Falcon: Unfolded Variational Model for Blind Deconvolution and Segmentation in 3D Dental Imaging

We propose FALCON, an unfolded variational network for 3D blind deconvolution in Cone Beam Computed Tomography (CBCT), derived from a convexified Mumford-Shah formulation. The method unrolls a Split Bregman solver into a fixed number of learnable stages, combining explicit modelbased regularization with data-driven parameter adaptation, while jointly refining a Gaussian PSF parameter. On dental CBCT volumes, FALCON improves structural sharpness and boundary definition relative to a classical blind variational solver, without requiring paired$\mu \text{CT}$supervision at inference. We additionally report a simple clustering-based analysis on reconstructed volumes to qualitatively assess structural separability of canal and dentin regions.