Performance bounds for Poisson compressed sensing using Variance Stabilization Transforms

Garg, Deepak; Rajwade, Ajit

doi:10.1109/icassp.2017.7953324

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…Comparisons with Other Approaches: Besides our conference paper [18], our group has performed some other earlier work on Poisson CS for realistic matrices using a tractable estimator based on the Jensen-Shannon divergence (JSD) between y and Φx [51]. The work essentially makes use of the fact that the square-root of the JSD (SQJSD) is a metric, and that the SQJSD has values that scale as o( √ N ) but independent of I.…”

Section: Discussionmentioning

confidence: 99%

“…We implemented LASSO using CVX, and we set the ρ parameter either omnisciently (referred to henceforth as just LASSO), or we set it to 2 8 log m/I as per theorem 2 of [41] (referred to henceforth as LASSO-fixed). Additionally, we also compared the results to a version of P3 which we had used in [18], given by the following:…”

Section: Methods Comparedmentioning

confidence: 99%

“…A part of this work earlier appeared in our conference paper [18], but this work contains an extension to the Poisson-Gaussian case, as well as many refinements to the theory and experiments for the Poisson noise case. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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Variance-stabilization-based compressive inversion under Poisson or Poisson–Gaussian noise with analytical bounds

et al. 2019

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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 computationally tractable convex estimator with statistically motivated parameter selection. The estimator penalizes signal sparsity subject to a constraint that imposes a novel statistically motivated upper bound on a term based on variance stabilization transforms to approximate the Poisson or Poisson-Gaussian distributions by distributions with (nearly) constant variance. (2) The bounds 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 nonnegativity and flux-preservation. Our bounds are motivated by several properties of the variance stabilization transforms that we develop and analyze. We present extensive numerical results for signal reconstruction under varying number of measurements and varying signal intensity levels. Ours is the first piece of work to derive bounds on compressive inversion for the Poisson-Gaussian noise model. We also use the properties of the variance stabilizer to develop a principle for selection of the regularization parameter in penalized estimators for Poisson and Poisson-Gaussian inverse problems.

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Section: Discussionmentioning

confidence: 99%

Section: Methods Comparedmentioning

confidence: 99%

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Variance-stabilization-based compressive inversion under Poisson or Poisson–Gaussian noise with analytical bounds

et al. 2019

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“…In the context of Poisson CS, the VST converts a linear problem into a non-linear one. However, our group has recently shown the advantages of the VST for Poisson CS reconstructions in [44,38] with similar statistically motivated parameter selection. However in this paper, we present the result that the SQJSD also possesses such variance stabilizing properties for the Poisson distribution.…”

Section: Comparison With Vst-based Methodsmentioning

confidence: 99%

Reconstruction Error Bounds for Compressed Sensing under Poisson Noise using the Square Root of the Jensen-Shannon Divergence

Patil,

Gurumoorthy,

Rajwade

2016

Preprint

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Reconstruction error bounds in compressed sensing under Gaussian or uniform bounded noise do not translate easily to the case of Poisson noise. Reasons for this include the signal dependent nature of Poisson noise, and also the fact that the negative log likelihood in case of a Poisson distribution (which is directly related to the generalized Kullback-Leibler divergence) is not a metric and does not obey the triangle inequality. There exist prior theoretical results in the form of provable error bounds for computationally tractable estimators for compressed sensing problems under Poisson noise. However, these results do not apply to realistic compressive systems, which must obey some crucial constraints such as non-negativity and flux preservation.On the other hand, there exist provable error bounds for such realistic systems in the published literature, but they are for estimators that are computationally intractable. In this paper, we develop error bounds for a computationally tractable estimator which also applies to realistic compressive systems obeying the required constraints. The focus of our technique is on the replacement of the generalized Kullback-Leibler divergence, with an information theoretic metric -namely the square root of the Jensen-Shannon divergence, which is related to an approximate, symmetrized version of the Poisson log likelihood function. We show that this replacement allows for very simple proofs of the error bounds, as it proposes and proves several interesting statistical properties of the square root of Jensen-Shannon divergence, and exploits other known ones. Numerical experiments are performed showing the practical use of the technique in signal and image

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Multidimensional Multilayer Modulation for Broadcast UVLC With Photon Detectors

Si-Ma¹,

Yu²,

Zhang³

et al. 2020

IEEE Trans. Veh. Technol.

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Performance bounds for Poisson compressed sensing using Variance Stabilization Transforms

Cited by 3 publications

References 15 publications

Variance-stabilization-based compressive inversion under Poisson or Poisson–Gaussian noise with analytical bounds

Variance-stabilization-based compressive inversion under Poisson or Poisson–Gaussian noise with analytical bounds

Reconstruction Error Bounds for Compressed Sensing under Poisson Noise using the Square Root of the Jensen-Shannon Divergence

Multidimensional Multilayer Modulation for Broadcast UVLC With Photon Detectors

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