Transform coding techniques for lossy hyperspectral data compression

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING (SUBMITTED DEC. 2005) 11 akin to performing a 3D rate-distortion optimization, which is known to provide significantly better results than band-by-band optimization [16]. The performance evaluation is carried out on 16-bit radiance AVIRIS data cubes. AVIRIS scenes have 224 bands and 614 × 512 pixels resolution, but each scene has been cropped to 256 × 256 × 224 pixels. Scene 4 of Cuprite and scene 3 of Jasper Ridge have been employed; for brevity, we only report the set of results for Cuprite. B. Energy compaction results For clarity, in Tab. I we summarize the acronyms used in the figures to identify the eight 3D transforms that have been evaluated. TABLE I ACRONYMS OF THE EVALUATED TRANSFORMS Acronym DWT3D DWP3D DWT1D2D DWP1D-DWT2D DWP1D-DWP2D DWT1D-DWP2D DCT1D-DWT2D KLT1D-DWT2D Sect. II.E.1 II.E.2 II.E.3 II.E.4 II.E.5 II.E.6 II.E.7 II.E.8 We anticipate that, not surprisingly, we have found that the spectral correlation plays a crucial role for compression, since the transforms that are better able to capture this correlation are those that rank best for compression. It is already known for lossless compression (see e.g. [25]) that large bit-rate reductions can be achieved by employing an efficient model of the spectral correlation. As will be seen, exploiting this correlation in the lossy case calls for the use of separate spectral and spatial transforms. In Fig. 5 we compare the DWT3D and DWP3D transforms. Neither transform is computed separately in the spectral dimension. As can be seen, the rate-distortion curve of the DWP3D transform is significantly better than that of the DWT3D. This is due to the fact that the 3D square wavelet transform is isotropic in all three dimension. This may not be the most appropriate correlation model of a hyperspectral dataset, since the subband decomposition in the spectral dimension is not as fine as it could be. Hence, because of the rather rough tessellation of 3D frequency space, the DWT3D turns
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING (SUBMITTED DEC. 2005) 12 out to have poor performance as to energy compaction of spectral vectors. The DWP3D transform performs much better, since its ability to adaptively select the frequency tessellation allows it to refine the signal description along the spectral dimension, and hence to exploit much better the spectral correlation. The obtained decomposition tree is depicted in Fig. 6. It is possible to observe that both low and high spatial frequency components have been finely decomposed in the low spectral frequency components. Moreover, almost all the low spatial frequencies (along both the pixels and lines direction) have been finely decomposed. On the other hand, all the high frequency components along the three dimensions have not been further decomposed, as in the case of the 3D square DWT. 100 DWT3D DWP3D 90 80 PSNR (dB) 70 60 50 40 30 50 55 60 65 70 75 80 85 90 95 100 % of transform coefficients set to zero Fig. 5. Performance comparison of different transforms - DWT3D vs DWP3D. Fig. 7 compares the performance of wavelet and wavelet packet transforms computed separately in the spectral direction. Namely, we first compute a full 1D DWT or DWPT in the spectral direction, followed by a square 2D DWT or DWPT. The following remarks can be made. Spatial decorrelation is performed more effectively by the DWT than by the DWPT. This is somewhat counterintuitive, since one would expect that the optimized decomposition provides better results. As a matter of fact, in our evaluation procedure we zero out the least significant coefficients taken from the complete 3D set of transform coefficients, whereas the DWPT transform is optimized separately in the spectral and spatial directions. Thus, our procedure closely simulated a 3D rate allocation, which would work better with a three-dimensionally optimized transform. As an example, the 2D DWPT does not decompose the bands in the water absorption region because they contain little information; however, those bands
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Transform coding techniques for lossy hyperspectral data compression

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