  Most existing bounds for signal reconstruction from compressive measurements
make the assumption of additive signal-independent noise. However in many
compressive imaging systems, the noise statistics are more accurately
represented by Poisson or Poisson-Gaussian noise models. In this paper, we
derive upper bounds for signal reconstruction error from compressive
measurements which are corrupted by Poisson or Poisson-Gaussian noise. The
features of our bounds are as follows: (1) The bounds are derived for a
probabilistically motivated, computationally tractable convex estimator with
principled parameter selection. The estimator penalizes signal sparsity subject
to a constraint that imposes an upper bound on a term based on variance
stabilization transforms to approximate the Poisson or Poisson-Gaussian
negative log-likelihoods. (2) They are applicable to signals that are sparse as
well as compressible in any orthonormal basis, and are derived for compressive
systems obeying realistic constraints such as non-negativity and
flux-preservation. We present extensive numerical results for signal
reconstruction under varying number of measurements and varying signal
intensity levels.
