Compression of imagery by quantization of the data's transform
coefficients introduces an error in the imagery upon decompression.
When processing compressed imagery, often a likelihood term is used to
provide a statistical description of how the observed data are related
to the original noise-free data. This work derives the statistical
relationship between compressed imagery and the original imagery,
which is found to be embodied in a (in general) non-diagonal
covariance matrix. Although the derivations are valid for transform
coding in general, the work is motivated by considering examples for
the specific cases of compression using the discrete cosine transform
and the discrete wavelet transform. An example application of
motion-compensated temporal filtering is provided to show how the
presented likelihood term might be used in a restoration scenario.