ி

ௌ

mising the posterior with respect to ߪி

ଶ leads to the calculation of

n below,

ߪி

ଶൌ^{܍௧Γ܍൅2ߚி}

2ߙி൅2 ൅ܭ

(5.27)

mising the posterior with respect to ߪௌ

ଶ leads to the calculation of

n below,

ߪௌ

ଶൌ

܌^௧܌൅2ߚௌ

2ߙௌ൅2 ൅ܰെ1

(5.28)

the posterior is maximised with respect to the baseline b, the

g equation is derived, which is similar to WH,

܊ൌߪி

ିଶ܈ିଵΓܛ

(5.29)

alled the mapping construction matrix and is defined as below,

ۉ

ۇ

ߪி

ିଶݐଵ൅ߪௌ

ିଶ

െߪௌ

ିଶ

െߪௌ

ିଶ

ߪி

ିଶݐଶ൅ߪௌ

ିଶ

⋯

0

0

⋮

⋱

⋮

0

0

⋯

ߪி

ିଶݐே൅ߪௌ

ିଶ

ۊ

(5.30)

ی

e 5.11 shows the estimated baseline using BWH for the spectra

Figure 5.5. In Figure 5.11, the grey line is the raw spectrum and

ine is the estimated baseline. An obvious benefit of BWH is that

spectrum generated by BWH will have small degrees of artifacts

d with those shown in Figures 5.7–5.9. The consequence is that

peak recognition will be more efficient.