Some spectroscopies are intrinsically poorly sensitive, such as Nuclear Magnetic Resonance (NMR) and Raman spectroscopy. This drawback can be overcome by using Singular Value Decomposition (SVD) and low-rank approximation to denoise spectra and consequently increase sensitivity. However SVD limits have not been deeply investigated until now. We applied SVD to NMR and Raman spectra and showed that best results were obtained with a square data set in time domain. Automatic thresholding was applied using Malinowski's indicators. 6×7380 noisy spectra with 41 signal-to-noise ratios were compared to their nonnoisy counterparts, highlighting that SVD induces a systematic error for Gaussian peaks but faithfully reproduces shape of Lorentzian peaks, thus allowing quantification. Used carefully, SVD can decrease experimental time by a factor of 2.3 for spectroscopies. This study may help scientists to apply SVD to denoise spectra in a more efficient way, without falling into pitfalls.
Spectroscopies are of fundamental importance but can suffer from low sensitivity.Singular Value Decomposition (SVD) is a highly interesting mathematical tool, which can be conjugated with low-rank approximation to denoise spectra and increase sensitivity. SVD is also involved in data mining with Principal Component Analysis (PCA). In this paper, we focussed on the optimisation of SVD duration, which is a time-consuming computation. Both Intel processors (CPU) and Nvidia graphic cards (GPU) were benchmarked. A 100 times gain was achieved when combining divide and conquer algorithm, Intel Math Kernel Library (MKL), SSE3 (Streaming SIMD Extensions) hardware instructions and single precision. In such case, the CPU can outperform the GPU driven by CUDA technology. These results give a strong background to optimise SVD computation at the user scale.
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