title: Denoising NMR time-domain signal by singular-value decomposition accelerated by graphics processing units.
abstract: We present a post-processing method that decreases the NMR spectrum noise without line shape distortion. As a result the signal-to-noise (S/N) ratio of a spectrum increases. This method is called Cadzow enhancement procedure that is based on the singular-value decomposition of time-domain signal. We also provide software whose execution duration is a few seconds for typical data when it is executed in modern graphic-processing unit. We tested this procedure not only on low sensitive nucleus (29)Si in hybrid materials but also on low gyromagnetic ratio, quadrupole nucleus (87)Sr in reference sample Sr(NO3)2. Improving the spectrum S/N ratio facilitates the determination of T/Q ratio of hybrid materials. It is also applicable to simulated spectrum, resulting shorter simulation duration for powder averaging. An estimation of the number of singular values needed for denoising is also provided.
authors.affiliation: Sorbonne Universités, UPMC Univ Paris 06, FR 2482, Institut des matériaux de Paris-Centre, Collège de France, F-75005 Paris, France; CNRS, FR 2482, Institut des matériaux de Paris-Centre, Collège de France, F-75005 Paris, France. Electronic address: pm@pascal-man.com.
authors.forename: Pascal P
authors.initials: PP
authors.lastname: Man
authors.affiliation: Sorbonne Universités, UPMC Univ Paris 06, UMR 7574, Chimie de la Matière Condensée de Paris, Collège de France, F-75005 Paris, France; CNRS, UMR 7574, Chimie de la Matière Condensée de Paris, Collège de France, F-75005 Paris, France.
authors.forename: Christian
authors.initials: C
authors.lastname: Bonhomme
authors.affiliation: Sorbonne Universités, UPMC Univ Paris 06, UMR 7574, Chimie de la Matière Condensée de Paris, Collège de France, F-75005 Paris, France; CNRS, UMR 7574, Chimie de la Matière Condensée de Paris, Collège de France, F-75005 Paris, France.
authors.forename: Florence
authors.initials: F
authors.lastname: Babonneau
keywords: (29)Si MAS NMR; Denoising; Hankel matrix; Hybrid materials; Powder pattern; QCPMG; SVD