Nonconvex Mixed TV/Cahn–Hilliard Functional for Super-Resolution/Segmentation of 3D Trabecular Bone Images

In this work, we investigate an inverse problem approach to 3D super-resolution/segmentation for an application to the analysis of trabecular bone micro-architecture from in vivo 3D X-ray CT images. The problem is expressed as the minimization of a functional including a data term and a prior. We consider here a regularization term combining total variation (TV) and a double-well potential to enforce the quasi-binarity of the resulting image. Three different schemes to minimize this nonconvex functional are presented and compared. The methods are applied to experimental new high-resolution peripheral quantitative CT images (voxel size $$82\,\upmu \hbox {m}$$ ) and evaluated with respect to a micro-CT image at higher spatial resolution (voxel size $$41\,\upmu \hbox {m}$$ ) considered as a ground truth. Our results show that a combination of double-well functional and TV term improves the contrast and the quality of the restoration even if the connectivity may be degraded.