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arXiv · 1707.00475

Reconstruction Error Bounds for Compressed Sensing under Poisson or Poisson-Gaussian Noise Using Variance Stabilization Transforms

Deepak Garg·Pakshal Bohra·Karthik S. Gurumoorthy·Ajit Rajwade
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Abstract

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.

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Deepak Garg, Pakshal Bohra, Karthik S. Gurumoorthy, Ajit Rajwade. 2018-02-12. Reconstruction Error Bounds for Compressed Sensing under Poisson or Poisson-Gaussian Noise Using Variance Stabilization Transforms. https://arxiv.org/abs/1707.00475

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