Two penalized estimators based on variance stabilization transforms for sparse compressive recovery with Poisson measurement noise

Ajit Rajwade, Karthik S. Gurumoorthy

Abstract: Highlights•We analyze two new estimators for Poisson compressed sensing using variance stabilization transforms.•The first estimator has been used earlier in the literature, but this is the first paper to provide a thorough theoretical analysis.•The second estimator is novel and has interesting pivotal properties with a very easy to tune regularization parameter. These pivotal properties are not shared by existing estimators that use the Lasso or the negative log likelihood of the Poisson distribution.•Our theoretical results make use of many different Poisson concentration inequalities.•We provide a series of numerical results to support our theory.