Joint Super-Resolution and segmentation from a set of Low Resolution images using a Bayesian approach with a Gauss-Markov-Potts Prior

Mansouri, Majdi; Mohammad-Djafari, Ali

doi:10.1504/ijsise.2010.038017

Cited by 4 publications

(3 citation statements)

References 32 publications

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“…For each of these prior models, we discuss their properties and the way to use them in a Bayesian approach resulting to many different inversion algorithms. We have applied these Bayesian algorithms in many different applications such as X-ray computed tomography [35,36], optical diffraction tomography [37][38][39], positron emission tomography [40], Microwave imaging [41,42], Sources separation [43][44][45][46], spectrometry [47,48], Hyper spectral imaging [49], super resolution [50][51][52], image fusion [53], image segmentation [54], synthetic aperture radar (SAR) imaging [29]. To save the place and be very synthetic, we did not give here any simulation results or any results on different applications of these methods.…”

Section: Resultsmentioning

confidence: 99%

Bayesian approach with prior models which enforce sparsity in signal and image processing

Mohammad-Djafari

2012

EURASIP J. Adv. Signal Process.

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In this review article, we propose to use the Bayesian inference approach for inverse problems in signal and image processing, where we want to infer on sparse signals or images. The sparsity may be directly on the original space or in a transformed space. Here, we consider it directly on the original space (impulsive signals). To enforce the sparsity, we consider the probabilistic models and try to give an exhaustive list of such prior models and try to classify them. These models are either heavy tailed (generalized Gaussian, symmetric Weibull, Student-t or Cauchy, elastic net, generalized hyperbolic and Dirichlet) or mixture models (mixture of Gaussians, Bernoulli-Gaussian, Bernoulli-Gamma, mixture of translated Gaussians, mixture of multinomial, etc.). Depending on the prior model selected, the Bayesian computations (optimization for the joint maximum a posteriori (MAP) estimate or MCMC or variational Bayes approximations (VBA) for posterior means (PM) or complete density estimation) may become more complex. We propose these models, discuss on different possible Bayesian estimators, drive the corresponding appropriate algorithms, and discuss on their corresponding relative complexities and performances.

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Section: Resultsmentioning

confidence: 99%

Bayesian approach with prior models which enforce sparsity in signal and image processing

Mohammad-Djafari

2012

EURASIP J. Adv. Signal Process.

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“…The samples are generated directly following Equation (). The choice of modeling the noise variance as an inverse γ distribution has been guided by existing works such as Ayasso and Mohammad‐Djafari 36 and Mansouri and Mohammad‐Djafari 37 …”

Section: Methodsmentioning

confidence: 99%

Marmoset brain segmentation from deconvolved magnetic resonance images and estimated label maps

Bazzi

Mescam

Diab

et al. 2021

Magnetic Resonance in Med

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Purpose The proposed method aims to create label maps that can be used for the segmentation of animal brain MR images without the need of a brain template. This is achieved by performing a joint deconvolution and segmentation of the brain MR images. Methods It is based on modeling locally the image statistics using a generalized Gaussian distribution (GGD) and couples the deconvolved image and its corresponding labels map using the GGD‐Potts model. Because of the complexity of the resulting Bayesian estimators of the unknown model parameters, a Gibbs sampler is used to generate samples following the desired posterior probability. Results The performance of the proposed algorithm is assessed on simulated and real MR images by the segmentation of enhanced marmoset brain images into its main compartments using the corresponding label maps created. Quantitative assessment showed that this method presents results that are comparable to those obtained with the classical method—registering the volumes to a brain template. Conclusion The proposed method of using labels as prior information for brain segmentation provides a similar or a slightly better performance compared with the classical reference method based on a dedicated template.

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“…Typically, this depends on the SISR model used and on the accurate choice of its hyperparameters. To overcome these limitations, a joint SR and IP approach performing both tasks at the same time has been proposed, e.g., in [10,6,3] based on a Bayesian approach.…”

Section: Introductionmentioning

confidence: 99%

Constrained and Unconstrained Inverse Potts Modelling for Joint Image Super-Resolution and Segmentation

Mylonopoulos¹,

Cascarano²,

Calatroni³

et al. 2022

Image Processing on Line

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In this work we consider two methods for joint single-image super-resolution and image partitioning. The proposed approaches rely on a constrained and on an unconstrained version of the inverse Potts model where an 0 regularization prior on the image gradient is used for promoting piecewise constant solutions. For the numerical solution of both models, we provide a unified implementation based on the Alternating Direction Method of Multipliers (ADMM). Upon suitable assumptions on both model operators and on the algorithmic parameters involved, we show that all the ADMM subproblems admit closed-form solutions, thus making the resulting algorithms computationally very cheap even when high-dimensional data are considered. Numerical details of the implementation of both models are given and several experiments are carried out on both synthetic and natural images to underline the accuracy and the computational efficiency of the models. Source CodeThe Matlab source code, the code online documentation and the online demo are available from the web page of this article 1 . Compilation and usage instruction are included in the README.txt file of the archive.

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Joint Super-Resolution and segmentation from a set of Low Resolution images using a Bayesian approach with a Gauss-Markov-Potts Prior

Cited by 4 publications

References 32 publications

Bayesian approach with prior models which enforce sparsity in signal and image processing

Bayesian approach with prior models which enforce sparsity in signal and image processing

Marmoset brain segmentation from deconvolved magnetic resonance images and estimated label maps

Constrained and Unconstrained Inverse Potts Modelling for Joint Image Super-Resolution and Segmentation

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