## 1 Introduction  
Magnetic resonance imaging (MRI) images usually suffer from different types of noise, such as Gaussian noise, Poisson noise, speckle noise, etc. [1]. Currently, many particular methods for eliminating noise in MRI images have been developed for cases where the type of noise is known. The traditional approach to suppressing these types of noise is associated with the correction of the multiplicative and additive coefficients of the MRI scanner matrix [2]. This provides a sufficiently high uniformity of radiation intensity in the field of view. Examples of such methods are the full variation method and the median method of filtering one-dimensional signals [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12], which are known to be effective approaches for eliminating Gaussian and Poisson noise [13; 14; 15; 16]. Both types of noise (Poisson and Gaussian) have been well-studied, but their combination in a recorded signal [17], which is often present in biomedical signals and electron microscopy images, is also important [18; 19]. However, these approaches are not without drawbacks, which are associated with the following:  
* the need to use reference optical emitters (at least two);
* high uniformity requirements for the optical emitters in the field of view;the need to use several reference emitters during the calibration process (if the dynamic range of the signals varies in space or time); and,
* the need to periodically repeat the calibration procedure (if the spectral composition of the transmission and signal processing channels changes over time).  
In recent years, a number of studies have aimed to develop algorithms and practical application of mathematical models to suppress Gaussian and Poisson noise in information systems [20; 21; 22; 23]. For example, the concept of full variation in eliminating Gaussian noise was first applied [13] based on the use of full variation in image processing tasks (Rudin-Osher-Fatem (ROF) model). This model is designed to eliminate Gaussian noise [13; 14]; however, it can be used to eliminate other types of noise. Median filters are also quite often used as a software tool for image preprocessing in practice [24; 25].  
Some MRI images are characterized by an increased noise level, or they contain noise or artifacts, which leads to an incorrect diagnosis. The quality of an MRI image depends on many factors: spatial resolution and image contrast, slice thickness, the reconstruction algorithm, physical processes in the measurement system, etc. The ambient temperature is one factor that affects the reliability of the obtained data. Fluctuations in temperature lead to an increase in the level of Gaussian noise in the MRI image and a decrease in measurement accuracy.  
Developing methods and a means for eliminating noise and image artifacts in tomography is an urgent task. New ways to increase the signal-to-noise ratio have become possible thanks to the digitization of measurement results and the use of the DICOM (Digital Imaging and Communications in Medicine) 3.0 protocol. The use of this model to eliminate mixed noise from MRI images allows one to increase the signal-to-noise ratio and the quality of the images obtained, by eliminating Gaussian noise and by the further computer processing of images.  
It is necessary to develop an approach for eliminating impulse noise and fluctuation noise in the temperature measurement channel in order to increase the reliability of diagnostics based on MRI images.  
The relevance of the formulation of such a problem is determined by the software algorithm for suppressing geometric noise from the recorded images; this expands the possibilities for applying the results to other fields of biomedical research.  
The aim of this work is to develop a comprehensive mathematical model for eliminating impulse noise, which is caused by various regular geometric structures of the photoelectric elements of the electronic matrix and the structure of the signal transmission channel, from MRI images.