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

Abstract

Electron micrography (EM) is a detection method for determining the structure of macromolecular complexes and biological specimens. However, some restrictions in the EM system, including poor signal-to-noise, limited range of tilt angles, only a sub-region subject to electron exposure and unintentional movements of the specimen, make the reconstruction procedure severely ill-posed. Because of these limitations, there may be severe artifacts in reconstructed images. In this paper, we first design an algorithm that can quickly calculate the radiological paths. Then we combine an iterative reconstruction algorithm using the Mumford-Shah model with an artifact reduction strategy. The combined method can not only regularize the ill-posedness and provide the reconstruction and segmentation simultaneously but also smooth additional artifacts due to the limited data. Also we improved the algorithm used for the calculation of radiological paths to accelerate the reconstruction. The proposed algorithm was translated into OpenCL programs and kernel functions to asynchronously and in parallel update the reconstructed image along rays by GPUs. We tested the method on both simulated and real EM data. The results show that our artifact reduced Mumford-Shah algorithm can reduce the noise and artifacts while preserving and enhancing the edges in the reconstructed image.