Wavelets and related time‐frequency techniques in magnetic resonance spectroscopy

Abstract

We survey the various applications in MRS of the wavelet transform and related time-frequency methods. For the sake of completeness, we first quickly review the mathematical tools needed.

MRS signal quantitation: A review of time- and frequency-domain methods

“…A generalization of the method and advices to use it are given in [46]. Wavelets have also been used for water removal (see, e.g., [100][101][102][103]) and, in [101], the Gabor transform is proposed as a good alternative to the wavelets. In a review of filtering approaches to solvent suppression in MRS [102], 5 filtering methods are compared: a Gabor transform based method [101], the method of Marion et al [98], the method of Sodano and Delepierre [104], the Cross method [105], the maximum-phase Finite Impulse Response (MP-FIR) filter method [24].…”

Frequency-selective quantitation of short-echo time 1H magnetic resonance spectra

“…Water suppression methods should not influence the parameter estimates and should have a low computational complexity. They can be categorized in two main groups: on one hand, the convolution-based methods [2,[14][15][16][17][18][19] convolve the original signal with the coefficients of a filtering window, and, on the other hand, the SVD-based methods [3,20,21] make use of the singular value decomposition of a Hankel matrix. In their review, Coron et al [22] compare five convolution-based methods: the Gabor transform based method [17], the method by Marion et al [14], the filtering method of Sodano and Delepierre [15], the highpass butterworth filter described by Cross [16], and the maximum phase finite impulse response filter (MP-FIR) by Sundin et al [2] which we study in this paper.…”

Signal Reconstruction in Unstable Magnetic Field NMR with Wavelet Analysis

“…The continuous wavelet transform (CWT) is a mathematical tool which permits one to decompose a signal into elementary contributions called wavelets. The CWT of g(t) is defined as follows [5,9,11]:…”

“…Since wavelet transform can handle multi-scale information efficiently and has an energy shift-insensitive property, it is a suitable method for improving feature extraction from NMR spectra [4]. Wavelet transform has been used in NMR signal processing in stable magnetic fields [5][6][7]. Wavelet energy spectrum reveals that NMR signal intensity is related not only to time but also to frequency.…”