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The basic task of computer tomography for reconstructing the body by its projections for an incomplete set of data is solved by using Radon’s retransformation and subsequent regularisation. The method proposed can be used successfully in geophysics and geotechnology.

The Moore-Penrose pseudoinversion method applied in solving systems of linear algebraic equations with incorrectly prescribed data lead to unstable solutions. This makes the method inapplicable in practice. The regularised version of that method is described which can be used as a basis for data processing in all branches of applied earth sciences.