l1-norm Mathematical Programming Model Applied to STEM Tomography

Resumen

Electron tomography is an image processing technique for reconstructing three-dimensional structures of materials at nanometer scale.These reconstructions are obtained thanks to STEM images (projections) provided by a microscope from different tilt angles. These projections are obtained by a group of parallel electron beams which go through the object modifying their intensities. The microscopes record the intensities on a detector creating sinograms which are the inputs of our reconstruction models. In the last years, electron tomography 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 propose to consider an l1-norm total variation model which providesgood quality reconstructions. The solutions obtained by the l1-norm model achieve accurate results with respect to the original objects and remove a high level of noise from the reconstruction recovered. This model contains a large number of variables and constraints, therefore,some linear programming techniques are used to provide one efficient way of solving this model for real experiments. Computational results are shown to validate the performance of this linear model to reconstruct electron tomography objects artificially produced. Finally, an experimental tomography reconstruction is carried out to check the quality of the object obtained.