An iterative Gibbsian technique for reconstruction of m-ary images

Chalmond, Bernard

doi:10.1016/0031-3203(89)90011-3

Cited by 121 publications

(73 citation statements)

References 10 publications

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“…Starting from a positive solution, the algorithm iterates until convergence, although the rate of converge is slow. Considering the unsatisfactory results of the maximum likelihood estimation, [3,13,21,23,25] shows that the noise in the reconstructions occurs when climbing the likelihood hill towards the maximum, a result which agrees with the experiments presented by [4,5]. An extension of their work was the iterative algorithm suggested by [2] which includes a penalty function controlling the smoothness of the reconstruction.…”

Section: Estimation Algorithmsupporting

confidence: 62%

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Modified Maximum Likelihood Estimation of the Spatial Resolution for the Elliptical Gamma Camera SPECT Imaging Using Binary Inhomogeneous Markov Random Fields Models

Zimeras¹

2013

ACT

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In this work a complete approach for estimation of the spatial resolution for the gamma camera imaging based on the [1] is analyzed considering where the body distance is detected (close or far way). The organ of interest most of the times is not well defined, so in that case it is appropriate to use elliptical camera detection instead of circular. The image reconstruction is presented which allows spatially varying amounts of local smoothing. An inhomogeneous Markov random field (M.r.f.) model is described which allows spatially varying degrees of smoothing in the reconstructions and a re-parameterization is proposed which implicitly introduces a local correlation structure in the smoothing parameters using a modified maximum likelihood estimation (MLE) denoted as one step late (OSL) introduced by [2].

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Section: Estimation Algorithmsupporting

confidence: 62%

“…Previously, various authors [3][4][5] had adopted maximum likelihood approaches with only moderate success. The prior model and data likelihood are combined to give the posterior distributions on which estimation is based.…”

Section: Introductionmentioning

confidence: 99%

Modified Maximum Likelihood Estimation of the Spatial Resolution for the Elliptical Gamma Camera SPECT Imaging Using Binary Inhomogeneous Markov Random Fields Models

Zimeras¹

2013

ACT

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“…The most widely used general method is the so-called ''Expectation-Maximization'' (EM) method [20]; however, its implementation in the hidden Markov fields context is difficult [6,20,24] and some alternative methods have been proposed [3,9,15,17,24,34,35]. In particular, one may consider Stochastic Gradient (SG [35]), whose aim is to approach the maximum of the likelihood p (y) in a stochastic manner to remedy the difficulties encountered by EM.…”

Section: Parameter Estimationmentioning

confidence: 99%

Unsupervised image segmentation using triplet Markov fields

Benboudjema¹,

Pieczynski²

2005

Computer Vision and Image Understanding

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Hidden Markov fields (HMF) models are widely applied to various problems arising in image processing. In these models, the hidden process of interest X is a Markov field and must be estimated from its observable noisy version Y. The success of HMF is mainly due to the fact that the conditional probability distribution of the hidden process with respect to the observed one remains Markovian, which facilitates different processing strategies such as Bayesian restoration. HMF have been recently generalized to ''pairwise'' Markov fields (PMF), which offer similar processing advantages and superior modeling capabilities. In PMF one directly assumes the Markovianity of the pair (X, Y). Afterwards, ''triplet'' Markov fields (TMF), in which the distribution of the pair (X, Y) is the marginal distribution of a Markov field (X, U, Y), where U is an auxiliary process, have been proposed and still allow restoration processing. The aim of this paper is to propose a new parameter estimation method adapted to TMF, and to study the corresponding unsupervised image segmentation methods. The latter are validated via experiments and real image processing.

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“…A major difficulty in applying the EM algorithm to MRFs is in the calculation of the conditional expectation, which is generally intractable because it requires summing over all possible configurations. Therefore, approximation techniques such as the mean field approximation (Celeux et al, 2003;Tonazzini et al, 2006;Zhang, 1992) and pseudo-likelihood method (Chalmond, 1989;Zhang et al, 1994) are used. The EM algorithm has been extended for parameter estimation on a quadtree (Bouman and Shapiro, 1994;Laferté et al, 2000).…”

Section: Related Workmentioning

confidence: 99%

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

Zhang¹

2007

Bull. Math. Biol.

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Cell membranes display a range of receptors that bind ligands and activate signaling pathways. Signaling is characterized by dramatic changes in membrane molecular topography, including the co-clustering of receptors with signaling molecules and the segregation of other signaling molecules away from receptors. Electron microscopy of immunogold-labeled membranes is a critical technique to generate topographical information at the 5-10 nm resolution needed to understand how signaling complexes assemble and function. However, due to experimental limitations, only two molecular species can usually be labeled at a time. A formidable challenge is to integrate experimental data across multiple experiments where there are from 10 to 100 different proteins and lipids of interest and only the positions of two species can be observed simultaneously. As a solution, we propose the use of Markov random field (MRF) modeling to reconstruct the distribution of multiple cell membrane constituents from pair-wise data sets. MRFs are a powerful mathematical formalism for modeling correlations between states associated with neighboring sites in spatial lattices. The presence or absence of a protein of a specific type at a point on the cell membrane is a state. Since only two protein types can be observed, i.e., those bound to particles, and the rest cannot be observed, the problem is one of deducing the conditional distribution of a MRF with unobservable (hidden) states. Here, we develop a multiscale MRF model and use mathematical programming techniques to infer the conditional distribution of a MRF for proteins of three types from observations showing the spatial relationships between only two types. Application to synthesized data shows that the spatial distributions of three proteins can be reliably estimated. Application to experimental data provides the first maps of the spatial relationship between groups of three different signaling molecules. The work is an important step toward a more complete understanding of membrane spatial organization and dynamics during signaling.

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An iterative Gibbsian technique for reconstruction of m-ary images

Cited by 121 publications

References 10 publications

Modified Maximum Likelihood Estimation of the Spatial Resolution for the Elliptical Gamma Camera SPECT Imaging Using Binary Inhomogeneous Markov Random Fields Models

Modified Maximum Likelihood Estimation of the Spatial Resolution for the Elliptical Gamma Camera SPECT Imaging Using Binary Inhomogeneous Markov Random Fields Models

Unsupervised image segmentation using triplet Markov fields

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

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