtering additive Gaussian noise. It is also worth mentioning such classical filters as the Lee filter [18], the Frost filter [19], and a family of order statistics-based filters [20; 21; 22; 23]. The Lee and Frost filters are usually used to filter multiplicative speckle noise. These filters use the local statistics of an image fragment to calculate the updated intensity value of a target pixel. For example, the Lee filter uses the local mean value and weights based on the local and global variance of the image to calculate the pixel intensity.