Local chemical rank estimation of two-way data in the presence of heteroscedastic noise: A morphological approach

Morphological analysis (MA) is proposed to determine the local chemical rank of two-way data from hyphenated chromatography in the presence of heteroscedastic noise, based on local least squares regression of each spectrum on its neighboring spectra. The MA method uses an approach different from ordinary analysis of variance to identify the different patterns of the structural and noisy spectra. It employs a morphological factor to distinguish different patterns of the spectral signal and the noise. The morphological factor possesses the property of scale invariance, being unaffected by heteroscedastic noise. A fast algorithm is also proposed based on the Gram-Schmidt orthogonalization technique for the local least squares regression. Both numerical simulation and real analytical data are used to illustrate the feasibility of the proposed method.