Digital breast tomosynthesis images provide volumetric morphological information of the breast helping physicians to detect malign lesions. In this work, we propose a new spatially adaptive total variation (SATV) regularization function allowing to preserve adequately the shape of small objects such as microcalcifications while ensuring a high quality restoration of the background tissues. First, an original formulation for the weighted gradient field is introduced, that efficiently incorporates prior knowledge on the location of small objects. Then, we derive our SATV regularization, and integrate it in a novel 3D reconstruction approach for DBT. Experimental results carried out on both phantom and clinical data show the great interest of our method for the recovery of DBT volumes showing small lesions.