Oversampled transforms for graph signals

Abstract

In this chapter, oversampled transforms for graph signals are introduced. Oversampling is done in two ways: One is oversampled graph Laplacian and the other is oversampled graph transforms. Both are described here. The advantage of the oversampled transforms is that we can take a good trade-off between performance (in context to sparsifying the graph signals) and storage/memory space for transformed coefficients. Furthermore, any graph can be converted into an oversampled bipartite graph by using the oversampled graph Laplacian. It leads to that well-known graph wavelet transforms/filter banks for bipartite graphs can be applied to the signals on any graphs with a slight sacrifice of redundancy. Actual performances are compared through several numerical experiments.