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Reconstruction from free‐breathing cardiac MRI data using reproducing kernel Hilbert spaces
Author(s) -
Cîndea Nicolae,
Odille Freddy,
Bosser Gilles,
Felblinger Jacques,
Vuissoz PierreAndré
Publication year - 2010
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.22170
Subject(s) - reproducing kernel hilbert space , hilbert space , kernel (algebra) , mathematics , sobolev space , interpolation (computer graphics) , representer theorem , kernel principal component analysis , artificial intelligence , algorithm , computer science , kernel method , mathematical analysis , pure mathematics , image (mathematics) , support vector machine
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. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.