Simultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomography

Electron micrography (EM) is an important method for determining the three-dimensional (3D) structure of macromolecular complexes and biological specimens. But there are several limitations such as poor signal-to-noise, limitation on range of tilt angles and sub-region subject to electron exposure, unintentional movements of the specimen, with EM systems that make the reconstruction procedure a severely ill-posed problem. A different choice of reconstruction method may lead to different results and create different additional artifacts in reconstructed images. In this paper, we combined the artifacts reduction strategy and the iterative reconstruction algorithm using a Mumford-Shah model. With the combined method, one can not only regularize the ill-posedness and provide segmentation simultaneously but also smooth additional artifacts due to the limited data. We applied the method to both simulated data from the Shepp-Logan phantom and cryo-specimen tomography. The results demonstrate the performance of the method in reducing the noise and artifacts while preserving and enhancing the edges in the reconstructed image.