Non-Gaussian observations in nonlinear compressed sensing via Stein discrepancies

摘要

Performance guarantees for estimates of unknowns in nonlinear compressed sensing models under non- Gaussian measurements can be achieved through the use of distributional characteristics that are sensitive to the distance to normality, and which in particular return the value of zero under Gaussian or linear sensing. The use of these characteristics, or discrepancies, improves some previous results in this area by relaxing conditions and tightening performance bounds. In addition, these characteristics are tractable to compute when Gaussian sensing is corrupted by either additive errors or mixing.