Transform coding techniques for lossy hyperspectral data compression

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING (SUBMITTED DEC. 2005) 13 LLL lines bands pixels Fig. 6. gain. Sub-cubes obtained by the 3D wavelet packet decomposition minimizing the cost function based on the coding contain many high-valued coefficients that have to be retained, at the expenses of other coefficients that are discarded. Therefore, the mismatch between the 3D coefficient selection and the separatedness of the DWPT transform makes it useless, and even disadvantageous, to perform best basis selection. Comparing Fig. 7 and Fig. 5, it can be seen that the performance of the DWT1D2D transform is very similar to that of the DWP3D transform, but with a significantly reduced computational effort, since it is not necessary to compute the optimal basis. In fact, this transform has been selected in [16] for its favorable trade-off between performance and complexity. Continuing the study of spectrally separable transforms, Fig. 8 compares the DWT1D2D, DCT1D- DWT2D, and KLT1D-DWT2D transforms. Following the results described above, these transforms have been selected in order to compare different spectral decorrelators, using the 2D DWT for spatial decorrelation because of its effectiveness. Not surprising, the KLT turns out to be the best transform; since we are employing the same transform for all spectral vectors, the overhead of describing the transform matrix in the compressed file is negligible. The performance gain of the KLT1D-DWT2D with respect to the DWT1D2D is about 2 dB at high quality levels, and significantly more at low bitrates. However, as outlined in Sect. II-F.8, the KLT1D-DWT2D requires the estimation (and averaging) of as many covariance matrices as samples per band, followed by the solution of the eigenvector
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING (SUBMITTED DEC. 2005) 14 100 90 DWT1D2D DWP1D−DWT2D DWT1D−DWP2D DWP1D2D 80 PSNR (dB) 70 60 50 40 50 55 60 65 70 75 80 85 90 95 100 % of transformed coefficients set to zero Fig. 7. Performance comparison of different transforms, with a separable transform in the spectral direction. problem. As expected, the DCT performs almost always worse than the DWT, except for a range in the very low bit-rate region. In summary, this analysis shows that the schemes with highest performance are based on hybrid rectangular/square transforms. Among these schemes, the 2D DWT should be preferred for spatial decorrelation. As far as spectral decorrelation is concerned, the 1D DWT provides good performance with limited complexity. The KLT achieves significantly better performance at all bit-rates, and especially in the low bit-rate region. It should be noticed that this KLT employs a single transform matrix for all spectral vectors. This approach is effective because, along the spectral dimension, the signal depend almost exclusively on pixel land cover; since only a few land covers are typically present in an image, the KLT works better than the other transforms. In the spatial dimension the signal depends on the scene geometry, which is less predictable with many discontinuities near region boundaries. In this case, due to the high degree of nonstationarity, the single KLT becomes far from optimal, and the DWT works better; the use of the optimal KLT would require the solution to multiple eigenvector problems, which is not realistic in a practical scenario. IV. PROPOSED LOW-COMPLEXITY KLT As has been seen, the spectral KLT can provide performance gains in excess of 2 dB with respect to the wavelet transform using a single “average” covariance matrix. However, although this is a somewhat simplified version of the transform, because it assumes that the spectral vectors are samples of a stationary signal, its complexity is still high for real-time applications, for the reasons outlined
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Transform coding techniques for lossy hyperspectral data compression

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