Microscope Image Processing

Equations 7.27 and 7.29 suggest that one can construct all of the scaling

functions and wavelets starting from only one scaling function.

A scaling function is an approximation function, which means that the

scaling functions are useful for analyzing general trends in the signal, whereas

the details in the signal are analyzed using the wavelets. Thus, any low-pass filter

that satisfies certain conditions can become a scaling function. The simplest

scaling function is the Haar scaling function,

f(x) ¼

1if0< x < 1

0 otherwise



whose filter coefficients are h

0

(n) ¼ [1=

ffiffiffi

2

p

,1=

ffiffiffi

2

p

], which is an average filter.

Due to the orthogonality between the wavelet and the scaling functions, h

1

(n)

and h

0

(n) are related as

h

1

(n) ¼ (1)

n

h

0

(1  n)(7:30)

The wavelet satisfying ...