Removal of curtaining effects by a variational model with directional forward differences

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. In order to accomplish the decomposition we exploit the fact that the single parts have certain spatial structures, which are penalized by different first and second order differences. By doing so, our approach generalizes discrete unidirectional total variational (TV) approaches. A minimizer of the proposed model is computed by well-known primal dual techniques. Numerical examples show the very good performance of our new method for artificial as well as 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.