BWH fidelity is defined as below, where w is the upper-bound

,

݁௜ൌቄ^{ݏ௜െܾ௜}

݂݅ݏ௜൏ܾ௜൅ݓ

∞

otherwise

(5.17)

d on the definition, ܾ௜൅ݓ defines a homogeneous upper-bound

above a baseline. Because of this, the noise from both sides of a

will be finally removed during a baseline estimation process for

ng peaks. Therefore, the likelihood of false signals can be

d.

has introduced an indicator for the peaks. If a wave number (a

nalyser value) does not correspond to a peak, a unit value is

otherwise a zero is assigned. The definition of this indicator is

porating peak information into a baseline estimation process. This

is defined as below,

ݐ௜ൌቄ¹

݂݅݁௜൏∞

0

otherwise

(5.18)

spondingly, a vector t, which is also called an aligner vector, is

all wave numbers (spectra analyser values). A density function of

ty is defined as below [Taylor, 1992], where N stands for the

ength, i.e., the number of wave numbers, e is an error vector and

ሺܜሻ,

݂۳|۰ୀ܊ሺ܍ሻൌ

1

ሺ2ߨߪி

ଶሻே/ଶ^{exp ቆെ܍௧Γ܍}

2ߪி

ଶ^ቇ

(5.19)

rior of the smoothness is defined as a Gaussian distribution as

ylor, 1992],

݂۲ୀ܌|ఙೄ

మሺ܌ሻൌ

1

ሺ2ߨߪௌ

ଶሻሺேିଵሻ/ଶ^{exp ቆെ܌௧܌}

2ߪௌ

ଶ^ቇ

(5.20)