## 1 Introduction  
Computed tomography is an increasingly popular imaging technique with applications in the fields of medicine, diagnostics, scientific research and industry. A variety of artifacts arise during tomographic imaging. They are caused by various physical phenomena during the emission of radiation. Ring artifacts are one of the most common artifacts. They arise as a result of imperfections in the detector's pixel elements or fiber optic matrix, or defects on scintillator crystals [1]. Ring artifacts can also result from contamination of any of the previously mentioned elements, as well as various types of drift, for example, thermal drift or drift in the X-ray-gene spectrum [2]. Scintillators are the element located in front of the detector optical fiber matrix and have the function of converting ionizingradiation into visible or near-visible emission. There are a number of materials that exhibit scintillation properties that can exist in crystalline, liquid or gaseous form. Optical fibers behind the scintillator direct radiation in the visible spectrum emitted by the scintillator directly to individual pixels located on the CCD or CMOS array of the detector (Figure 1). The attenuation or extinguishing of individual pixels during acquisition causes the formation of artifacts in the image [3]. Ring artifacts visible on tomograms appear in the form of circles spreading from the center of the image to its edges. There may be several to dozens of them. The visible circles can range in width from single pixels up to several pixels. They can have different grayscale brightness. They significantly affect the qualitative and quantitative analysis of the measured data. They can also distort important morphometric information in the tomographic image. Artifacts hinder such processes as noise reduction, binarization and segmentation in the image [4; 5; 6; 7]. Methods for removing these artifacts can be divided into three types: pre-acquisition, pre-reconstruction and post-reconstruction methods. The commonly used pre-acquisition method of reducing ring artifacts resulting from unbalanced detector sensitivity is called flat-field correction. Flat-field correction involves pixel correction so that all pixels have an identical gray value when they are exposed to a beam with specific parameters. These parameters are identical to those used during the acquisition of the research object [8]. In this method, measurement of the bright- and dark-field images is performed. The bright-field image is collected during homogeneous unconstrained radiation of the detector with the X-ray beam, and the dark-field image is the image formed while the radiation is disabled. The correction is calculated as follows for a pixel in the (x, y) position: The intensity of the pixel for the bright field is \(I_{B}(x,y)\), and for the dark field is \(I_{D}(x,y)\), and the average intensity for both fields is \(\mu_{B}\) and \(\mu_{D}\). Based on this information, the specific gain of the pixel \(G(x,y)\) and the displacement of the pixel \(O(x,y)\) can be counted according to the following formula:  
\[G(x,y)=\frac{\mu_{B}-\mu_{D}}{I_{B}(x,y)-I_{D}(x,y)} \tag{1}\]  
\[O(x,y)=\mu_{B}-G(x,y)I_{B}(x,y) \tag{2}\]  
The resulting data can be applied to correct the raw signal \(I_{U}(x,y)\) obtained during acquisition, the result being a corrected pixel value \(I_{C}(x,y)\):  
\[I_{C}(x,y)=I_{u}(x,y)G(x,y)+O(x,y) \tag{3}\]  
The presented method significantly improves image acquisition; however, it does not provide complete removal of ring artifacts [9]. This is due to the nonlinearity of the response function of the photosensitive components of the detector, and to the nonlinearity in time of the uniformity of the radiation beam. Pre-reconstruction and post-reconstruction methods involve post-acquisition pixel correction. They implement image filtering methods involving entire images or specific areas of artifact occurrence.