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Title of Journal: J Math Chem

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Abbravation: Journal of Mathematical Chemistry

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Springer International Publishing

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DOI

10.1007/bf01035224

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1572-8897

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Padé optimization of noisecorrupted magnetic reso

Authors: Dževad Belkić Karen Belkić
Publish Date: 2014/10/07
Volume: 52, Issue: 10, Pages: 2680-2713
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Abstract

We apply the fast Padé transform FPT to time signals as encoded via magnetic resonance spectroscopy MRS in breast fibroadenoma Realistic levels of noise are considered The conventional fast Fourier transform FFT is also used for comparison with the FPT For N = 2048 signal points the FFT generated uninformative total shape spectra with only a few distorted peaks whereas the FPT yielded converged envelope spectra at partial signal length N mathrmP= 1700 To match the FPT based at time signals sampled at N = 2048 the FFT requires N = 65536 signal points ie a 32fold lengthening of each transient Via the parametric FPT at N mathrmP = 1700 all the resonances were resolved and metabolite concentrations precisely computed including those that were almost completely overlapping phosphocholine and phosphoethanolamine whose chemical shifts are separated by 0001 parts per million The multifaceted signal–noise separation SNS procedure was applied through identification of polezero cancellations zero or near zero amplitudes plus the stability test against different levels of noise Via SNS all the spurious resonances were confidently identified thus leaving only genuine metabolites in the output list Practical implications are underscored the high resolution of the FPT will shorten the examination time of the patient Using the FPT the cancer biomarker phosphocholine plus other informative metabolites can be identified and their concentrations exactly determined Applying the fast Padé transform to time signals encoded in vivo from the breast therefore will be a key step for MRS to realize its potential to become a reliable costeffective method for breast cancer diagnostics

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