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: Remote sensing Military surveillance Food quality analysis Pharmaceutical Fig.1: Hyperspectral image acquired over Moffett Field (CA, USA)

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

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

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: Block diagram Quantisation Table Coding Tables 8 x 8 x 8 block DCT Lossy Compressed Data Entropy Encoder Quantiser

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

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

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

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

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

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

Performance Comparison Objective assessment

Performance Comparison Objective assessment

Performance Comparison Objective assessment

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

Performance Comparison Quality-assured assessment

Performance Comparison Quality-assured assessment

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?