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# Context Modeler for Wavelet Compression of Spectral Hyperspectral Images

- Wednesday, 27 January 2010

A context-modeling subalgorithm has been developed as part of an algorithm that effects three-dimensional (3D) wavelet-based compression of hyperspectral image data. The context-modeling subalgorithm, hereafter denoted the context modeler, provides estimates of probability distributions of wavelet-transformed data being encoded. These estimates are utilized by an entropy coding subalgorithm that is another major component of the compression algorithm. The estimates make it possible to compress the image data more effectively than would otherwise be possible.

The following background discussion is prerequisite to a meaningful summary of the context modeler. This discussion is presented relative to “ICER-3D,” which is the name attached to a particular compression algorithm and the software that implements it. The ICER-3D software is summarized briefly in the preceding article, “ICER-3D Hyperspectral Image Compression Software” (NPO-43238). Some aspects of this algorithm were previously described, in a slightly more general context than the ICER-3D software, in “Improving 3D Wavelet-Based Com pression of Hyperspectral Images” (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. In turn, ICER-3D is a product of generalization of ICER, another previously reported algorithm and computer program that can perform both lossless and lossy wavelet-based compression and decompression of gray-scale-image data.

In ICER-3D, hyperspectral image data are decomposed using a 3D discrete wavelet transform (DWT). Following wavelet decomposition, mean values are subtracted from spatial planes of spatially low-pass subbands prior to encoding. The resulting data are converted to sign-magnitude form and compressed. In ICER-3D, compression is progressive, in that compressed information is ordered so that as more of the compressed data stream is received, successive reconstructions of the hyperspectral image data are of successively higher overall fidelity.

Before encoding each bit, the probability that the bit is a zero is estimated. The probability-of-zero estimate relies only on previously encoded information. The bit and its probability-of-zero estimate are sent to the entropy coding subalgorithm (hereafter denoted the entropy encoder), which effects the desired compression of the sequence of bits that it receives. Better probability- of-zero estimates allow the entropy coder to achieve better data compression. It is the job of the context modeler to produce these probability-of-zero estimates. This concludes the background discussion.

In the context modeling subalgorithm, a bit of a DWT coefficient to be encoded is first classified into one of 19 contexts based on the values of previously encoded bits. Each context amounts to a class for which separate probability-of-zero statistics are gathered. ICER-3D employs a one-dimensional spectral- context model involving context definitions that rely on two neighbors in the spectral direction but no neighbors in the same spatial plane. For comparison, ICER uses a two-dimensional context model relying on eight spatial-frequencydomain neighbors.

During the encoding process, DWT coefficients are assigned to categories in preparation for assigning them to contexts. There are four categories, numbered 0 – 3. The category of a coefficient is initially 0 and remains 0 so as long as the magnitude bits encoded for the coefficient are all zeros. After the first “1” bit from the coefficient is encoded, the category of the coefficient becomes 1. When the next magnitude bit of the coefficient is encoded, its category becomes 2. When one more magnitude bit from the coefficient is encoded, its category becomes 3 and remains 3 permanently. The context of a bit is determined from the category of the DWT coefficient that contains the bit and the category and signs of the two neighboring coefficients in the spectral dimension.

Compared to the 2D context model used by ICER, the ICER- 3D context modeler provides noticeable improvement in compression of sign bits and bits in category 0, and slight improvement for the other categories of bits that are compressed.

*This work was done by Aaron Kiely, Hua Xie, Matthew Klimesh,
and Nazeeh Aranki of Caltech for NASA’s Jet Propulsion Laboratory.
*

*The software used in this innovation is available for commercial
licensing. Please contact Karina Edmonds of the California Institute of
Technology at (626) 395-2322. Refer to NPO-43239.*

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