Discrete representation of local orientation in grains using diffraction contrast tomography

In this work we introduce a new model for dealing with the problem of local orientation reconstruction in grains, when using data from X-ray Diffraction Contrast Tomography experiments. The model explores the use of well established minimization algorithms from the field of mathematical optimization, like FISTA, and the possible use of recent mathematical devices for the solution of highly undetermined systems of equations, like the l₁-minimization over the Haar transform of the tomographic volumes. Along with a detailed explanation of how such algorithms can be applied to our six-dimensional problem, we report encouraging results obtained on simulated data.