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We address the reconstruction of a 3D image from a set of incomplete X-ray tomographic data. In the case where the image is composed of one or several objects lying in a uniform background, we define a sparse parameterization by considering the active voxels, i.e., the voxels that do not lay inside the background. Estimation of the active voxel densities is performed using the maximum a posteriori (MAP) estimator. In order to implement sparse parameter estimation, we design an original multiresolution scheme, which handles coarse to fine resolution images. This scheme affords automatic selection of active voxels at each resolution level, and provides a drastic decrease of the computation time. We finally show the performance of our method on synthetic data.