This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms-Theory and Practice

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or tempora...

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Vydáno v:	IEEE transactions on image processing Ročník 21; číslo 3; s. 1084 - 1096
Hlavní autoři:	Harmany, Z. T., Marcia, R. F., Willett, R. M.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.03.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Applied sciences Approximation Approximation methods Compressed sensing (CS) Convergence convex optimization Detectors Estimation Exact sciences and technology Image processing Image reconstruction Information, signal and communications theory Inverse problems Mathematical analysis Mathematical models Minimization multiscale Noise photon-limited imaging Poisson noise Reconstruction Sampling, quantization Signal and communications theory Signal processing sparse approximation Studies Telecommunications and information theory total variation (TV) wavelets Iterative method photon-limited imaging Poisson process Convex programming Poisson noise Optimization Gaussian noise Least squares method Imaging Quadratic approximation Sparse representation Likelihood function Discrete event system Photon counting Logarithmic function Poisson distribution Algorithm Photodetector Inverse problem Gaussian process Television Multiscale method Compressed sensing (CS) total variation (TV) wavelets sparse approximation convex optimization Objective function multiscale Compressed sensing
ISSN:	1057-7149, 1941-0042, 1941-0042
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Popis
Shrnutí:	Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon ( f* ) from Poisson data ( y ) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. 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). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l 1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	1057-7149 1941-0042 1941-0042
DOI:	10.1109/TIP.2011.2168410