  Focused ion beam (FIB) tomography provides high resolution volumetric images
on a micro scale. However, due to the physical acquisition process the
resulting images are often corrupted by a so-called curtaining or waterfall
effect. In this paper, a new convex variational model for removing such effects
is proposed. More precisely, an infimal convolution model is applied to split
the corrupted 3D image into the clean image and two types of corruptions,
namely a striped part and a laminar one. As regularizing terms different
direction dependent first and second order differences are used to cope with
the specific structure of the corruptions. This generalizes discrete
unidirectional total variational (TV) approaches. A minimizer of the model is
computed by well-known primal dual techniques. Numerical examples show the very
good performance of our new method for artificial and real-world data. Besides
FIB tomography, we have also successfully applied our technique for the removal
of pure stripes in Moderate Resolution Imaging Spectroradiometer (MODIS) data.
