Chebyshev Polynomial Approximation for Distributed Signal Processing

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals collected by sensor networks. The proposed method features approximations of the graph Fourier multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be used in a distributed denoising task, and show that the communication requirements of the method scale gracefully with the size of the network.Comment: 8 pages, 5 figures, to appear in the Proceedings of the IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS), June, 2011, Barcelona, Spai

Accelerated filtering on graphs using Lanczos method

Signal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames constructed from graphs, like wavelets on graphs, has substantially increased. To attain scalability for large graphs, fast graph-signal filtering techniques are needed. In this contribution, we propose an accelerated algorithm based on the Lanczos method that adapts to the Laplacian spectrum without explicitly computing it. The result is an accurate, robust, scalable and efficient algorithm. Compared to existing methods based on Chebyshev polynomials, our solution achieves higher accuracy without increasing the overall complexity significantly. Furthermore, it is particularly well suited for graphs with large spectral gaps

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