2,851 research outputs found
On the rate distortion function of Bernoulli Gaussian sequences
In this paper, we study the rate distortion function of the i.i.d sequence of
multiplications of a Bernoulli random variable and a gaussian random
variable . We use a new technique in the derivation of the lower
bound in which we establish the duality between channel coding and lossy source
coding in the strong sense. We improve the lower bound on the rate distortion
function over the best known lower bound by if distortion
is small. This has some interesting implications on sparse signals where
is small since the known gap between the lower and upper bound is .
This improvement in the lower bound shows that the lower and upper bounds are
almost identical for sparse signals with small distortion because
.Comment: In preparation for IEEE Transactions on I
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
- …