Graduated nonconvexity algorithm for image estimation using compound Gauss Markov field models

Simchony, T.; Chellappa, Rama; Lichtenstein, Z.

doi:10.1109/icassp.1989.266704

Cited by 20 publications

(18 citation statements)

References 8 publications

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“…The weak membrane [10], in the regularization setup, and the compound Gauss Markov random field [9], in the Bayesian setup, were conceived to model piecewise-smooth images. Algorithms [10], [25]- [27], and [28] are but a few examples using piecewise-smooth priors. By signaling boundaries between smooth regions with discrete random variables, the so-called line field, these priors improve the modeling accuracy near the edges in comparison with the classical quadratic ones.…”

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confidence: 99%

Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors

Bioucas-Dias¹

2006

IEEE Trans. on Image Process.

162

173

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Abstract-Image deconvolution is formulated in the wavelet domain under the Bayesian framework. The well-known sparsity of the wavelet coefficients of real-world images is modeled by heavy-tailed priors belonging to the Gaussian scale mixture (GSM) class; i.e., priors given by a linear (finite of infinite) combination of Gaussian densities. This class includes, among others, the generalized Gaussian, the Jeffreys, and the Gaussian mixture priors. Necessary and sufficient conditions are stated under which the prior induced by a thresholding/shrinking denoising rule is a GSM. This result is then used to show that the prior induced by the "nonnegative garrote" thresholding/shrinking rule, herein termed the garrote prior, is a GSM. To compute the maximum a posteriori estimate, we propose a new generalized expectation maximization (GEM) algorithm, where the missing variables are the scale factors of the GSM densities. The maximization step of the underlying expectation maximization algorithm is replaced with a linear stationary second-order iterative method. The result is a GEM algorithm of ( log ) computational complexity. In a series of benchmark tests, the proposed approach outperforms or performs similarly to state-of-the art methods, demanding comparable (in some cases, much less) computational complexity.

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confidence: 99%

Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors

Bioucas-Dias¹

2006

IEEE Trans. on Image Process.

162

173

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“…with k i (r(n) r(n ; 1)) = k i (r(n)) for k = 1 : : : 4 , and 5 i (r(n) r(n ; 1)) = 1 2 kr i (n) ; r i (n ; 1)k 2 (20) where k( )k stands for Euclidian norm.…”

Section: A Modeling Image Sequencesmentioning

confidence: 99%

Wall position and thickness estimation from sequences of echocardiographic images

Dias

Leitao

1996

IEEE Trans. Med. Imaging

130

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This paper presents a new method for endocardial (inner) and epicardial (outer) contour estimation from sequences of echocardiographic images. The framework herein introduced is ne-tuned for parasternal short axis views at the papillary muscle level. The underlying model is probabilistic it captures the relevant features of the image generation physical mechanisms and of the heart morphology. Contour sequences are assumed two-dimensional noncausal rst order Markov random processes each variable has a spatial index and a temporal index. The image pixels are modelled as Rayleigh distributed random variables with means depending on their positions (inside endocardium, between endocardium and pericardium, or outside pericardium). The complete probabilistic model is built under the Bayesian framework. As estimation criterion the maximum a posteriori (MAP) is adopted. To solve the optimization problem one is led to (joint estimation of contours and distributions' parameters), we introduce an algorithm herein named iterative multigrid dynamic programming (IMDP). It is a fully data driven scheme with no ad-hoc parameters. The method is implemented on an ordinary workstation, leading to computation times compatible with operational use. Experiments with simulated and real images are presented.Key words: Echocardiography, Contour Estimation, Bayesian, Dynamic Programming. 1Refererence 1] is a short version of this work.

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“…In practice, the (intensity) MRF described above is often used together with a line field that characterizes the line structure in an image to form a coupled MRF. (4) can be reduced and simplified into a set of independent model parameters, thereby overcoming the second difficulty described above. In other words, after the parameter reduction, various and 21, is similarly defined.…”

Section: Introductionmentioning

confidence: 99%

Parameter reduction for the compound Gauss-Markov model

Zhang¹

1995

IEEE Trans. on Image Process.

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The efficacy of the compound Gauss-Markov (CGM) model, initially proposed by Jeng and Woods (1990), has been demonstrated in several image processing applications. However, parameter estimation for the CGM model is difficult since it is not clear as to how the constraints or interdependence amongst the model parameters can be incorporated into the estimation procedures. As result, the parameter estimates tend to be inconsistent. It is shown that, under some reasonable symmetry constraints, the 80 interdependent parameters of the CGM model can be reduced to seven independent ones. This guarantees the consistency of model parameters obtained from parameter estimation algorithms, thereby removing a main obstacle for the parameter estimation of the CGM model.

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Graduated nonconvexity algorithm for image estimation using compound Gauss Markov field models

Cited by 20 publications

References 8 publications

Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors

Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors

Wall position and thickness estimation from sequences of echocardiographic images

Parameter reduction for the compound Gauss-Markov model

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