Mesh denoising is a typical problem in computer graphics. The key challenge we face in this field is to denoise the mesh and maintain the structure of the mesh at the same time. And it is becoming the hottest topic in this area. We propose a global mesh denoising method using -sparsity. This method is motivated by the fundamental theory of sparse representation in the field of signal processing. The global optimization of an energy function is used to remove noises from the mesh while the features are preserved. There are two steps in our method. The first step is the filtering of the face normals. We formulate a global optimization model to optimize the face normals of the noised mesh. Then we use the -norm to ensure the sparsity of the solution

which preserves the structures of mesh features. The second step is the reconstruction of the denoised mesh. Given the new filtered face normals

we create a vertex reconstruction model under the least-square sense according to the definition of the face normal. The denoised mesh is updated by the solution of the reconstruction model. Furthermore

our model solves the denoising problem globally

which avoids problems of existing methods

such as the convergence problem. A large number of experiments demonstrate that our method is able to remove noises

at the same time

preserving the features of the mesh

especially for the CAD models.