4,920 research outputs found
Centralized and distributed semi-parametric compression of piecewise smooth functions
This thesis introduces novel wavelet-based semi-parametric centralized and distributed
compression methods for a class of piecewise smooth functions. Our proposed compression schemes are based on a non-conventional transform coding structure with simple
independent encoders and a complex joint decoder.
Current centralized state-of-the-art compression schemes are based on the conventional structure where an encoder is relatively complex and nonlinear. In addition, the
setting usually allows the encoder to observe the entire source. Recently, there has been
an increasing need for compression schemes where the encoder is lower in complexity
and, instead, the decoder has to handle more computationally intensive tasks. Furthermore, the setup may involve multiple encoders, where each one can only partially
observe the source. Such scenario is often referred to as distributed source coding.
In the first part, we focus on the dual situation of the centralized compression where
the encoder is linear and the decoder is nonlinear. Our analysis is centered around a
class of 1-D piecewise smooth functions. We show that, by incorporating parametric
estimation into the decoding procedure, it is possible to achieve the same distortion-
rate performance as that of a conventional wavelet-based compression scheme. We also
present a new constructive approach to parametric estimation based on the sampling
results of signals with finite rate of innovation.
The second part of the thesis focuses on the distributed compression scenario, where
each independent encoder partially observes the 1-D piecewise smooth function. We
propose a new wavelet-based distributed compression scheme that uses parametric estimation to perform joint decoding. Our distortion-rate analysis shows that it is possible
for the proposed scheme to achieve that same compression performance as that of a
joint encoding scheme.
Lastly, we apply the proposed theoretical framework in the context of distributed
image and video compression. We start by considering a simplified model of the video
signal and show that we can achieve distortion-rate performance close to that of a joint
encoding scheme. We then present practical compression schemes for real world signals.
Our simulations confirm the improvement in performance over classical schemes, both
in terms of the PSNR and the visual quality
Compression for Smooth Shape Analysis
Most 3D shape analysis methods use triangular meshes to discretize both the
shape and functions on it as piecewise linear functions. With this
representation, shape analysis requires fine meshes to represent smooth shapes
and geometric operators like normals, curvatures, or Laplace-Beltrami
eigenfunctions at large computational and memory costs.
We avoid this bottleneck with a compression technique that represents a
smooth shape as subdivision surfaces and exploits the subdivision scheme to
parametrize smooth functions on that shape with a few control parameters. This
compression does not affect the accuracy of the Laplace-Beltrami operator and
its eigenfunctions and allow us to compute shape descriptors and shape
matchings at an accuracy comparable to triangular meshes but a fraction of the
computational cost.
Our framework can also compress surfaces represented by point clouds to do
shape analysis of 3D scanning data
A Multiscale Pyramid Transform for Graph Signals
Multiscale transforms designed to process analog and discrete-time signals
and images cannot be directly applied to analyze high-dimensional data residing
on the vertices of a weighted graph, as they do not capture the intrinsic
geometric structure of the underlying graph data domain. In this paper, we
adapt the Laplacian pyramid transform for signals on Euclidean domains so that
it can be used to analyze high-dimensional data residing on the vertices of a
weighted graph. Our approach is to study existing methods and develop new
methods for the four fundamental operations of graph downsampling, graph
reduction, and filtering and interpolation of signals on graphs. Equipped with
appropriate notions of these operations, we leverage the basic multiscale
constructs and intuitions from classical signal processing to generate a
transform that yields both a multiresolution of graphs and an associated
multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure
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