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End-to-End Optimized
Image Compression
Hyeongmin Lee
PR-328
2021.6.27
Entropy Coding
Entropy Coding
? Image Compression
0011010100111...
Entropy Coding
? Entropy Coding
A,B,C,D: 4 Letters (need at least 2 bits per letter)
Sample Bits
A 00
B 10
C 01
D 11
100100001111110101000100010001
(30 bits)
https://www.programiz.com/dsa/huffman-coding
Entropy Coding
? Entropy Coding
A,B,C,D: 4 Letters (need at least 2 bits per letter)
Sample Bits
A 11
B 100
C 0
D 101
1000111110110110100110110110
(28 bits)
Lower Bound??
Huffman Coding
Entropy Coding
? Entropy
?? = ? ? ????????????????
Sample ????
A 5/15
B 1/15
C 6/15
D 3/15
Image Compression
Image Compression
? Image Compression
0011010100111...
Lossless Coding: bmp ? Coding the Integers Itself
Lossy Coding: JPEG ? Reducing the Entropy of samples
Image Compression
? JPEG
8x8 cutting
Discrete Cosine Transform Quantization
Entropy Coding...
https://www.whydomath.org/node/wavlets/basicjpg.html
Image Compression
? JPEG
High Quality
High Entropy
High Bitrate
Low Quality
Low Entropy
Low Bitrate
Image Compression
? Bitrate-Distortion Tradeoff
End-to-End Optimized
Image Compression
[Network Structure]
Network Structure
? Image Compression Pipeline
Transform Quantization
Entropy Coding
Decoding
Inverse
Transform
Network Structure
? Image Compression Pipeline
Transform Quantization
Entropy Coding
Decoding
Inverse
Transform
Neural Net
Neural Net
Approximation
Network Structure
? Overall Structure
Network Structure
? Nonlinear Transformation
Encoder
GDN
Network Structure
? Nonlinear Transformation
Decoder
IGDN
Network Structure
? Nonlinear Transformation
Structure
End-to-End Optimized
Image Compression
[Optimization]
Optimization
? Loss Function
MSE Loss
Optimization
? Entropy of Quantized Vectors
Optimization
? Continuous Relaxation
?
?? = ?? + ??? ~ ??(?
??
??
,
??
??
)
???
?? ?? = ?
?

???? ?? ??
?
??
??,
??
??
(?? ? ??) ???? = ?
???
??
??
??+
??
??
???? ?? ???? = ????(??)
Optimization
? Loss Functions
Piecewise Linear Approximation of ???
????
Optimization
? Relationship to VAE
Experimental Results
Experimental Results
? Quantitative Evaluation
Experimental Results
? Visual Comparison
Thank You!

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PR-328: End-to-End Optimized Image Compression