Electrical and Electronic Engineering, Imperial College London
Doi
Abstract
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
