title: Efficient total variation algorithm for fetal brain MRI reconstruction.
abstract: Fetal MRI reconstruction aims at finding a high-resolution image given a small set of low-resolution images. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has considered several regularization terms s.a. Dirichlet/Laplacian energy, Total Variation (TV)- based energies and more recently non-local means. Although TV energies are quite attractive because of their ability in edge preservation, standard explicit steepest gradient techniques have been applied to optimize fetal-based TV energies. The main contribution of this work lies in the introduction of a well-posed TV algorithm from the point of view of convex optimization. Specifically, our proposed TV optimization algorithm or fetal reconstruction is optimal w.r.t. the asymptotic and iterative convergence speeds O(1/n2) and O(1/√ε), while existing techniques are in O(1/n2) and O(1/√ε). We apply our algorithm to (1) clinical newborn data, considered as ground truth, and (2) clinical fetal acquisitions. Our algorithm compares favorably with the literature in terms of speed and accuracy.
authors.forename: Sébastien
authors.initials: S
authors.lastname: Tourbier
authors.forename: Xavier
authors.initials: X
authors.lastname: Bresson
authors.forename: Patric
authors.initials: P
authors.lastname: Hagmann
authors.forename: Jean-Philippe
authors.initials: JP
authors.lastname: Thiran
authors.forename: Reto
authors.initials: R
authors.lastname: Meuli
authors.forename: Meritxell Bach
authors.initials: MB
authors.lastname: Cuadra
mesh_terms: D061085:Agenesis of Corpus Callosum / Q000196:embryology / Q000473:pathology*; D000465:Algorithms; D000704:Analysis of Variance; D001921:Brain / Q000002:abnormalities* / Q000473:pathology*; D003627:Data Interpretation, Statistical; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D011296:Prenatal Diagnosis / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity