4,530 research outputs found
On empirical cumulant generating functions of code lengths for individual sequences
We consider the problem of lossless compression of individual sequences using
finite-state (FS) machines, from the perspective of the best achievable
empirical cumulant generating function (CGF) of the code length, i.e., the
normalized logarithm of the empirical average of the exponentiated code length.
Since the probabilistic CGF is minimized in terms of the R\'enyi entropy of the
source, one of the motivations of this study is to derive an
individual-sequence analogue of the R\'enyi entropy, in the same way that the
FS compressibility is the individual-sequence counterpart of the Shannon
entropy. We consider the CGF of the code-length both from the perspective of
fixed-to-variable (F-V) length coding and the perspective of
variable-to-variable (V-V) length coding, where the latter turns out to yield a
better result, that coincides with the FS compressibility. We also extend our
results to compression with side information, available at both the encoder and
decoder. In this case, the V-V version no longer coincides with the FS
compressibility, but results in a different complexity measure.Comment: 15 pages; submitted for publicatio
Weighted universal image compression
We describe a general coding strategy leading to a family of universal image compression systems designed to give good performance in applications where the statistics of the source to be compressed are not available at design time or vary over time or space. The basic approach considered uses a two-stage structure in which the single source code of traditional image compression systems is replaced with a family of codes designed to cover a large class of possible sources. To illustrate this approach, we consider the optimal design and use of two-stage codes containing collections of vector quantizers (weighted universal vector quantization), bit allocations for JPEG-style coding (weighted universal bit allocation), and transform codes (weighted universal transform coding). Further, we demonstrate the benefits to be gained from the inclusion of perceptual distortion measures and optimal parsing. The strategy yields two-stage codes that significantly outperform their single-stage predecessors. On a sequence of medical images, weighted universal vector quantization outperforms entropy coded vector quantization by over 9 dB. On the same data sequence, weighted universal bit allocation outperforms a JPEG-style code by over 2.5 dB. On a collection of mixed test and image data, weighted universal transform coding outperforms a single, data-optimized transform code (which gives performance almost identical to that of JPEG) by over 6 dB
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