Electron paramagnetic resonance image reconstruction with total variation and curvelets regularization

Sylvain Durand 1, 2 Yves-Michel Frapart 2, 3 Maud Kerebel 3, 1, 2
2 TGE Réseau National de RPE interdisciplinaire - 3443 - RENARD
LCBPT - UMR 8601 - Laboratoire de Chimie et de Biochimie Pharmacologiques et Toxicologiques, UPD5 - Université Paris Descartes - Paris 5 : FR 3443, FR-CNRS 3443, CNRS - Centre National de la Recherche Scientifique : FR 3443
Abstract : Spatial electron paramagnetic resonance imaging (EPRI) is a recent method to localize and characterize free radicals in vivo or in vitro, leading to applications in material and biomedical sciences. To improve the quality of the reconstruction obtained by EPRI, a variational method is proposed to inverse the image formation model. It is based on a least-square data-fidelity term and the total variation and Besov seminorm for the regularization term. To fully comprehend the Besov seminorm, an implementation using the curvelet transform and the L1 norm enforcing the sparsity is proposed. It allows our model to reconstruct both image where acquisition information are missing and image with details in textured areas, thus opening possibilities to reduce acquisition times. To implement the minimization problem using the algorithm developed by Chambolle and Pock, a thorough analysis of the direct model is undertaken and the latter is inverted while avoiding the use of filtered backprojection (FBP) and of non-uniform Fourier transform. Numerical experiments are carried out on simulated data, where the proposed model outperforms both visually and quantitatively the classical model using deconvolution and FBP. Improved reconstructions on real data, acquired on an irradiated distal phalanx, were successfully obtained.
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Sylvain Durand, Yves-Michel Frapart, Maud Kerebel. Electron paramagnetic resonance image reconstruction with total variation and curvelets regularization. 2017. ⟨hal-01419832v2⟩

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