Transform coding techniques for lossy hyperspectral data compression

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING (SUBMITTED DEC. 2005) 19 tile mosaicking. Part 2 of the standard provides specific tools that can be applied to hyperspectral images. In particular, the multicomponent transformation feature allows for spectral decorrelation by means of an external transform, followed by the application of JPEG 2000 to a whole block of decorrelated bands; the bands are separately decorrelated in the spatial directions by means of the 2D wavelet transform, whereas the rate allocation is optimized across the whole block. Since JPEG 2000 standardizes the decoder, Part 2 provides the syntax (i.e. the MCC, MCT, and MCO marker segments) to embed into the codestream the inverse spectral transform that must be carried out after performing JPEG 2000 decoding of each component. Three types of spectral transformations are supported, namely i) array-based transformations (i.e., those that can be described by a set of linear equations in the input coefficients, e.g. the DCT or the KLT); ii) dependency transformations (i.e., those of the causal predictive type, like causal DPCM); iii) wavelet transforms. For each class, reversible and irreversible modes are foreseen. Irreversible transforms are specified for example by storing the transform matrix coefficients in floating-point format in the relevant marker segments within the codestream. Reversible transforms are defined as a set of single element linear transformations and rounding operations; this structure can accommodate lifting-based integer implementations of classical transforms such as DCT and wavelets (see e.g. [27], [28]). D. Integration of low-complexity KLT within JPEG 2000 The proposed technique employs a hybrid 3D transform; it first applies the low-complexity KLT as multicomponent extension to JPEG 2000, and then the JPEG 2000 2D DWT, rate allocation and entropy coding to the spectrally transformed bands. Three decomposition levels are performed for the 2D spatial transform, employing the (9,7) filter. The inverse KLT transform matrix is written in an MCT marker segment in the compressed file. Notably, the post-compression rate-distortion optimization is operated on the complete 3D set of transformed coefficients, ensuring optimal performance. On a related note, a very desirable feature of a compression system for remote sensing images is the ability to generate quicklook images without having to fully decode the compressed file. In a typical scenario, a user would download a low spatial resolution false-color quicklook of the scene. To do so, full spectral decorrelation is necessary in order to extract the three false-color bands, and then reduced resolution decoding of each band has to be carried out. This procedure is impractical, because it requires to perform the full spectral decorrelation to extract few channels. Moreover, it is not compliant with the JPEG 2000 standard, which requires that the spatial inverse transforms are performed before the spectral one. On the other hand, JPEG 2000 Part 2 provides an interesting
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING (SUBMITTED DEC. 2005) 20 feature, in that, through suitable marker segments, it is possible to specify different transformations for selected groups of bands [26]. For example, the three bands to be used to generate false-color quicklooks can be skipped by the spectral decorrelator and compressed in intraband mode; this yields a slight performance loss, but allows increased flexibility in the access to selected portions of the data. This procedure can be extended to the proposed scheme, where the bands to be used to generate the quicklooks could be canceled from the spectral vectors in the computation of the covariance matrix, and then of the transform coefficients. However, this goes beyond the scope of the present paper, and is left for further work. V. EXPERIMENTAL RESULTS The proposed scheme, based on the low-complexity KLT and JPEG 2000, has been compared with other state-of-the-art lossy compression schemes. First, in Sect. V-A we evaluate the complexity of the low- and full-complexity KLT; this allows to assess the actual computational advantage in a realistic compression setting. Then, in Sect. V-B we compare the compression performance of various algorithms. Finally, in Sect. V-C we report the results of some experiments aimed at evaluating the effect of lossy compression on remote sensing applications, and specifically on SAM classification. In the results described in this section, we have employed a set of AVIRIS radiance data using 256 lines with 512 pixels and all bands, unless otherwise noted. The AVIRIS sensor is a representative hyperspectral one, and the data are publicly available on the Internet at aviris.jpl.nasa.gov; since these data are widely used in the literature, comparisons with other techniques are facilitated. In particular, the Cuprite, Jasper Ridge and Moffett Field scenes have been used. PSNR has been used as quality metric for lossy compression 1 . JPEG 2000 has been run without error resilience options, and no quality layers have been formed. A. Complexity Fig. 12 shows the compression performance and the computation time of the proposed algorithm as a function of ρ, on the Cuprite scene. The computation times have been measured on a Pentium IV PC at 3 GHz, and refer only to the evaluation of the covariance matrix. As can be seen, the performance loss is very smooth as ρ decreases, allowing one to select the best performance-complexity tradeoff for a given application. As had been noted in the previous experiment, the values ρ =0.1 and ρ =0.01 yield a very small loss, and can be used as starting point for a fine optimization. These values provide a complexity reduction of about 20 and 100 times with respect to the full-complexity transform. 1 Since the data have only 15 significant bits in modulus, 2 15 − 1 has been used as peak value for PSNR computation.
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