Abstract: In volume visualization, noise in regions of homogeneous material and at boundaries between different materials poses a great challenge in extracting, analyzing and rendering features of interest. In this paper, we present a novel volume denoising / smoothing method based on the L0 gradient minimization framework. This framework globally controls how many voxels with a non-zero gradient are in the result in order to approximate important features’ structures in a sparse way. This procedure can be solved quickly by the alternating optimization strategy with half-quadratic splitting. While the proposed L0 volume gradient minimization method can effectively remove noise in homogeneous materials, a blurring-sharpening strategy is proposed to diminish noise or smooth local details on the boundaries. This generates salient features with smooth boundaries and visually pleasing structures. We compare our method with the bilateral filter and anisotropic diffusion, and demonstrate the effectiveness and efficiency of our method with several volumes in different modalities.