title: Reconstruction from free-breathing cardiac MRI data using reproducing kernel Hilbert spaces.
abstract: This paper describes a rigorous framework for reconstructing MR images of the heart, acquired continuously over the cardiac and respiratory cycle. The framework generalizes existing techniques, commonly referred to as retrospective gating, and is based on the properties of reproducing kernel Hilbert spaces. The reconstruction problem is formulated as a moment problem in a multidimensional reproducing kernel Hilbert spaces (a two-dimensional space for cardiac and respiratory resolved imaging). Several reproducing kernel Hilbert spaces were tested and compared, including those corresponding to commonly used interpolation techniques (sinc-based and splines kernels) and a more specific kernel allowed by the framework (based on a first-order Sobolev RKHS). The Sobolev reproducing kernel Hilbert spaces was shown to allow improved reconstructions in both simulated and real data from healthy volunteers, acquired in free breathing.
authors.affiliation: IADI, Nancy-Université, Nancy, France.
authors.forename: Nicolae
authors.initials: N
authors.lastname: Cîndea
authors.forename: Freddy
authors.initials: F
authors.lastname: Odille
authors.forename: Gilles
authors.initials: G
authors.lastname: Bosser
authors.forename: Jacques
authors.initials: J
authors.lastname: Felblinger
authors.forename: Pierre-André
authors.initials: PA
authors.lastname: Vuissoz
mesh_terms: D000465:Algorithms; D006321:Heart / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D019028:Magnetic Resonance Imaging, Cine / Q000295:instrumentation / Q000379:methods*; D009038:Motion; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D015656:Respiratory Mechanics; D012680:Sensitivity and Specificity