Wavelet Compression/Reconstruction and Visualization of Pulmonary X-Ray Images for Achieving of Asbestosis Infected Patients Data - Visual Computing: Scientific Visualization and Imaging Systems - page 119

Fig. 6.1 Compression part
of the algorithm

Input image

2D-DWT

Packing into vector
of coefficients

1D-DWT

Desired level?

Saved coefficients

C ¼ A ð N Þj H ð N Þj V ð N Þj D ð N Þj ... ½

H ð N 1 Þj V ð N 1 Þj D ð N 1 Þj ...
...
H ð 1 Þj V ð 1 Þj D ð 1 Þ

ð 6 : 6 Þ

where A denotes approximation, H horizontal details, V vertical

details, and D diagonal details.

Step 2: Downsampling of the vector C.

In this step, both approximation and details are downsampled to reduce
data.

Step 3: 1D DWT of the vector C.

Since produce algorithm is 1D vector, new vector formed will be:

C i ¼ A i ð N Þj H i ð N Þj V i ð N Þj D i ð N Þj ½ H i ð N 1 Þj

V i ð N 1 Þj D i ð N 1 Þj ...H i ð 1 Þj V i ð 1 Þj D i ð 1 Þ

ð 6 : 7 Þ

Step 4: Downsampling of the vector C 1 . Downsampling is organized to reduce

number of horizontal coefficients at first. Then vertical and diagonal
coefficients are downsampled, respectively. Result is new vector:

C i ¼ A i ð N Þj H i ð N Þj V i ð N Þj D i ð N Þj ½ H i ð N 2 Þj

V i ð N 2 Þj D i ð N 2 Þj ...H i ð j Þj V i ð j Þj D i ð j Þ

ð 6 : 8 Þ

where j can be 1 or 2 depending on parity (weather N is even or odd).