27,433 research outputs found
Metric mean dimension and analog compression
Wu and Verd\'u developed a theory of almost lossless analog compression,
where one imposes various regularity conditions on the compressor and the
decompressor with the input signal being modelled by a (typically
infinite-entropy) stationary stochastic process. In this work we consider all
stationary stochastic processes with trajectories in a prescribed set of
(bi-)infinite sequences and find uniform lower and upper bounds for certain
compression rates in terms of metric mean dimension and mean box dimension. An
essential tool is the recent Lindenstrauss-Tsukamoto variational principle
expressing metric mean dimension in terms of rate-distortion functions. We
obtain also lower bounds on compression rates for a fixed stationary process in
terms of the rate-distortion dimension rates and study several examples.Comment: v3: Accepted for publication in IEEE Transactions on Information
Theory. Additional examples were added. Material have been reorganized (with
some parts removed). Minor mistakes were correcte
New Uniform Bounds for Almost Lossless Analog Compression
Wu and Verd\'u developed a theory of almost lossless analog compression,
where one imposes various regularity conditions on the compressor and the
decompressor with the input signal being modelled by a (typically
infinite-entropy) stationary stochastic process. In this work we consider all
stationary stochastic processes with trajectories in a prescribed set
of (bi)infinite sequences and find
uniform lower and upper bounds for certain compression rates in terms of metric
mean dimension and mean box dimension. An essential tool is the recent
Lindenstrauss-Tsukamoto variational principle expressing metric mean dimension
in terms of rate-distortion functions.Comment: This paper is going to be presented at 2019 IEEE International
Symposium on Information Theory. It is a short version of arXiv:1812.0045
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
On Match Lengths, Zero Entropy and Large Deviations - with Application to Sliding Window Lempel-Ziv Algorithm
The Sliding Window Lempel-Ziv (SWLZ) algorithm that makes use of recurrence
times and match lengths has been studied from various perspectives in
information theory literature. In this paper, we undertake a finer study of
these quantities under two different scenarios, i) \emph{zero entropy} sources
that are characterized by strong long-term memory, and ii) the processes with
weak memory as described through various mixing conditions.
For zero entropy sources, a general statement on match length is obtained. It
is used in the proof of almost sure optimality of Fixed Shift Variant of
Lempel-Ziv (FSLZ) and SWLZ algorithms given in literature. Through an example
of stationary and ergodic processes generated by an irrational rotation we
establish that for a window of size , a compression ratio given by
where depends on and approaches 1 as
, is obtained under the application of FSLZ and SWLZ
algorithms. Also, we give a general expression for the compression ratio for a
class of stationary and ergodic processes with zero entropy.
Next, we extend the study of Ornstein and Weiss on the asymptotic behavior of
the \emph{normalized} version of recurrence times and establish the \emph{large
deviation property} (LDP) for a class of mixing processes. Also, an estimator
of entropy based on recurrence times is proposed for which large deviation
principle is proved for sources satisfying similar mixing conditions.Comment: accepted to appear in IEEE Transactions on Information Theor
Network vector quantization
We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples
Multiresolution vector quantization
Multiresolution source codes are data compression algorithms yielding embedded source descriptions. The decoder of a multiresolution code can build a source reproduction by decoding the embedded bit stream in part or in whole. All decoding procedures start at the beginning of the binary source description and decode some fraction of that string. Decoding a small portion of the binary string gives a low-resolution reproduction; decoding more yields a higher resolution reproduction; and so on. Multiresolution vector quantizers are block multiresolution source codes. This paper introduces algorithms for designing fixed- and variable-rate multiresolution vector quantizers. Experiments on synthetic data demonstrate performance close to the theoretical performance limit. Experiments on natural images demonstrate performance improvements of up to 8 dB over tree-structured vector quantizers. Some of the lessons learned through multiresolution vector quantizer design lend insight into the design of more sophisticated multiresolution codes
On the Information Rates of the Plenoptic Function
The {\it plenoptic function} (Adelson and Bergen, 91) describes the visual
information available to an observer at any point in space and time. Samples of
the plenoptic function (POF) are seen in video and in general visual content,
and represent large amounts of information. In this paper we propose a
stochastic model to study the compression limits of the plenoptic function. In
the proposed framework, we isolate the two fundamental sources of information
in the POF: the one representing the camera motion and the other representing
the information complexity of the "reality" being acquired and transmitted. The
sources of information are combined, generating a stochastic process that we
study in detail. We first propose a model for ensembles of realities that do
not change over time. The proposed model is simple in that it enables us to
derive precise coding bounds in the information-theoretic sense that are sharp
in a number of cases of practical interest. For this simple case of static
realities and camera motion, our results indicate that coding practice is in
accordance with optimal coding from an information-theoretic standpoint. The
model is further extended to account for visual realities that change over
time. We derive bounds on the lossless and lossy information rates for this
dynamic reality model, stating conditions under which the bounds are tight.
Examples with synthetic sources suggest that in the presence of scene dynamics,
simple hybrid coding using motion/displacement estimation with DPCM performs
considerably suboptimally relative to the true rate-distortion bound.Comment: submitted to IEEE Transactions in Information Theor
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