Multi-level tomography reconstructions with level-set and TV regularization methods

The discrete tomographic reconstruction problem is generally considered for binary image. In this work, we consider the reconstruction of an image with more than two grey levels and compare two reconstruction methods. The first one is based on a classical TV regularization and the second one is a level-set regularization method. In this second method, the discrete tomographic problem is formulated as a shape optimization problem with several level-set functions and regularized with Total Variation-Sobolev terms. The two methods are applied to an image size of 128 × 128, with several additive Gaussian noises on the raw projection data and several number of projections.