156 research outputs found
Estimating the granularity coefficient of a Potts-Markov random field within an MCMC algorithm
This paper addresses the problem of estimating the Potts parameter B jointly
with the unknown parameters of a Bayesian model within a Markov chain Monte
Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem
because performing inference on B requires computing the intractable
normalizing constant of the Potts model. In the proposed MCMC method the
estimation of B is conducted using a likelihood-free Metropolis-Hastings
algorithm. Experimental results obtained for synthetic data show that
estimating B jointly with the other unknown parameters leads to estimation
results that are as good as those obtained with the actual value of B. On the
other hand, assuming that the value of B is known can degrade estimation
performance significantly if this value is incorrect. To illustrate the
interest of this method, the proposed algorithm is successfully applied to real
bidimensional SAR and tridimensional ultrasound images
Adaptive Markov random fields for joint unmixing and segmentation of hyperspectral image
Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm
Segmentation of skin lesions in 2D and 3D ultrasound images using a spatially coherent generalized Rayleigh mixture model
This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images
Gradient Scan Gibbs Sampler: an efficient algorithm for high-dimensional Gaussian distributions
This paper deals with Gibbs samplers that include high dimensional
conditional Gaussian distributions. It proposes an efficient algorithm that
avoids the high dimensional Gaussian sampling and relies on a random excursion
along a small set of directions. The algorithm is proved to converge, i.e. the
drawn samples are asymptotically distributed according to the target
distribution. Our main motivation is in inverse problems related to general
linear observation models and their solution in a hierarchical Bayesian
framework implemented through sampling algorithms. It finds direct applications
in semi-blind/unsupervised methods as well as in some non-Gaussian methods. The
paper provides an illustration focused on the unsupervised estimation for
super-resolution methods.Comment: 18 page
Bayesian Inference for Inverse Problems
Inverse problems arise everywhere we have indirect measurement. Regularization and Bayesian inference methods are two main approaches to handle inverse problems. Bayesian inference approach is more general and has much more tools for developing efficient methods for difficult problems. In this chapter, first, an overview of the Bayesian parameter estimation is presented, then we see the extension for inverse problems. The main difficulty is the great dimension of unknown quantity and the appropriate choice of the prior law. The second main difficulty is the computational aspects. Different approximate Bayesian computations and in particular the variational Bayesian approximation (VBA) methods are explained in details
Sampling high-dimensional Gaussian distributions for general linear inverse problems
International audienceThis paper is devoted to the problem of sampling Gaussian distributions in high dimension. Solutions exist for two specific structures of inverse covariance: sparse and circulant. The proposed algorithm is valid in a more general case especially as it emerges in linear inverse problems as well as in some hierarchical or latent Gaussian models. It relies on a perturbation-optimization principle: adequate stochastic perturbation of a criterion and optimization of the perturbed criterion. It is proved that the criterion optimizer is a sample of the target distribution. The main motivation is in inverse problems related to general (non-convolutive) linear observation models and their solution in a Bayesian framework implemented through sampling algorithms when existing samplers are infeasible. It finds a direct application in myopic,unsupervised inversion methods as well as in some non-Gaussian inversion methods. An illustration focused on hyperparameter estimation for super-resolution method shows the interest and the feasibility of the proposed algorithm
Task adapted reconstruction for inverse problems
The paper considers the problem of performing a task defined on a model
parameter that is only observed indirectly through noisy data in an ill-posed
inverse problem. A key aspect is to formalize the steps of reconstruction and
task as appropriate estimators (non-randomized decision rules) in statistical
estimation problems. The implementation makes use of (deep) neural networks to
provide a differentiable parametrization of the family of estimators for both
steps. These networks are combined and jointly trained against suitable
supervised training data in order to minimize a joint differentiable loss
function, resulting in an end-to-end task adapted reconstruction method. The
suggested framework is generic, yet adaptable, with a plug-and-play structure
for adjusting both the inverse problem and the task at hand. More precisely,
the data model (forward operator and statistical model of the noise) associated
with the inverse problem is exchangeable, e.g., by using neural network
architecture given by a learned iterative method. Furthermore, any task that is
encodable as a trainable neural network can be used. The approach is
demonstrated on joint tomographic image reconstruction, classification and
joint tomographic image reconstruction segmentation
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