On an efficient modification of singular value decomposition using independent component analysis for improved MRS denoising and quantification

Abstract

An efficient modification of singular value decomposition (SVD) is proposed in this paper aiming at denoising and more importantly at quantifying more accurately the statistically independent spectra of metabolite sources in magnetic resonance spectroscopy (MRS). Although SVD is known in MRS applications and several efficient algorithms exist for estimating SVD summation terms in which the raw MRS data are analyzed, however, it would be more beneficial for such an analysis if techniques with the ability to estimate statistically independent spectra could be employed. SVD is known to separate signal and noise subspaces but it assumes orthogonal properties for the components comprising signal subspace, which is not always the case, and might impose heavy constraints for the MRS case. A much more relaxing constraint would be to assume statistically independent components. Therefore, a modification of the main methodology incorporating techniques for calculating the assumed statistically independent spectra is proposed by applying SVD on the MRS spectrogram through application of the short time Fourier transform (STFT). This approach is based on combining SVD on STFT spectrogram followed by an iterative application of independent component analysis (ICA). Moreover, it is shown that the proposed methodology combined with a regression analysis would lead to improved quantification of the MRS signals. An experimental study based on synthetic MRS signals has been conducted to evaluate the herein proposed methodologies. The results obtained have been discussed and it is shown to be quite promising.