CIF:Small: Collaborative Research: Blue-Noise Graph Sampling

This proposal focuses on random kernels in signal processing. We also refer to these operators as filtering with Bernoulli weights or Shrodinger sampling. The methods can be applied to a broad class of fundamental signal processing functions, but we concentrate on workhorse operators used in signal processing practice. Random kernels can be thought of as a special case of random matrix theory. The connection lies in probabilistic notions that, in one hand, are applied to matrices and on the other they are applied to kernels or inner products. Much like matrices play a critical role in mathematics and numerous engineering fields, inner products are at the heart of signal processing algorithms. Random matrices and random kernels share similar construction principles but the objectives, as formulated in this proposal, are different. Random matrix theory studies the characteristics of the underlying Eigenstructures and the applications in linear algebra and matrix spectral theory. Random kernels, in this proposal, focus on inner products and their applications in signal processing. At the core of the problem lies the notion of probabilistic ensembles. Random matrices often focus on Gaussian independent and identically distributed ensembles. Random kernels also build on probabilistic ensembles but these may neither be Gaussian nor i.i.d.