(Discrete Cosine Transformation ,DCT) (data hiding)

2.1 2.2 2.3

2.1

1. (Discrete Wavelet Transformation , DWT) 2. (Discrete Cosine Transformation , DWT)

2.12.22.316DCT

2.1DCT0~15

2.2DCT

(wave number) N 0~15

2.302220(basis wave)00

(frequency domain)2.10(Direct Current , DC)(Altermating Current , AC)

2.2

2.2.1(Forward Discrete Cosine Transformation , FDCT)(Inverse DCT , IDCT)FDCTIDCT

2.2.18*8(block)2.4[4]FDCT128IDCT128

O(x,y)(x,y)f(x,y)O(x,y)128D(i,j)(I,j)(D(I,j) | i=0 to N-1j=0 to N=1)N*N(f(x,y) | i=0 to N-1j=0 to N-1)FDCT

2.2.1FDCTIDCTFDCTIDCT(truncation error)

2.2.2 (FDCT)

(IDCT)

2.2.3 8*8(0,0)aIDCT8*88*8DCT(basis image)b(0,0)

(0,1)IDCT8*8(0,1)(7,7)8*86464*64DCT(basis image of 2D DCT)

2.2

DCT

DCTACDC(0,0)0(0,0)(DC)(0,0)(AC)

FDCT(2.1)(0,0)

DCT(low frequency)(high frequency)(medium frequency)DC

DCT2.9DCDC

(vertical edge)(horizontal edges)(diagonal edges)

(horizontal energy)(vertiacl energy)(diagonal energy)

abbadc

2.2.4 FDCT IDCT

8*8

2.23(0,0)2000(0,0)200IDCT2.23

2.25(0,7)2000(0,7)200IDCT2.25

2.27(7,0)2000(7,0)200IDCT2.27

2.29FDCTDC(7,7)

2.3012128128128IDCT3IDCT32.29IDCT

200(0,0)200(7,7)

2.3