Image recovery from Fourier domain measurements via classification using Bayesian approach and total variation regularization

Chama, Zouaouia; Mansouri, Boualem; Anani, M.; Mohammad-Djafari, Ali

doi:10.1016/j.aeue.2012.03.008

Cited by 7 publications

(4 citation statements)

References 7 publications

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“…In the traditional way, clustering approaches, such fuzzy mean, are used to achieve image segmentation [2] and many manually created low-level features, like pixel value distribution and gradient histogram, can be clustered using a genetic algorithm [3]. In image segmentation, probabilistic techniques are also frequently employed [4]− [6]. In [7] a framework for regression segmentation is proposed is proposed for detection of vascular abnormalities in cardiac magnetic resonance imaging by delimiting the two ventricles' boundaries.…”

Section: Introductionmentioning

confidence: 99%

Adaptive segmentation algorithm based on level set model in medical imaging

Mansouri¹,

Khobzaoui²,

Damou³

et al. 2023

TELKOMNIKA

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For image segmentation, level set models are frequently employed. It offer best solution to overcome the main limitations of deformable parametric models. However, the challenge when applying those models in medical images stills deal with removing blurs in image edges which directly affects the edge indicator function, leads to not adaptively segmenting images and causes a wrong analysis of pathologies wich prevents to conclude a correct diagnosis. To overcome such issues, an effective process is suggested by simultaneously modelling and solving systems' two-dimensional partial differential equations (PDE). The first PDE equation allows restoration using Euler's equation similar to an anisotropic smoothing based on a regularized Perona and Malik filter that eliminates noise while preserving edge information in accordance with detected contours in the second equation that segments the image based on the first equation solutions. This approach allows developing a new algorithm which overcome the studied model drawbacks. Results of the proposed method give clear segments that can be applied to any application. Experiments on many medical images in particular blurry images with high information losses, demonstrate that the developed approach produces superior segmentation results in terms of quantity and quality compared to other models already presented in previeous works.

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Section: Introductionmentioning

confidence: 99%

Adaptive segmentation algorithm based on level set model in medical imaging

Mansouri¹,

Khobzaoui²,

Damou³

et al. 2023

TELKOMNIKA

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“…Many applications are found in image processing (Giovannelli and Idier, 2015;Zhu et al, 2011;Cai et al, 2011;Chama et al, 2012;Nissinen et al, 2011;Kozawa et al, 2012, for example), but there are great variety of applications in many fields as in geothermal prospection (Cui et al, 2011(Cui et al, , 2019, network analysis (Hazelton, 2010;Sun et al, 2015), heat transfer (Kaipio and Fox, 2011), pollution and ecology (Keats et al, 2010;Hutchinson et al, 2017), fusion physics (Osthus et al, 2019), tumor growth (Collis et al, 2017;Kahle et al, 2019), to mention a few. As with most terms, "UQ" has a level of arbitrariness: indeed, all of statistics is partly concerned with quantifying uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Error Control of the Numerical Posterior with Bayes Factors in Bayesian Uncertainty Quantification

et al. 2022

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In this paper, we address the numerical posterior error control problem for the Bayesian approach to inverse problems or recently known as Bayesian Uncertainty Quantification (UQ). We generalize the results of Capistrán et al. (2016) to (a priori) expected Bayes factors (BF) and in a more general, infinitedimensional setting. In this inverse problem, the unavoidable numerical approximation of the Forward Map (FM, i.e., the regressor function), arising from the numerical solution of a system of differential equations, demands error estimates of the corresponding approximate numerical posterior distribution. Our approach is to make such comparisons in the setting of Bayesian model selection and BFs. The main result of this paper is a bound on the absolute global error tolerated by the numerical solver of the FM in order to keep the BF of the numerical versus the theoretical posterior near one. For two examples, we provide a detailed analysis of the computation and implementation of the introduced bound. Furthermore, we show that the resulting numerical posterior turns out to be nearly identical from the theoretical posterior, given the control of the BF near one.

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“…Schwab and Stuart, 2012) that provide a sound theoretical background to the field. There are several applications in the (Bayesian dominated) field of image processing of various kinds (Zhu et al, 2011;Cai et al, 2011;Fall et al, 2011;Chama et al, 2012;Kolehmainen et al, 2007;Nissinen et al, 2011;Kozawa et al, 2012, to mention some recent references), and also we find a whole range of emerging application areas in the Bayesian Analysis of inverse problems (Calvetti et al, 2006;Keats et al, 2010;Cui et al, 2011;Wan and Zabaras, 2011;Hazelton, 2010;Kaipio and Fox, 2011). However, only a handful of publications mentions or uses Bayesian predicting tools, that is, the posterior (predictive) distribution of yet to observe variables (Vehtari and Lampinen, 2000;Somersalo et al, 2003;Kaipio and Fox, 2011;Capistrán et al, 2012), and even less consider formally the model selection and model comparison tools developed in Bayesian statistics.…”

Section: Introduction 1context and Issuesmentioning

confidence: 99%

Bayesian Analysis of ODEs: Solver Optimal Accuracy and Bayes Factors

Capistrán¹,

Christen²,

Donnet³

2016

SIAM/ASA J. Uncertainty Quantification

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In most relevant cases in the Bayesian analysis of ODE inverse problems, a numerical solver needs to be used. Therefore, we cannot work with the exact theoretical posterior distribution but only with an approximate posterior deriving from the error in the numerical solver. To compare a numerical and the theoretical posterior distributions we propose to use Bayes Factors (BF), considering both of them as models for the data at hand. We prove that the theoretical vs a numerical posterior BF tends to 1, in the same order (of the step size used) as the numerical forward map solver does. For higher order solvers (eg. Runge-Kutta) the Bayes Factor is already nearly 1 for step sizes that would take far less computational effort. Considerable CPU time may be saved by using coarser solvers that nevertheless produce practically error free posteriors. Two examples are presented where nearly 90% CPU time is saved while all inference results are identical to using a solver with a much finer time step.

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Image recovery from Fourier domain measurements via classification using Bayesian approach and total variation regularization

Cited by 7 publications

References 7 publications

Adaptive segmentation algorithm based on level set model in medical imaging

Adaptive segmentation algorithm based on level set model in medical imaging

Error Control of the Numerical Posterior with Bayes Factors in Bayesian Uncertainty Quantification

Bayesian Analysis of ODEs: Solver Optimal Accuracy and Bayes Factors

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