Osteoporosis is a major cause of bone fracture and can be characterised by both mass loss and microstructure deterioration of the bone. The modern way of osteoporosis assessment is through the measurement of bone mineral density, which is not able to unveil the pathological condition from the mesoscale aspect. To obtain mesoscale information from computed tomography (CT), the super‐resolution (SR) approach for volumetric imaging data is required. A deep learning model AESR3D is proposed to recover high‐resolution (HR) Micro‐CT from low‐resolution Micro‐CT and implement an unsupervised segmentation for better trabecular observation and measurement. A new regularisation overcomplete autoencoder framework for the SR task is proposed and theoretically analysed. The best performance is achieved on structural similarity measure of trabecular CT SR task compared with the state‐of‐the‐art models in both natural and medical image SR tasks. The HR and SR images show a high correlation (r = 0.996, intraclass correlation coefficients = 0.917) on trabecular bone morphological indicators. The results also prove the effectiveness of our regularisation framework when training a large capacity model.