7,301 research outputs found
Joint universal lossy coding and identification of stationary mixing sources with general alphabets
We consider the problem of joint universal variable-rate lossy coding and
identification for parametric classes of stationary -mixing sources with
general (Polish) alphabets. Compression performance is measured in terms of
Lagrangians, while identification performance is measured by the variational
distance between the true source and the estimated source. Provided that the
sources are mixing at a sufficiently fast rate and satisfy certain smoothness
and Vapnik-Chervonenkis learnability conditions, it is shown that, for bounded
metric distortions, there exist universal schemes for joint lossy compression
and identification whose Lagrangian redundancies converge to zero as as the block length tends to infinity, where is the
Vapnik-Chervonenkis dimension of a certain class of decision regions defined by
the -dimensional marginal distributions of the sources; furthermore, for
each , the decoder can identify -dimensional marginal of the active
source up to a ball of radius in variational distance,
eventually with probability one. The results are supplemented by several
examples of parametric sources satisfying the regularity conditions.Comment: 16 pages, 1 figure; accepted to IEEE Transactions on Information
Theor
Statistical mechanics of lossy data compression using a non-monotonic perceptron
The performance of a lossy data compression scheme for uniformly biased
Boolean messages is investigated via methods of statistical mechanics. Inspired
by a formal similarity to the storage capacity problem in the research of
neural networks, we utilize a perceptron of which the transfer function is
appropriately designed in order to compress and decode the messages. Employing
the replica method, we analytically show that our scheme can achieve the
optimal performance known in the framework of lossy compression in most cases
when the code length becomes infinity. The validity of the obtained results is
numerically confirmed.Comment: 9 pages, 5 figures, Physical Review
Efficient LDPC Codes over GF(q) for Lossy Data Compression
In this paper we consider the lossy compression of a binary symmetric source.
We present a scheme that provides a low complexity lossy compressor with near
optimal empirical performance. The proposed scheme is based on b-reduced
ultra-sparse LDPC codes over GF(q). Encoding is performed by the Reinforced
Belief Propagation algorithm, a variant of Belief Propagation. The
computational complexity at the encoder is O(.n.q.log q), where is the
average degree of the check nodes. For our code ensemble, decoding can be
performed iteratively following the inverse steps of the leaf removal
algorithm. For a sparse parity-check matrix the number of needed operations is
O(n).Comment: 5 pages, 3 figure
JPEG2000 Image Compression on Solar EUV Images
For future solar missions as well as ground-based telescopes, efficient ways
to return and process data have become increasingly important. Solar Orbiter,
e.g., which is the next ESA/NASA mission to explore the Sun and the
heliosphere, is a deep-space mission, which implies a limited telemetry rate
that makes efficient onboard data compression a necessity to achieve the
mission science goals. Missions like the Solar Dynamics Observatory (SDO) and
future ground-based telescopes such as the Daniel K. Inouye Solar Telescope, on
the other hand, face the challenge of making petabyte-sized solar data archives
accessible to the solar community. New image compression standards address
these challenges by implementing efficient and flexible compression algorithms
that can be tailored to user requirements. We analyse solar images from the
Atmospheric Imaging Assembly (AIA) instrument onboard SDO to study the effect
of lossy JPEG2000 (from the Joint Photographic Experts Group 2000) image
compression at different bit rates. To assess the quality of compressed images,
we use the mean structural similarity (MSSIM) index as well as the widely used
peak signal-to-noise ratio (PSNR) as metrics and compare the two in the context
of solar EUV images. In addition, we perform tests to validate the scientific
use of the lossily compressed images by analysing examples of an on-disk and
off-limb coronal-loop oscillation time-series observed by AIA/SDO.Comment: 25 pages, published in Solar Physic
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