Variable-density sampling on the dual lattice

Sampling from certain probability distribution shows better recovery performance than uniform sampling in literature. However, a comprehensive theoretical analysis concerning more realistic signal models is still lacking. In this paper, we consider the sampling of stochastic processes and random fields in the Fourier domain. We propose a new variable-density sampling and linear reconstruction technique, and prove its theoretical recovery guarantee. For high dimensional random fields, uniform sampling requires a number of samples increasing exponentially with the dimension, while the variable density sampling scheme guarantees faithful recovery performance with a polynomial size of random samples.