Inter-band Distortion Allocation in Lossy Hyperspectral Data Compression

The problem of distortion allocation varying with wavelength in lossy compression of hyperspectral imagery is investigated. Distortion is generally measured either as maximum absolute deviation (MAD) for near-lossless methods, e.g. differential pulse code modulation (DPCM), or as mean square error (MSE) for lossy methods (e.g. spectral decorrelation followed by JPEG 2000). Also the absolute angular error, or spectral angle mapper (SAM), is used to quantify spectral distortion. A band add-on (BAO) technique was recently introduced to calculate a modified version of SAM. Spectral bands are iteratively selected in order to increase the angular separation between two pixel spectra by exploiting a mathematical decomposition of SAM. As a consequence, only a subset of the original hyperspectral bands contributes to the new distance metrics, referred to as BAO-SAM, whose operational definition guarantees its monotonicity as the number of bands increases. Two strategies of inter-band distortion allocation are compared: given a target average bit rate, distortion, either MAD or MSE, may be set to be constant varying with wavelength. Otherwise it may be allocated proportionally to the noise level on each band, according to the virtually-lossless protocol. Thus, a different quantization step size depending on the estimated standard deviation of the noise, is used to quantize either prediction residuals (DPCM) or wavelet coefficients (JPEG 2000) of each spectral band, thereby determining band-varying MAD/MSE values. Comparisons with the uncompressed originals show that the average spectral angle mapper (SAM) is minimized by constant distortion allocation. Conversely, the average BAO-SAM is minimized by the noise-adjusted variable spectral distortion allocation according to the virtually lossless protocol.