Hyperspectral Imagery
Compression Using Three
Dimensional Discrete Transforms
Tong Qiao (t.qiao@strath.ac.uk)
Supervisor: Dr. Jinchang Ren
04/07/2013
Structure
• Introduction to hyperspectral imagery
• 3D discrete wavelet transform (DWT) based
compression
• 3D discrete cosine transform (DCT) based
compression
• Performance comparison
• Conclusion
Hyperspectral Imagery
• High definition electro-optic
images with hundreds of
spectral bands
• Applications:
Fig.1: Hyperspectral
image acquired over
Moffett Field (CA, USA)
–
–
–
–
Remote sensing
Military surveillance
Food quality analysis
Pharmaceutical
Hyperspectral Imagery
• Problems
– Huge amount of data
– High cost for storage and transmission
• Therefore, COMPRESSION is needed.
Principles of Compression
• Compression
– Lossless (Compression ratio of 3:1)
– Lossy (Compression ratio of 50:1 or more)
• Transform coding
• Transform coding
– DWT based compression
• JPEG 2000 standard
– DCT based compression
• JPEG standard
3D DWT Based Compression
Fig.2: The 3D discrete wavelet transform
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
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
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
3D DWT Based Compression
• Entropy encoding
– But only a little improvement
– This step is left out.
3D DCT Based Compression
• Adapted from JPEG standard
• Equation: F (u, v, w)  2 2c(Nu)cN(v)c(w)  f ( x, y,  ) cos(22xN 1 u ) cos(22yN 1 v ) cos(22N 1 w )
N 1 N 1 N 1
x 0 y 0  0
u, v, w  0,1,..., N  1
 1
,k  0

c(k )   2
1, k  0

• Block diagram
8x8x8
block
DCT
Quantisation
Table
Coding
Tables
Quantiser
Entropy
Encoder
Lossy
Compressed
Data
3D DCT Based Compression
• Quantisation
𝐹 𝑢, 𝑣, 𝑤
𝐶 𝑢, 𝑣, 𝑤 = 𝑟𝑜𝑢𝑛𝑑
𝑄 𝑢, 𝑣, 𝑤
• Dequantisation
𝑅 𝑢, 𝑣, 𝑤 = 𝐶(𝑢, 𝑣, 𝑤) × 𝑄 𝑢, 𝑣, 𝑤
3D DCT Based Compression
• Quantisation table for hyperspectral images
𝑄50 = 𝑟𝑜𝑢𝑛𝑑 𝑢 + 𝑣 + 𝑘𝑤 + 3
– k: [0, 8]
– Weak inter-band correlation: lower k
– Strong inter-band correlation: higher k
3D DCT Based Compression
• Quality level (q)
– q: [1,99]
𝑄 𝑢, 𝑣, 𝑤 =
100−𝑞
× 𝑄50
50
50
× 𝑄50
𝑞
𝑞 > 50
𝑞 < 50
3D DWT Based Compression
• Encoding stage
– Huffman encoder
– DC coefficients
• Differential coding
• Diff = DCi – DCi-1
Fig.5: The differential coding of DC coefficients
– AC coefficients
• 3D zig-zag scanning order
• Run-length coding
Performance Comparison
• Four datasets
Fig.6: Moffett field
Fig.8: Salinas valley and its ground truth
Fig.7: Indian pines and its ground truth
Fig.9: Pavia University and its ground truth
Performance Comparison
• Subjective assessment
– Compression bit rate = 0.1 bpppb
– Left: DWT, right: DCT
Performance Comparison
• Subjective assessment
– Compression bit rate: 0.2, 0.5, 0.8 and 1 bpppb
– Top: DWT, bottom: DCT
Performance Comparison
• Objective assessment
– Rate-distortion measurement
• SNR (Signal-to-Noise Ratio) vs. bit rate
Moffett field
40
35
SNR (dB)
30
25
20
DWT
15
DCT
10
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Compression bit rate (bpppb)
0.8
0.9
1
Performance Comparison
• Objective assessment
Indian pines
40
35
SNR (dB)
30
25
20
DWT
15
DCT
10
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Compression bit rate (bpppb)
0.8
0.9
1
Performance Comparison
• Objective assessment
SNR (dB)
Salinas valley
45
40
35
30
25
20
15
10
5
0
DWT
DCT
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Compression bit rate (bpppb)
0.8
0.9
1
Performance Comparison
• Objective assessment
Pavia University
40
35
SNR (dB)
30
25
20
DWT
15
DCT
10
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Compression bit rate (bpppb)
0.8
0.9
1
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
Performance Comparison
• Quality-assured assessment
Indian pines
100.00%
Prediction accuracy
90.00%
80.00%
70.00%
60.00%
DWT
50.00%
DCT
40.00%
Original
30.00%
20.00%
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Bit rate (bpppb)
0.8
0.9
1
Performance Comparison
• Quality-assured assessment
Salinas Valley
Prediction accuracy
100.00%
95.00%
90.00%
85.00%
DWT
80.00%
DCT
75.00%
Original
70.00%
65.00%
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Bit rate (bpppb)
0.8
0.9
1
Performance Comparison
• Quality-assured assessment
Pavia University
100.00%
Prediction accuracy
95.00%
90.00%
85.00%
80.00%
DWT
75.00%
DCT
70.00%
Original
65.00%
60.00%
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Bit rate (bpppb)
0.8
0.9
1
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
Thank you!
Questions?