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Fig 1. Synthesized spectra of proton MR spectroscopy with typical line shapes as seen in vivo and their spectral fitting estimated by using the method of SVD. The same noise was added to the synthesized signals in the time domain. A, An apparent single spectral peak (black) consisting of 3 Lorentzian peaks with zero phase (red, green, and blue) is estimated correctly when the 3 fitted components have identical phases. The complex combination of these components (red) coincides perfectly with the synthesized peak in black, as is true for all the other fittings (B–D). B, A single peak with a Gaussian line shape (black) is decomposed into 4 components, each with differing phases. Unlike the peaks identified in A, where the phases are identical, these components cannot be interpreted as valid peaks even though their combination constitutes a "perfect" fit. C, A single peak with an asymmetric line shape (black), simulating the distortion caused by inhomogeneity of the magnetic field, is decomposed into 5 components (colored), each with differing phases. None of the components can be regarded as a valid peak. D, The synthesized signal (black) consists of 2 components, 1 the same as that in C and the other its duplicate but reduced in amplitude by a factor of 5 and shifted in frequency by 10 Hz. The signal is decomposed into 6 components, each with differing phases (colored), none of which can be interpreted as valid. Freq indicates frequency.
