Hyperspectral Imagery Compression Using Three

Dimensional Discrete TransformsTong Qiao (t.qiao@strath.ac.uk)

Supervisor: Dr. Jinchang Ren

04/07/2013

• Introduction to hyperspectral imagery• 3D discrete wavelet transform (DWT)

based compression• 3D discrete cosine transform (DCT) based

compression• Performance comparison• Conclusion

Structure

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)

• Problems– Huge amount of data– High cost for storage and transmission

• Therefore, COMPRESSION is needed.

Hyperspectral Imagery

• 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

Principles of Compression

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

• 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.

3D DWT Based Compression

Fig.4: 3D parent-child relationships between subbands of a 3D DWT

• 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 DWT Based Compression

• Adapted from JPEG standard• Equation:

• Block diagram

3D DCT Based Compression

8 x 8 x 8

block DCT

Quantiser

Quantisation

Table

EntropyEncoder

CodingTables

Lossy Compresse

d Data

0,1

0,2

1

)(

1,...,1,0,,

)2

12cos()

2

12cos()

2

12cos(),,(

)()()(22),,(

1

0

1

0

1

0

k

kkc

Nwvu

wN

vN

yu

N

xyxf

NN

wcvcucwvuF

N

x

N

y

N

• Quantisation

• Dequantisation

3D DCT Based Compression

• Quantisation table for hyperspectral images

– 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]

3D DCT Based Compression

• Encoding stage– Huffman encoder

– DC coefficients• Differential coding• Diff = DCi – DCi-1

– AC coefficients• 3D zig-zag scanning order• Run-length coding

3D DWT Based Compression

Fig.5: The differential coding of DC coefficients

• Four datasets

Performance Comparison

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

• 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

Performance Comparison

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 105

10152025303540

Moffett field

DWTDCT

Compression bit rate (bpppb)

SNR

(dB)

• Objective assessment

Performance Comparison

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 105

10152025303540

Indian pines

DWTDCT

Compression bit rate (bpppb)

SNR

(dB)

• Objective assessment

Performance Comparison

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 105

1015202530354045

Salinas valley

DWTDCT

Compression bit rate (bpppb)

SNR

(dB)

• Objective assessment

Performance Comparison

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 105

10152025303540

Pavia University

DWTDCT

Compression bit rate (bpppb)

SNR

(dB)

• 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

Performance Comparison

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 120.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%

100.00%

Indian pines

DWTDCTOriginal

Bit rate (bpppb)

Pred

ictio

n ac

cura

cy

• Quality-assured assessment

Performance Comparison

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 165.00%

70.00%

75.00%

80.00%

85.00%

90.00%

95.00%

100.00%

Salinas Valley

DWTDCTOriginal

Bit rate (bpppb)

Pred

ictio

n ac

cura

cy

• Quality-assured assessment

Performance Comparison

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 160.00%65.00%70.00%75.00%80.00%85.00%90.00%95.00%

100.00%

Pavia University

DWTDCTOriginal

Bit rate (bpppb)

Pred

ictio

n ac

cura

cy

• 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

Conclusion

Thank you!Questions?