## 3 Results and Discussion  
Clinical testing of models for eliminating noise in MRI images of the heart was performed to diagnose cancerous tumors in the heart, which form as a result of the progression of an underlying disease. The MRI images used in this work were obtained on a 1.5 Tesla MRI scanner using the closed-screen electrocardiological ECG protocol. The MRI studies included a morphological review covering the whole heart with fast spin-echo sequences, sequential gradient echo sequences, and sequential precession echo sequences, which can significantly reduce the examination time. Reliability analysis of the models was performed for several medical histories of tumor detection in patients, including those with lung cancer, with melanoma, with renal cell cancer, with sarcoma of the heart, with cardiac lymphoma, and with myxoma in the atrium [26]. The contour extraction method was used to identify cancerous areas that, after applying the model to eliminate mixed noise, had an increased contrast of volumetric heterogeneous formations in the region of the heart [27]. This method was developed by the authors when analyzing thermal images to assess the condition of the coronary vessels of the myocardium under cardiopulmonary bypass. The contours of the cancerous regions in the examples used for applying the model to eliminate mixed noise (Figures 4-9) are highlighted in yellow and they represent the visual boundary of the distribution of volumetric heterogeneous formations. 1. For a patient with a history of lung cancer: during MRI with contrast enhancement, the volumetric formation of a heterogeneous structure in the left ventricle was determined (Figure 4). 2. For a patient with a history of melanoma: during MRI with contrast enhancement, a volumetric formation adjacent to the atrial septum was visualized in the left atrium (Figure 5). 3. For a patient with renal cell carcinoma: during MRI with contrast enhancement in the right ventricle and interventricular septum, the volumetric formation of a heterogeneous structure in the form of infiltrated metastases was determined (Figure 6). Figure 3: Example of applying median filtering to a model signal: \(a_{k}\) is the model signal; \(b_{k}\) is the result of median filtering. For a patient with sarcoma of the heart: during MRI, a volumetric mass was determined in the lateral wall of the right atrium (Figure 7). * For a patient with heart and pericardial lymphoma: during MRI with contrast enhancement, the volumetric formation of a heterogeneous structure in the right atrium and thickened pericardium was determined (Figure 8). * For a patient with myxoma in the left atrium: during MRI with contrast enhancement in the left atrium, a hypodense mass formation, which causes mitral valve stenosis, was visualized (Figure 9). A histological examination of all surgically removed emboli was performed to confirm the oncological diagnosis of these patients. The quality of software processing was compared with other methods of noise elimination, for example, the ROF model, modified ROF model, and median filtering [24,25]. A mathematical model with a one-dimensional signal effectively eliminates combined Gaussian and Poisson noise, accounting for these types of noise. As a result of research into and application of the filter model to eliminate impulse noise, and fluctuations and geometric noise from MRI images of the heart, it has become possible to detect and eliminate the random components of the image (noise), as well as reliably isolate and increase the contrast of cancerous volumetric heterogeneous formations in the heart region. The block-match and three-dimensional (3D) filtering (BM3D) filter [28] mentioned in the review [21] has shown good results in many areas, including MRI [29]. BM3D utilizes the notion that natural images have self-spatial similarities. First, the algorithm searches for patches in the image that are similar to the intensities of the patch that has to be denoised.