Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Self-taught semi-supervised dictionary learning with non-negative constraint

This paper investigates classification by dictionary learning. A novel unified framework termed self-taught semisupervised dictionary learning with non-negative constraint (NNST-SSDL) is proposed for simultaneously optimizing the components of a dictionary and a graph Laplacian. Specifically, an atom graph Laplacian regularization is built by using sparse coefficients to effectively capture the underlying manifold structure. It is more robust to noisy samples and outliers because atoms are more concise and representative than training samples. A non-negative constraint imposed on the sparse coefficients guarantees that each sample is in the middle of its related atoms. In this way the dependency between samples and atoms is made explicit. Furthermore, a self-taught mechanism is introduced to effectively feed back the manifold structure induced by atom graph Laplacian regularization and the supervised information hidden in unlabeled samples in order to learn a better dictionary. An efficient algorithm, combining a block coordinate descent method with the alternating direction method of multipliers is derived to optimize the unified framework. Experimental results on several benchmark datasets show the effectiveness of the proposed model

Graph learning and its applications : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computer Science, Massey University, Albany, Auckland, New Zealand

Since graph features consider the correlations between two data points to provide high-order information, i.e., more complex correlations than the low-order information which considers the correlations in the individual data, they have attracted much attention in real applications. The key of graph feature extraction is the graph construction. Previous study has demonstrated that the quality of the graph usually determines the effectiveness of the graph feature. However, the graph is usually constructed from the original data which often contain noise and redundancy. To address the above issue, graph learning is designed to iteratively adjust the graph and model parameters so that improving the quality of the graph and outputting optimal model parameters. As a result, graph learning has become a very popular research topic in traditional machine learning and deep learning. Although previous graph learning methods have been applied in many fields by adding a graph regularization to the objective function, they still have some issues to be addressed. This thesis focuses on the study of graph learning aiming to overcome the drawbacks in previous methods for different applications. We list the proposed methods as follows. • We propose a traditional graph learning method under supervised learning to consider the robustness and the interpretability of graph learning. Specifically, we propose utilizing self-paced learning to assign important samples with large weights, conducting feature selection to remove redundant features, and learning a graph matrix from the low dimensional data of the original data to preserve the local structure of the data. As a consequence, both important samples and useful features are used to select support vectors in the SVM framework. • We propose a traditional graph learning method under semi-supervised learning to explore parameter-free fusion of graph learning. Specifically, we first employ the discrete wavelet transform and Pearson correlation coefficient to obtain multiple fully connected Functional Connectivity brain Networks (FCNs) for every subject, and then learn a sparsely connected FCN for every subject. Finally, the ℓ1-SVM is employed to learn the important features and conduct disease diagnosis. • We propose a deep graph learning method to consider graph fusion of graph learning. Specifically, we first employ the Simple Linear Iterative Clustering (SLIC) method to obtain multi-scale features for every image, and then design a new graph fusion method to fine-tune features of every scale. As a result, the multi-scale feature fine-tuning, graph learning, and feature learning are embedded into a unified framework. All proposed methods are evaluated on real-world data sets, by comparing to state-of-the-art methods. Experimental results demonstrate that our methods outperformed all comparison methods