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End-to-End Optimized
Image Compression
Hyeongmin Lee
PR-328
2021.6.27
Entropy Coding
Entropy Coding
īĩ Image Compression
0011010100111...
Entropy Coding
īĩ 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
īĩ 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
īĩ Entropy
đ‘¯đ‘¯ = − īŋŊ 𝒑𝒑𝒊𝒊𝒍𝒍𝒍𝒍𝒈𝒈𝟐𝟐𝒑𝒑𝒊𝒊
Sample 𝒑𝒑𝒊𝒊
A 5/15
B 1/15
C 6/15
D 3/15
Image Compression
Image Compression
īĩ Image Compression
0011010100111...
Lossless Coding: bmp  Coding the Integers Itself
Lossy Coding: JPEG  Reducing the ‘Entropy’ of samples
Image Compression
īĩ JPEG
8x8 cutting
Discrete Cosine Transform Quantization
Entropy Coding...
https://www.whydomath.org/node/wavlets/basicjpg.html
Image Compression
īĩ JPEG
High Quality
High Entropy
High Bitrate
Low Quality
Low Entropy
Low Bitrate
Image Compression
īĩ Bitrate-Distortion Tradeoff
End-to-End Optimized
Image Compression
[Network Structure]
Network Structure
īĩ Image Compression Pipeline
Transform Quantization
Entropy Coding
Decoding
Inverse
Transform
Network Structure
īĩ Image Compression Pipeline
Transform Quantization
Entropy Coding
Decoding
Inverse
Transform
Neural Net
Neural Net
Approximation
Network Structure
īĩ Overall Structure
Network Structure
īĩ Nonlinear Transformation
Encoder
GDN
Network Structure
īĩ Nonlinear Transformation
Decoder
IGDN
Network Structure
īĩ Nonlinear Transformation
Structure
End-to-End Optimized
Image Compression
[Optimization]
Optimization
īĩ Loss Function
MSE Loss
Optimization
īĩ Entropy of Quantized Vectors
Optimization
īĩ Continuous Relaxation
īŋŊ
𝒚𝒚 = 𝒚𝒚 + ∆𝒚𝒚 ~ đ‘ŧđ‘ŧ(−
𝟏𝟏
𝟐𝟐
,
𝟏𝟏
𝟐𝟐
)
𝒑𝒑īŋŊ
𝒚𝒚 𝒏𝒏 = īŋŊ
−∞
∞
𝒑𝒑𝒚𝒚 𝒙𝒙 𝒖𝒖
−
𝟏𝟏
𝟐𝟐,
𝟏𝟏
𝟐𝟐
(𝒏𝒏 − 𝒙𝒙) 𝒅𝒅𝒅𝒅 = īŋŊ
𝒏𝒏−
𝟏𝟏
𝟐𝟐
𝒏𝒏+
𝟏𝟏
𝟐𝟐
𝒑𝒑𝒚𝒚 𝒙𝒙 𝒅𝒅𝒅𝒅 = 𝑷𝑷𝒒𝒒(𝒏𝒏)
Optimization
īĩ Loss Functions
Piecewise Linear Approximation of 𝒑𝒑īŋŊ
𝒚𝒚𝒊𝒊
Optimization
īĩ Relationship to VAE
Experimental Results
Experimental Results
īĩ Quantitative Evaluation
Experimental Results
īĩ Visual Comparison
Thank You!

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