Osteoporosis is a disease characterized by loss of bone mass and degradation of bone microarchitecture. Although osteoporosis is not a fatal disease, the fractures it causes can lead to serious complications (damage to vessels and nerves, infections, stiffness), sometimes accompanied with risk of death. The bone micro-architecture plays an important role for the diagnosis of osteoporosis. Two common CT devices to scan bone micro architecture is High resolution-peripheral Quantitative CT and Micro CT. The former device gives access to in vivo investigation, but its spatial resolution is inferior. Micro CT gives better spatial resolution, but it is constrained to ex vivo measurement. In this thesis, we attempt to improve the spatial resolution of high resolution peripheral CT images so that the quantitative analysis of the resolved images is close to the one given by Micro CT images. We started from the total variation regularization, to a combination of total variation and double-well potential to enhance the contrast of results. Then we consider to use dictionary learning method to recover more structure details. Afterward, a deep learning method has been proposed to solve a joint super resolution and segmentation problem. The results show that the deep learning method is very promising for future applications.