wo estimated peak spectra derived from the spectra with the estimated baselines

igure 5.9.

Bayesian Whittaker-Henderson algorithm

esian Whittaker-Henderson smoother algorithm (BWH) has been

for providing a better baseline estimation performance [Lau, et

]. The algorithm is an extension from several old algorithms by

the Whittaker-Henderson smoother into the Bayesian learning

rk. Moreover, BWH can align multiple spectra. The algorithm

that a signal, if it is true, should occur in more than one replicate

ctra data set with more than one replicate. Based on this

on, BWH can support more robust signal detection for a spectra

f multiple replicates.

e working principle of BWH

ctra smoothing algorithms assume that only spectra intensities

baseline are treated as noise and spectra intensities above a

are not treated as noise. However, BWH treats artifacts on both

a baseline as noises. This means that the noise is assumed to

on both sides of a baseline when using BWH to estimate a

for a spectrum. BWH also assumes both the fidelity and the

ess follow independent and identical Gaussian distributions. They

ed as below, where ߪி

ଶ and ߪௌ

ଶ are variances,