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

  title={Variance-stabilization-based compressive inversion under Poisson or Poisson–Gaussian noise with analytical bounds},
  author={Pakshal Bohra and Deepak Garg and Karthik S. Gurumoorthy and Ajit V. Rajwade},
  journal={Inverse Problems},
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… 
Reconstruction Of Sparse Signals Using Likelihood Maximization from Compressive Measurements with Gaussian And Saturation Noise
A new data fidelity function which is directly based on ensuring a certain form of consistency between the signal and the saturated measurements, and can be expressed as the negative logarithm of a certain carefully designed likelihood function is proposed.
Compressive Phase Retrieval under Poisson Noise
A technique for compressive phase retrieval under Poisson noise using the theory of variance stabilization transforms (VSTs) is presented, and the proposed modification allows for easy and very principled parameter tuning.
A Compressed Sensing Approach to Group-testing for COVID-19 Detection
We propose Tapestry, a novel approach to pooled testing with application to COVID-19 testing with quantitative Polymerase Chain Reaction (PCR) that can result in shorter testing time and conservation


Minimax Optimal Sparse Signal Recovery With Poisson Statistics
This work derives a minimax matching lower bound on the mean-squared error of the maximum likelihood decoder and shows that the constrained ML decoder is minimax optimal for this regime.
Reconstruction Error Bounds for Compressed Sensing under Poisson Noise using the Square Root of the Jensen-Shannon Divergence
The focus of the 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 a symmetrized version of the Poisson log likelihood function.
Compressed Sensing Performance Bounds Under Poisson Noise
It is shown that, as the overall intensity of the underlying signal increases, an upper bound on the reconstruction error decays at an appropriate rate, but that for a fixed signal intensity, the error bound actually grows with the number of measurements or sensors.
Sparse signal recovery with exponential-family noise
  • I. Rish, G. Grabarnik
  • Computer Science
    2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
  • 2009
It is shown that, under standard restricted isometry property (RIP) assumptions on the design matrix, l1-minimization can provide stable recovery of a sparse signal in presence of the exponential-family noise, provided that certain sufficient conditions on the noise distribution are satisfied.
Minimax Optimal Rates for Poisson Inverse Problems With Physical Constraints
This paper considers fundamental limits for solving sparse inverse problems in the presence of Poisson noise with physical constraints. Such problems arise in a variety of applications, including
This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms—Theory and Practice
The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative) for estimation of f* from y in an inverse problem setting.
Image Denoising in Mixed Poisson–Gaussian Noise
The denoising process is expressed as a linear expansion of thresholds (LET) that is optimized by relying on a purely data-adaptive unbiased estimate of the mean-squared error (MSE) derived in a non-Bayesian framework (PURE: Poisson-Gaussian unbiased risk estimate).
Sparsity regularization for image reconstruction with Poisson data
This work investigates three penalized-likelihood expectation maximization (EM) algorithms for image reconstruction with Poisson data where the images are known a priori to be sparse in the space domain, and demonstrates that the penalty based on the sum of logarithms produces sparser images than the ML solution.
A discrepancy principle for Poisson data
In applications of imaging science, such as emission tomography, fluorescence microscopy and optical/infrared astronomy, image intensity is measured via the counting of incident particles (photons,