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Improving 3D WaveletBased Compression of Hyperspectral Images
 Created: Sunday, 01 March 2009
Detrimental effects of spectral ringing are reduced or eliminated.
Two methods of increasing the effectiveness of threedimensional (3D) waveletbased compression of hyperspectral images have been developed. (As used here, “images” signifies both images and digital data representing images.) The methods are oriented toward reducing or eliminating detrimental effects of a phenomenon, referred to as spectral ringing, that is described below.
In 3D waveletbased compression, an image is represented by a multiresolution wavelet decomposition consisting of several subbands obtained by applying wavelet transforms in the two spatial dimensions corresponding to the two spatial coordinate axes of the image plane, and by applying wavelet transforms in the spectral dimension. Spectral ringing is named after the more familiar spatial ringing (spurious spatial oscillations) that can be seen parallel to and near edges in ordinary images reconstructed from compressed data. These ringing phenomena are attributable to effects of quantization. In hyperspectral data, the individual spectral bands play the role of edges, causing spurious oscillations to occur in the spectral dimension. In the absence of such corrective measures as the present two methods, spectral ringing can manifest itself as systematic biases in some reconstructed spectral bands and can reduce the effectiveness of compression of spatiallylowpass subbands.One of the two methods is denoted mean subtraction. The basic idea of this method is to subtract mean values from spatial planes of spatially lowpass subbands prior to encoding, because (a) such spatial planes often have mean values that are far from zero and (b) zeromean data are better suited for compression by methods that are effective for subbands of twodimensional (2D) images. In this method, after the 3D wavelet decomposition is performed, mean values are computed for and subtracted from each spatial plane of each spatiallylowpass subband. The resulting data are converted to signmagnitude form and compressed in a manner similar to that of a baseline hyperspectralimagecompression method. The mean values are encoded in the compressed bit stream and added back to the data at the appropriate decompression step. The overhead incurred by encoding the mean values — only a few bits per spectral band — is negligible with respect to the huge size of a typical hyperspectral data set.
The other method is denoted modified decomposition. This method is so named because it involves a modified version of a commonly used multiresolution wavelet decomposition, known in the art as the 3D Mallat decomposition, in which (a) the first of multiple stages of a 3D wavelet transform is applied to the entire dataset and (b) subsequent stages are applied only to the horizontally, vertically, and spectrallylowpass subband from the preceding stage. In the modified decomposition, in stages after the first, not only is the spatiallylowpass, spectrallylowpass subband further decomposed, but also spatiallylowpass, spectrallyhighpass subbands are further decomposed spatially.
Either method can be used alone to improve the quality of a reconstructed image (see figure). Alternatively, the two methods can be combined by first performing modified decomposition, then subtracting the mean values from spatial planes of spatiallylowpass subbands.
This work was done by Matthew Klimesh, Aaron Kiely, Hua Xie, and Nazeeh Aranki of Caltech for NASA’s Jet Propulsion Laboratory. For further information, contact This email address is being protected from spambots. You need JavaScript enabled to view it..
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