Electron Paramagnetic Resonance Image Reconstruction with Total Variation Regularization

This work focuses on the reconstruction of two and three dimensional images of the concentration of paramagnetic species from electron paramagnetic resonance (EPR) measurements. A direct operator, modeling how the measurements are related to the paramagnetic sample to be imaged, is derived in the continuous framework taking into account the physical phenomena at work during the acquisition process. Then, this direct operator is discretized to closely take into account the discrete nature of the measurements and provide an explicit link between them and the discrete image to be reconstructed. A variational inverse problem with total variation regularization is formulated and an efficient resolvant scheme is implemented. The setting of the reconstruction parameters is thoroughly studied and facilitated thanks to the introduction of appropriate normalization factors. Moreover, an a contrario algorithm is proposed to derive the optimal resolution at which the data should be acquired. Finally, an in-depth experimental study over real EPR datasets is done to illustrate the potential and limitations of the presented image reconstruction model.