3,074 research outputs found
Low Rate Scalar Quantization for Gaussian Sources and Absolute Error
This paper considers low resolution scalar quantization for a memoryless Gaussian source with respect to absolute error distortion. It shows that slope of the operational rate-distortion function of scalar quantization is infinite at the point D_(max) where the rate becomes zero. Thus, unlike the situation for squared error distortion, or for Laplacian and exponential sources with squared or absolute error distortion, for a Gaussian source and absolute error, scalar quantization at low rates is far from the Shannon rate-distortion function, i.e. far from the performance of the best lossy coding technique
Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
We deal with zero-delay source coding of a vector-valued Gauss-Markov source
subject to a mean-squared error (MSE) fidelity criterion characterized by the
operational zero-delay vector-valued Gaussian rate distortion function (RDF).
We address this problem by considering the nonanticipative RDF (NRDF) which is
a lower bound to the causal optimal performance theoretically attainable (OPTA)
function and operational zero-delay RDF. We recall the realization that
corresponds to the optimal "test-channel" of the Gaussian NRDF, when
considering a vector Gauss-Markov source subject to a MSE distortion in the
finite time horizon. Then, we introduce sufficient conditions to show existence
of solution for this problem in the infinite time horizon. For the asymptotic
regime, we use the asymptotic characterization of the Gaussian NRDF to provide
a new equivalent realization scheme with feedback which is characterized by a
resource allocation (reverse-waterfilling) problem across the dimension of the
vector source. We leverage the new realization to derive a predictive coding
scheme via lattice quantization with subtractive dither and joint memoryless
entropy coding. This coding scheme offers an upper bound to the operational
zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then
for "r" active dimensions of the vector Gauss-Markov source the gap between the
obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1
bits/vector. We further show that it is possible when we use vector
quantization, and assume infinite dimensional Gauss-Markov sources to make the
previous gap to be negligible, i.e., Gaussian NRDF approximates the operational
zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian
sources of any finite memory under mild conditions. Our theoretical framework
is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in
Signal Processin
Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms
It is well known that Shannon's rate-distortion function (RDF) in the colored
quadratic Gaussian (QG) case can be parametrized via a single Lagrangian
variable (the "water level" in the reverse water filling solution). In this
work, we show that the symmetric colored QG multiple-description (MD) RDF in
the case of two descriptions can be parametrized in the spectral domain via two
Lagrangian variables, which control the trade-off between the side distortion,
the central distortion, and the coding rate. This spectral-domain analysis is
complemented by a time-domain scheme-design approach: we show that the
symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma
modulation and differential pulse-code modulation. Specifically, two source
prediction loops, one for each description, are embedded within a common noise
shaping loop, whose parameters are explicitly found from the spectral-domain
characterization.Comment: Accepted for publications in the IEEE Transactions on Information
Theory. Title have been shortened, abstract clarified, and paper
significantly restructure
A Novel Rate Control Algorithm for Onboard Predictive Coding of Multispectral and Hyperspectral Images
Predictive coding is attractive for compression onboard of spacecrafts thanks
to its low computational complexity, modest memory requirements and the ability
to accurately control quality on a pixel-by-pixel basis. Traditionally,
predictive compression focused on the lossless and near-lossless modes of
operation where the maximum error can be bounded but the rate of the compressed
image is variable. Rate control is considered a challenging problem for
predictive encoders due to the dependencies between quantization and prediction
in the feedback loop, and the lack of a signal representation that packs the
signal's energy into few coefficients. In this paper, we show that it is
possible to design a rate control scheme intended for onboard implementation.
In particular, we propose a general framework to select quantizers in each
spatial and spectral region of an image so as to achieve the desired target
rate while minimizing distortion. The rate control algorithm allows to achieve
lossy, near-lossless compression, and any in-between type of compression, e.g.,
lossy compression with a near-lossless constraint. While this framework is
independent of the specific predictor used, in order to show its performance,
in this paper we tailor it to the predictor adopted by the CCSDS-123 lossless
compression standard, obtaining an extension that allows to perform lossless,
near-lossless and lossy compression in a single package. We show that the rate
controller has excellent performance in terms of accuracy in the output rate,
rate-distortion characteristics and is extremely competitive with respect to
state-of-the-art transform coding
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