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Laboratory X-ray microtomography is a convenient method of studying the threedimensional structure of objects of different types. Modern laboratory microtomography setups allow us to carry out measurements with submicron resolution. The laboratory sources of X-ray radiations used in such setups have low intensity, so the recorded tomographic projections are noisy. This often leads to the situation when the reconstructed tomographic images are also noisy, and artifacts may appear on them (objects of a characteristic shape, which are absent in the real object). In this work, we describe the methods of noise and artifacts suppression at all stages of data processing: reducing noise in the original projection images, the inclusion of regularizing members in the tomographic reconstruction procedure, filtering of reconstructed data. The reduction of noise and artifacts on tomographic data allows not only to reconstruct the internal structure of the objects under study but also to make a step towards temporal resolution and spectral tomography on laboratory sources. [ABSTRACT FROM AUTHOR]