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

Multi-channel Sampling on Graphs and Its Relationship to Graph Filter Banks

In this paper, we consider multi-channel sampling (MCS) for graph signals. We generally encounter full-band graph signals beyond the bandlimited one in many applications, such as piecewise constant/smooth and union of bandlimited graph signals. Full-band graph signals can be represented by a mixture of multiple signals conforming to different generation models. This requires the analysis of graph signals via multiple sampling systems, i.e., MCS, while existing approaches only consider single-channel sampling. We develop a MCS framework based on generalized sampling. We also present a sampling set selection (SSS) method for the proposed MCS so that the graph signal is best recovered. Furthermore, we reveal that existing graph filter banks can be viewed as a special case of the proposed MCS. In signal recovery experiments, the proposed method exhibits the effectiveness of recovery for full-band graph signals

Dynamic Sensor Placement Based on Graph Sampling Theory

In this paper, we consider a dynamic sensor placement problem where sensors can move within a network over time. Sensor placement problem aims to select M sensor positions from N candidates where M < N. Most existing methods assume that sensors are static, i.e., they do not move, however, many mobile sensors like drones, robots, and vehicles can change their positions over time. Moreover, underlying measurement conditions could also be changed that are difficult to cover the statically placed sensors. We tackle the problem by allowing the sensors to change their positions in their neighbors on the network. Based on a perspective of dictionary learning, we sequentially learn the dictionary from a pool of observed signals on the network based on graph sampling theory. Using the learned dictionary, we dynamically determine the sensor positions such that the non-observed signals on the network can be best recovered from the observations. Furthermore, sensor positions in each time slot can be optimized in a decentralized manner to reduce the calculation cost. In experiments, we validate the effectiveness of the proposed method via the mean squared error (MSE) of the reconstructed signals. The proposed dynamic sensor placement outperforms the existing static ones both in synthetic and real data