ECE/VT
ECE 4580
Image Compression (II)
Jason J. Xuan


Department of Electrical & Computer Engineering
Virginia Tech
ECE/VT
JPEG – DCT Compression
ECE/VT
Basic Framework of JPEG
ECE/VT
Discrete Cosine Transform (DCT)
DCT vs. DFT
ECE/VT
Discrete Cosine Transform (DCT)
• 1-D 1
0
1
0
(2 1)
( ) ( ) ( )cos
2
(2 1)
( ) ( ) ( )cos
2
N
x
N
x
x u
C u u f x
N
x u
f x u C u
N








 
   
 
 
   
 
1
, 0
( )
2
, 0
u
N
u
u
N

 
 
 
  
 
  
where
N = size
f = pixel
C = coefficients
ECE/VT
2-D DCT
1
0
1
0
1
0
1
0
(2 1) (2 1)
( , ) ( ) ( ) ( , )cos cos
2 2
(2 1) (2 1)
( , ) ( ) ( ) ( , )cos cos
2 2
N
x
N
x
N
x
N
x
x u x v
C u v u v f x y
N N
x u x v
f x y u v C u v
N N
 
 
 
 








    
     
   
    
    
  


DCT basis functions:
A frequency view
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DCT in a Pipeline
ECE/VT
Quantization
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Quantization
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Example Quantization Table
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Zigzag Scan
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JPEG Encoder
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JPEG Decoder
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DC Coding

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AC Coding
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Examples
Fourier DCT
Walsh-
Hadamard
ECE/VT
DCT vs. FFT
FFT
DCT
ECE/VT
JPEG2000 - A Wavelet Coding System
ECE/VT
Question
• Comments





























































































































































































































































































































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