17,007 research outputs found
An EM approach for Poisson-Gaussian noise modeling
International audienceThis paper deals with noise parameter estimation. We assume observations corrupted by noise modelled as a sum of two random processes: one Poisson and the other a (nonzero mean) Gaussian. Such problems arise in various applications, e.g. in astronomy and confocal microscopy imaging. To estimate noise parameters, we propose an iterative algorithm based on an Expectation-Maximization approach. This allows us to jointly estimate the scale parameter of the Poisson component and the mean and variance of the Gaussian one. Moreover, an adequate initialization based on cumulants is provided. Numerical difficulties arising from the procedure are also addressed. To validate the proposed method in terms of accuracy and robustness, tests are performed on synthetic data. The good performance of the method is also demonstrated in a denoising experiment on real data
Bayesian Image Restoration for Poisson Corrupted Image using a Latent Variational Method with Gaussian MRF
We treat an image restoration problem with a Poisson noise chan- nel using a
Bayesian framework. The Poisson randomness might be appeared in observation of
low contrast object in the field of imaging. The noise observation is often
hard to treat in a theo- retical analysis. In our formulation, we interpret the
observation through the Poisson noise channel as a likelihood, and evaluate the
bound of it with a Gaussian function using a latent variable method. We then
introduce a Gaussian Markov random field (GMRF) as the prior for the Bayesian
approach, and derive the posterior as a Gaussian distribution. The latent
parameters in the likelihood and the hyperparameter in the GMRF prior could be
treated as hid- den parameters, so that, we propose an algorithm to infer them
in the expectation maximization (EM) framework using loopy belief
propagation(LBP). We confirm the ability of our algorithm in the computer
simulation, and compare it with the results of other im- age restoration
frameworks.Comment: 9 pages, 6 figures, The of this manuscript is submitting to the
Information Processing Society of Japan(IPSJ), Transactions on Mathematical
Modeling and its Applications (TOM
A proximal iteration for deconvolving Poisson noisy images using sparse representations
We propose an image deconvolution algorithm when the data is contaminated by
Poisson noise. The image to restore is assumed to be sparsely represented in a
dictionary of waveforms such as the wavelet or curvelet transforms. Our key
contributions are: First, we handle the Poisson noise properly by using the
Anscombe variance stabilizing transform leading to a {\it non-linear}
degradation equation with additive Gaussian noise. Second, the deconvolution
problem is formulated as the minimization of a convex functional with a
data-fidelity term reflecting the noise properties, and a non-smooth
sparsity-promoting penalties over the image representation coefficients (e.g.
-norm). Third, a fast iterative backward-forward splitting algorithm is
proposed to solve the minimization problem. We derive existence and uniqueness
conditions of the solution, and establish convergence of the iterative
algorithm. Finally, a GCV-based model selection procedure is proposed to
objectively select the regularization parameter. Experimental results are
carried out to show the striking benefits gained from taking into account the
Poisson statistics of the noise. These results also suggest that using
sparse-domain regularization may be tractable in many deconvolution
applications with Poisson noise such as astronomy and microscopy
On the Inversion of High Energy Proton
Inversion of the K-fold stochastic autoconvolution integral equation is an
elementary nonlinear problem, yet there are no de facto methods to solve it
with finite statistics. To fix this problem, we introduce a novel inverse
algorithm based on a combination of minimization of relative entropy, the Fast
Fourier Transform and a recursive version of Efron's bootstrap. This gives us
power to obtain new perspectives on non-perturbative high energy QCD, such as
probing the ab initio principles underlying the approximately negative binomial
distributions of observed charged particle final state multiplicities, related
to multiparton interactions, the fluctuating structure and profile of proton
and diffraction. As a proof-of-concept, we apply the algorithm to ALICE
proton-proton charged particle multiplicity measurements done at different
center-of-mass energies and fiducial pseudorapidity intervals at the LHC,
available on HEPData. A strong double peak structure emerges from the
inversion, barely visible without it.Comment: 29 pages, 10 figures, v2: extended analysis (re-projection ratios,
2D
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