Adaptive DPCM methods using linear prediction are described for the lossless compression of hyperspectral (224-band) images recorded by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The methods have two stages-predictive decorrelation (which produces residuals) and residual encoding. Good predictors are described, whose performance closely approaches limits imposed by sensor noise. It is imperative that these predictors make use of the high spectral correlations between bands. The residuals are encoded using variable-length coding (VLC) methods, and compression is improved by using eight codebooks whose design depends on the sensor's noise characteristics. Rice (1979) coding has also been evaluated; it loses 0.02-0.05 b/pixel compression compared with better VLC methods but is much simpler and faster. Results for compressing ten AVIRIS images are reported.

The matrix for the noise-adjusted principal components (NAPC) transform is the solution of a generalized symmetric eigenvalue problem. Applied to remote sensing imagery, this entails the simultaneous diagonalization of data and noise covariance matrices. One of the two PC transforms of the original NAPC transform is replaced by several short, fast procedures. The total operation count for the computation of the NAPC transform matrix is halved.>

Reversible image compression rarely achieves compression ratios larger than about 3:1. An explanation of this limit is offered, which hinges upon the additive noise the sensor introduces into the image. Simple models of this noise allow lower bounds on the bit rate to be estimated from sensor noise parameters rather than from ensembles of typical images. The model predicts that an 8-b single-band image subject to noise with unit standard deviation can be compressed reversibly to no less than 2.0 b/pixel, equivalent to a maximum compression ratio of about 4:1. The model has been extended to multispectral imagery. The Airborne Visible and Infra Red Imaging Spectrometer (AVIRIS) is used as an example, as the noise in its 224 bands is well characterized. The model predicts a lower bound on the bit rate for the compressed data of about 5.5 b/pixel when a single codebook is used to encode all the bands. A separate codebook for each band (i.e., 224 codebooks) reduces this bound by 0.5 b/pixel to about 5.0 b/pixel, but 90% of this reduction is provided by only four codebooks. Empirical results corroborate these theoretical predictions.>