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...[ Read more ]

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.