Inverse problem for reconstruction of components from derivative envelope in ovarian MRS: Citrate quartet as a cancer biomarker with considerably decreased levels in malignant vs benign samples

Abstract The harmonic inversion (HI) problem in nuclear magnetic resonance spectroscopy (NMR) is conventionally considered by means of parameter estimations. It consists extracting the fundamental pairs complex frequencies and amplitudes from encoded time signals. This linear nonlinear that are entrenched damped exponentials (harmonics) within signal. Nonlinear problems usually solved approximately some suitable linearization procedures. However, with equidistantly sampled signals, HI can be linearized exactly. solution obtained relying exclusively upon algebra, workhorse computer science. fast Padé transform (FPT) solve problem. exact analytical uniquely for signals at most four harmonics (four metabolites a sample). Moreover, using only unique numerical solutions, machine accuracy (the epsilon), any level complexity chemical composition specimen which encoded. recovered rooting secular or characteristic polynomial through equivalent operation, solves extremely sparse Hessenberg companion matrix eigenvalue analytically as closed formula employing Cauchy residue calculus. From amplitudes, components built their sum gives total shape spectrum envelope. component spectra magnitude mode described quantitatively found peak positions, widths heights all physical resonances. key question whether same said quantifiers reconstructed estimations alone. possible derivative (dFPT) applied nonparametric processor (shape estimator) onset analysis. In end, this signal analyzer determine true input other words, it quantify Its performance presently illustrated utilizing high-field proton NMR spectrometer. scanned samples ovarian cyst fluid two patients, one histopathologically diagnosed having benign lesion malignant lesion. These findings correlated reconstruction results Padé-based Special attention paid to citrate samples. goal focus see citrates could also cancer biomarkers they now prostate (low cancerous, high normal tissue). Cancer whose concentration levels help discriminate between lesions.