Fundamentals of Digital Image Processing - Control of Color Imaging Systems: Analysis and Design - page 58

FIGURE 2.26 4 4 HT basis functions.

and

2
4

3
5

11111111
1 11 11 1 11

11 1 111 1 1

H 4 H 4
H 4 H 4

1 11

1111 1 1 1 1
1

1 111 1

H 8 ¼ ¼ ( 2 : 79 )

11 1 11 11

11 1 1 1 111

1 1 11 111 1

The basis functions for the 4 4 HT are shown in Figure 2.26.

2.5.3.1 Inverse Hadamard Transform

The columns of matrix A are forming a set of orthogonal vectors of unit norm. This
implies that A is unitary, which implies that A 1

¼ A. Now to find the inverse HT,

pre-multiply and post-multiply Equation 2.74 by A 1

A 1 FA 1

¼ f ( 2 : 80 )

f ¼ AFA ( 2 : 81 )