The visualization of volume maps obtained by electron tomographic reconstruction is severely hampered by noise. As electron tomography is usually applied to individual, nonrepeatable structures, e.g., cell sections or cell organelles, the noise cannot be removed by averaging as is done implicitly in electron crystallography or explicitly in single particle analysis. In this paper, an approach for noise reduction is presented, based on a multiscale transformation, e.g., the wavelet transformation, in conjunction with a nonlinear filtration of the transform coefficients. After a brief introduction to the theoretical background, the effect of this type of noise reduction is demonstrated by test calculations as well as by applications to tomographic reconstructions of ice-embedded specimens. Regarding noise reduction and structure preservation, the method turns out to be superior to conventional filter techniques, such as the median filter or the Wiener filter. Results obtained with the use of different types of multiscale transformations are compared and the choice of suitable filter parameters is discussed. (C) 1997 Academic Press.