Electron paramagnetic resonance image reconstruction with total variation and curvelets regularization. (26th October 2017)

• Record Type: Journal Article
• Authors: Durand, Sylvain; Frapart, Yves-Michel; Kerebel, Maud
• Is Part Of: Inverse problems. Volume 33:Number 11(2017:Nov.)
• Publication Date: 2017-10-26
• Subjects: electron paramagnetic resonance -- variational method -- Radon transform -- total variation -- curvelets -- EPR imaging; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa8412
• Languages: English
• ISSNs: 0266-5611

Abstract

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 L 1 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.