REVERSIBLE IMAGE COMPRESSION BOUNDED BY NOISE

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.