In many signal processing problems, it may be fruitful to represent the signal under study in a redundant linear decomposition called a frame. If a probabilistic approach is adopted, it becomes then necessary to estim...
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ISBN:
(纸本)9781424442959
In many signal processing problems, it may be fruitful to represent the signal under study in a redundant linear decomposition called a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general, the frame synthesis operator is not bijective and consequently, the frame coefficients are not directly observable. In this work, a hierarchical Bayesian model is introduced to solve this problem. A hybrid MCMC algorithm is subsequently proposed to sample from the derived posterior distribution. We show that through classical Bayesian estimators, this algorithm allows us to determine these hyper-parameters, as well as the frame coefficients in applications to image denoising with uniform noise.
Many research groups have sought to measure phase response curves (PRCs) from real neurons. However, methods of estimating PRCs from noisy spike-response data have yet to be established. In this paper, we propose a Ba...
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Many research groups have sought to measure phase response curves (PRCs) from real neurons. However, methods of estimating PRCs from noisy spike-response data have yet to be established. In this paper, we propose a Bayesian approach for estimating PRCs. First, we analytically obtain a likelihood function of the PRC from a detailed model of the observation process formulated as Langevin equations. Then we construct a maximum a posteriori (MAP) estimation algorithm based on the analytically obtained likelihood function. The MAP estimation algorithm derived here is equivalent to the spherical spin model. Moreover, we analytically calculate a marginal likelihood corresponding to the free energy of the spherical spin model, which enables us to estimate the hyper-parameters, i.e., the intensity of the Langevin force and the smoothness of the prior.
High resolution wide-field imaging of the human retina calls for a 3D deconvolution. In this communication, we report on a regularized 3D deconvolution method, developed in a Bayesian framework in view of retinal imag...
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ISBN:
(纸本)9780819474308
High resolution wide-field imaging of the human retina calls for a 3D deconvolution. In this communication, we report on a regularized 3D deconvolution method, developed in a Bayesian framework in view of retinal imaging, which is fully unsupervised, i.e., in which all the usual tuning parameters, a.k.a. "hyper-parameters", are estimated from the data. The hyper-parameters are the noise level and all the parameters of a suitably chosen model for the object's power spectral density (PSD). They are estimated by a maximum likelihood (ML) method prior to the deconvolution itself. This 3D deconvolution method takes into account the 3D nature of the imaging process, can take into account the non-homogeneous noise variance due to the mixture of photon and detector noises, and can enforce a positivity constraint on the recovered object. The performance of the ML hyper-parameter estimation and of the deconvolution are illustrated both on simulated 3D retinal images and on non-biological 3D experimental data.
In this paper, a synthesis method developed in the last few years is applied to derive a cellular non-linear network (CNN) able to find an approximate solution to a variational image-fusion problem. The functional to ...
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In this paper, a synthesis method developed in the last few years is applied to derive a cellular non-linear network (CNN) able to find an approximate solution to a variational image-fusion problem. The functional to be minimized is based on regularization theory and takes into account two complementary principles, namely, knowledge source corroboration and belief enhancement/withdrawal, both typical of data-fusion approaches. The obtained CNN has been tested by simulations (i.e. by numerically integrating the circuit state equations) in some case studies. The quality of the results is good, as turns out from comparisons with some standard methods. Copyright (C) 2006 John Wiley & Sons, Ltd.
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