THESIS
2018
xviii, 125 pages : illustrations ; 30 cm
Abstract
Unlike periodically sampled signals in time and/or space, like digital audio
and images, irregularly sampled signals bring challenges to the design and evaluation
of processing tools. In this thesis, we introduce new techniques to handle
irregularity in data sampling for three applications: compression, denoising and
quality assessment.
First, irregularly sampled signals are represented as signals on graphs describing
the underlying data kernels, and we process them using graph signal
processing (GSP) tools.
• For compression, we employ critically sampled wavelet filterbanks that compactly
represent bipartite graph signals. When the original graph is not bipartite,
we decompose it into a sequence of bipartite subgraphs so that the
filterbanks can be applied successively on ea...[
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Unlike periodically sampled signals in time and/or space, like digital audio
and images, irregularly sampled signals bring challenges to the design and evaluation
of processing tools. In this thesis, we introduce new techniques to handle
irregularity in data sampling for three applications: compression, denoising and
quality assessment.
First, irregularly sampled signals are represented as signals on graphs describing
the underlying data kernels, and we process them using graph signal
processing (GSP) tools.
• For compression, we employ critically sampled wavelet filterbanks that compactly
represent bipartite graph signals. When the original graph is not bipartite,
we decompose it into a sequence of bipartite subgraphs so that the
filterbanks can be applied successively on each subgraph. Unlike previous
proposals that are heuristic in nature, we derive new metrics that directly
measure the energy compaction in bipartite subgraphs, and develop new
bipartite subgraph decomposition algorithms with better compression performance
than state-of-the-art schemes.
• For denoising, we consider the 3D point cloud and model it as overlapping
surface patches residing on a manifold. By assuming a low-dimensional
patch manifold prior, we seek self-similarity patches to denoise them simultaneously.
Towards a speedy implementation, we approximate the manifold
dimension with graph Laplacian regularizer, and propose a new discrete patch similarity measure for graph construction that is robust to noise. The
proposed method is shown experimentally to outperform the state-of-the-art
methods with better structural feature preservation.
Second, we consider images displayed with a variety of subpixel rendering
techniques and design a new quality assessment that overcomes the difficulty
of balancing apparent resolution and color fidelity caused by the irregularity of
subpixel sampling pattern. Guided by an extensive user study, the visual quality
of a subpixel image is decomposed into fundamental local subpixel features and
global pixel features. With these features as the basis, the assessment metric
is obtained and experimentally justified to better correlate with user preference
than existing metrics.
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