1. Hyperspectral Imagery Compression Using Three Dimensional Discrete Transforms
Tong Qiao
Supervisor: Dr. Jinchang Ren
04/07/2013

2. Structure Introduction to hyperspectral imagery
3D discrete wavelet transform (DWT) based compression
3D discrete cosine transform (DCT) based compression
Performance comparison
Conclusion

3. Hyperspectral Imagery
High definition electro-optic images with hundreds of spectral bands
Applications:
Remote sensing
Military surveillance
Food quality analysis
Pharmaceutical
Fig.1: Hyperspectral image acquired over Moffett Field (CA, USA)

4. Hyperspectral Imagery
Problems
Huge amount of data
High cost for storage and transmission
Therefore, COMPRESSION is needed.

5. Principles of Compression
Lossless (Compression ratio of 3:1)
Lossy (Compression ratio of 50:1 or more)
Transform coding
DWT based compression
JPEG 2000 standard
DCT based compression
JPEG standard

6. 3D DWT Based Compression
Fig.2: The 3D discrete wavelet transform

7. 3D DWT Based Compression
Wavelet filter
Cohen-Daubechies-Feauveau (CDF) 9/7-tap filter (lossy compression)
CDF 5/3-tap filter (lossless compression)
Fig.3: 3D dyadic DWT with 2 decomposition levels

8. 3D DWT Based Compression
Encoding stage
3D SPIHT ( Set Partitioning in Hierarchical Trees)
No child at the root node in the
highest level
Each of other 7 nodes has a 2 x 2 x 2
child cube directing to the same
spatial orientation in the same level
Except at highest and lowest levels,
a pixel will have 8 offspring in the
next level.
Fig.4: 3D parent-child relationships between subbands of a 3D DWT

9. 3D DWT Based Compression
3D SPIHT algorithm
Initialisation
List of Insignificant Sets (LIS)
List of Insignificant Pixels (LIP)
List of Significant Pixels (LSP)
Coding passes
Sorting pass
Refinement pass
Coefficients and trees are stored in lists processed in sequence

10. 3D DWT Based Compression
Entropy encoding
But only a little improvement
This step is left out.

11. 3D DCT Based Compression
Adapted from JPEG standard
Equation:
Block diagram
Quantisation
Table
Coding
Tables
8 x 8 x 8
block DCT
Lossy Compressed Data
Entropy
Encoder
Quantiser

12. 3D DCT Based Compression
Quantisation
𝐶 𝑢,𝑣,𝑤 =𝑟𝑜𝑢𝑛𝑑 𝐹 𝑢,𝑣,𝑤 𝑄 𝑢,𝑣,𝑤
Dequantisation
𝑅 𝑢,𝑣,𝑤 =𝐶(𝑢,𝑣,𝑤)×𝑄 𝑢,𝑣,𝑤

13. 3D DCT Based Compression
Quantisation table for hyperspectral images
𝑄 50 =𝑟𝑜𝑢𝑛𝑑 𝑢+𝑣+𝑘𝑤+3
k: [0, 8]
Weak inter-band correlation: lower k
Strong inter-band correlation: higher k

14. 3D DCT Based Compression
Quality level (q)
q: [1,99]
𝑄 𝑢,𝑣,𝑤 = 100−𝑞 50 × 𝑄 50 𝑞> 𝑞 × 𝑄 50 𝑞<50

15. 3D DWT Based Compression
Encoding stage
Huffman encoder
DC coefficients
Differential coding
Diff = DCi – DCi-1
AC coefficients
3D zig-zag scanning order
Run-length coding
Fig.5: The differential coding of DC coefficients

16. Performance Comparison
Four datasets
Fig.6: Moffett field
Fig.7: Indian pines and its ground truth
Fig.8: Salinas valley and its ground truth
Fig.9: Pavia University and its ground truth

17. Performance Comparison
Subjective assessment
Compression bit rate = 0.1 bpppb
Left: DWT, right: DCT

18. Performance Comparison
Subjective assessment
Compression bit rate: 0.2, 0.5, 0.8 and 1 bpppb
Top: DWT, bottom: DCT

19. Performance Comparison
Objective assessment
Rate-distortion measurement
SNR (Signal-to-Noise Ratio) vs. bit rate

20. Performance Comparison
Objective assessment

21. Performance Comparison
Objective assessment

22. Performance Comparison
Objective assessment

23. Performance Comparison
Quality-assured assessment
SVM (Support Vector Machine)
50% for training and 50% for testing
Optimal models are learnt from original images, then applied to reconstructed images

24. Performance Comparison
Quality-assured assessment

25. Performance Comparison
Quality-assured assessment

26. Performance Comparison
Quality-assured assessment

27. Conclusion
3D DCT has great potential to produce better compression than 3D DWT
3D DCT based compression of hyperspectral imagery at a bit rate of no less than 0.5 bpppb is feasible

28. Thank you!
Questions?