Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Weighted superimposed codes and constrained integer compressed sensing
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Reconstruction From Noisy Random Projections
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Performance bounds for expander-based compressed sensing in the presence of poisson noise
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography
Journal of Scientific Computing
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This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent and bounded noise models used in the literature to analyze the performance of compressed sensing do not accurately model the effects of Poisson noise. However, Poisson noise is an appropriate noise model for a variety of applications, including low-light imaging, where sensing hardware is large or expensive, and limiting the number of measurements collected is important. In this paper, we describe how a feasible positivity-preserving sensing matrix can be constructed, and then analyze the performance of a compressed sensing reconstruction approach for Poisson data that minimizes an objective function consisting of a negative Poisson log likelihood term and a penalty term which could be used as a measure of signal sparsity.