Linear Optimization for Electron Tomography Reconstructions

Resumen

Electron tomography is a technique for imaging three-dimensional structures of materials at nanometer scale. This technique consists onreconstructing nano-objects thanks to projections provided by a microscope from different tilt angles. These projections are a group ofparallel electron beams which go through the particle to modify their intensities. These intensities, which are called sinograms, are the inputs of our reconstruction models. The idea behind this reconstruction model is to solve an optimization model that minimizes the norm of the difference between the sinogram and the theoretical projection. Among them, nowadays, most popular reconstruction models are based on total variation minimization considering the sum of the l2-norm of the image gradient as well as the deviation of the reconstructed sinogram with respect to the original data, measured with the l2-norm. We consider an l1-norm total variation model which provides good quality reconstructions. The model we propose removes a high level of noise from the reconstruction recovered. Furthermore, some linear programming techniques are used to provide one efficient way of solving the resulting complex model for real situations.