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In this article, we introduce a new ring artifacts reduction procedure that combines several ideas from existing methods into one complex and robust approach with a goal to overcome their individual weaknesses and limitations. The procedure differentiates two types of ring artifacts according to their cause and character in computed tomography (CT) data. Each type is then addressed separately in the sinogram domain. The novel iterative schemes based on relative total variations (RTV) were integrated to detect the artifacts. The correction process uses the image inpainting, and the intensity deviations smoothing method. The procedure was implemented in scope of lab-based X-ray nano CT with detection systems based on charge-coupled device (CCD) and scientific complementary metal–oxide–semiconductor (sCMOS) technologies. The procedure was then further tested and optimized on the simulated data and the real CT data of selected samples with different compositions. The performance of the procedure was quantitatively evaluated in terms of the artifacts’ detection accuracy, the comparison with existing methods, and the ability to preserve spatial resolution. The results show a high efficiency of ring removal and the preservation of the original sample’s structure.