Bone microstructure reconstructions from few projections with stochastic nonlinear diffusion

Abstract

In this work, we use a stochastic diffusion equation for the reconstruction of binary tomography cross-sections obtained from a small number of projections. The aim of this new method is to escape from local minima by changing the shape of the boundaries of the image. First, an initial binary image is reconstructed with a deterministic Total Variation regularization method, and then this binary reconstructed image is refined by a stochastic partial differential equation with singular diffusivity and a gradient dependent noise. This method is tested on a 256 × 256 experimental micro-CT trabecular bone image with different additive Gaussian noises. The reconstruction images are clearly improved.