Digital Signal Processing Reference
In-Depth Information
The inverse DWT is expressed as
From these equations we can see that DWT coefficients are calculated by
a recursive equation. It means the calculation is fast and simple. Especially in
the case where Haar function is utilized as a mother wavelet one the
calculation is the simplest and furthermore it has an interesting nature
expressed in the next section.
3.
IMAGE COMPRESSION
3.1
Haar wavelet function
The Haar function has a simple structure shown in Eq. (7):
Fig. 14 -1 shows a two dimensional DWT with a Haar mother wavelet
function.
The left upper quadrant is called a level-1 DWT approximation. This
looks very similar to the original image but the size is a half of the original
one through a down sampling. The right upper, the left lower and the right
lower quadrant is called the vertical, the horizontal and the diagonal detail
respectively. The vertical detail includes the information about a vertical
element of the original image. Then it is concerned with a horizontal
directional (one dimensional) difference of the original image. Actually the
horizontal directional difference image of the DWT approximation is similar
to the vertical detail.
