A wavelet packets decomposition algorithm for quantification of in vivo 1H-MRS parameters

In this paper a novel method for the extraction of magnetic resonance spectroscopy (MRS) parameters is presented. The method applies the traditional time-domain linear prediction singular value decomposition (LPSVD) on the set of orthonormal sub-signals obtained by wavelet packets (WP) decomposition of the original free induction decay (FID) signal. Using the properties of WP the desired, optimal, sub-band FID decomposition is obtained and used to progressively separate the different metabolic components in distinct sub-bands. A pseudo-optimal WP tree is obtained using the minimum description length (MDL) criteria. The proposed algorithm preserves all the advantages of the traditional LPSVD method, but the WP decomposition considerably improves the LPSVD performances in the presence of noise. The paper addresses this aspect in details by comparing the innovative sub-band and the traditional full-band approaches. Algorithms are tested on simulated signals that mimic real MRS data.