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The recently introduced concept of envelope partitioning for shape estimation within the fast Padé transform (FPT) is presently further explored and solidified. Earlier, noise-free time signals were used and the results were reported for a single model order  Currently, partitioned envelopes are computed for several values of model orders  by employing noise-corrupted time signals of increasing standard deviations,  00289 0289289 in units of root-mean-square of the noise-free time signal. Moreover, spectra averaging is exploited to stabilize shape estimation in face of sensitivity to changes in model order. The main goal of this study is to establish the robustness of the non-parametric FPT for reconstructions of partitioned average envelopes computed with noisy time signals. Both the previous and present illustrations concern synthesized time signals typically encountered in single-voxel magnetic resonance spectroscopy (MRS), akin to in vitro encoding from malignant breast tissue. This particular problem area is chosen for a twofold reason: clinical urgency in cancer medicine, and a huge challenge to reliably identify a key cancer biomarker (phosphocholine), completely hidden underneath a dominant peak (phosphoethanolamine), with a separation of mere 0.001 parts per million of chemical shift. Upon successful benchmarking of partitioned envelopes for noisy simulated MRS time signals, the road would be paved for applications of this special shape estimation to the associated data from in vivo encodings. Partitioned envelopes are important since they offer possibilities to peer into the tightly overlapped resonances by splitting their components apart already at the level of sole total shape spectra. Although constrained by non-parametric estimations, they can still qualitatively decompose the regions of higher spectral density. This would enable subsequent focusing on the most critical spectral regions of interest when solving the local quantification problem by parametric estimations. Such a stepwise strategy is expected to be especially beneficial for multi-voxel magnetic resonance spectroscopic imaging (MRSI), where thousands of noisy spectra need to be processed. The FPT-based partitioned envelopes, followed by accurate local spectral analysis in narrow frequency intervals are poised to help MRSI become an efficient diagnostic modality for everyday clinical practice.

journal of mathematical chemistry

Robust identification of the cancer biomarker phosphocholine through partitioned envelopes in noisy magnetic resonance spectroscopic data by the non-parametric fast Padé transform