Ring artefacts are the most disturbing artefacts when reconstructed volumes are segmented. A lot of effort has already been put into better X-ray optics, scintillators and detectors in order to minimize the appearance of these artefacts. However, additional processing is often required after standard flat-field correction. Several methods exist to suppress artefacts. One group of methods is based on minimization of the Tikhonov functional. An analytical formula for processing of a single sinogram was developed. In this paper a similar approach is used and a formula for processing two-dimensional projections is found. Thus suppression of ring artefacts is organized as a two-dimensional convolution of `averaged' projections with a given filter. Several approaches are discussed in order to find elements of the filter in a faster and accurate way. Examples of experimental datasets processed by the proposed method are considered.