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EURASIP Journal on Image and Video Processing

Table 7 The approximations of DCT generated by the proposed procedure in the case of the symmetric scenario (Ď€(V)=0.131042)

From: Approximate calculation of 8-point DCT for various scenarios of practical applications

Name

Adds

Shifts

\(\chi _{3}(U,\overline {U})\)

\(\epsilon _{A}^{(III)}(U,\overline {U})\)

\(\text {tr}(\overline {U}^{T}\overline {U})/N\)

Ď€(U)

{ a, b, c, d, e, f, g }

Orthogonality

APRXIII.1

14

0

0.656552

0.000000

1.000000

0.184816

{ 1, 0, 1, 0, 0, 0, 1 }

+

APRXIII.2

16

0

0.656434

0.000000

1.000000

0.184783

{ 1, 1, 1, 0, 0, 0, 1 }

+

APRXIII.3

16

2

0.625912

0.000000

1.000000

0.176191

{ 1, 2, 1, 0, 0, 0, 1 }

+

APRXIII.4

20

2

0.620702

0.000000

1.000000

0.174724

{ 1, 2, 1, 1, 0, 0, 1 }

+

APRXIII.5

20

6

0.619900

0.021828

1.000000

0.168354

{ 1, 2, 1, 0, 0, \( \kern0.3em \frac{1}{8} \), 1 }

-

APRXIII.6

20

10

0.617859

0.005585

1.000000

0.172352

{ 1, 2, 1, 0, 0, \( \kern0.3em \frac{1}{8} \), 2 }

-

APRXIII.7

22

0

0.539839

0.000000

1.000000

0.151962

{ 1, 1, 0, 0, 1, 1, 1 }

+

APRXIII.8

24

0

0.539742

0.000000

1.000000

0.151934

{ 1, 1, 1, 0, 1, 1, 1 }

+

APRXIII.9

24

2

0.514646

0.000000

1.000000

0.144870

{ 1, 1, \( \kern0.3em \frac{1}{2} \), 0, 1, 1, 1 }

+

APRXIII.10

26

8

0.503287

0.004210

1.000000

0.140487

{ 1, 0, 1, \( \kern0.3em \frac{1}{4},\kern0.3em \frac{1}{2} \), 1, 1 }

-

APRXIII.11

28

6

0.503197

0.004210

1.000000

0.140462

{ 1, 1, 1, \( \kern0.3em \frac{1}{4},\kern0.3em \frac{1}{2} \), 1, 1 }

-

APRXIII.12

28

10

0.479996

0.004210

1.000000

0.133931

{ 1, 2, 1, \( \kern0.3em \frac{1}{4},\kern0.3em \frac{1}{2} \), 1, 1 }

-

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