Toward Optimal Rate Allocation to Sampling Sets for Bandlimited Graph Signals

We study the problem of sampling signals on a graph and allocating rate to each vertex in the sampling set, in a scenario where information sampled at each of the graph nodes needs to be compressed for transmission. We formulate this problem as a constrained quadratic programming optimization and obtain analytic results stating that the reconstruction error due to quantization should be equally distributed over the nodes involved. Our solution can also be used to remove samples from an already selected sampling set with low additional complexity. We demonstrate through experiments that the optimal solution yields improved performance on various graphs.