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Signal-processing on graphs has developed into a very active field ofresearch during the last decade. In particular, the number of applicationsusing frames constructed from graphs, like wavelets on graphs, hassubstantially increased. To attain scalability for large graphs, fastgraph-signal filtering techniques are needed. In this contribution, we proposean accelerated algorithm based on the Lanczos method that adapts to theLaplacian spectrum without explicitly computing it. The result is an accurate,robust, scalable and efficient algorithm. Compared to existing methods based onChebyshev polynomials, our solution achieves higher accuracy without increasingthe overall complexity significantly. Furthermore, it is particularly wellsuited for graphs with large spectral gaps.

Accelerated filtering on graphs using Lanczos method