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

A Combined Noise Reduction and Partial Volume Estimation Method for Image Quantitation

Abstract- The partial volume effect is a corrupting artifact that affects nuclear imaging data such as PET and SPECT data, manifest as a blurring action on the resultant image data. This artifact is a result of the image acquisition process, where voxels in the PET or SPECT images are typically composed of a mixture of activity concentrations. This prevents accurate localization and quantitation of the target region activity. A further well-known image artifact found in most types of signal and image data is additive noise which is caused by limited photon count statistics for PET or SPECT imaging data. This work presents a novel methodology for statistically combining image noise reduction and partial volume estimation with particular application to low contrast to noise ratio image data, e.g. image data with poor target localization. Each possible partial volume mixture is modeled as a Gaussian distribution and neighborhood statistical information is also incorporated in the form of the voxel neighborhood intensity mean, which has previously been shown to also be Gaussian distributed. This leads to an analytical solution of the optimal expected mean (thus minimizing the mean square loss), providing an equation that can iteratively and adaptively reduce the noise in each image voxel. Once the noise is reduced a further step that estimates the partial volume mixtures using an adaptive Markov Chain Monte Carlo method is found to improve the partial volume estimates in comparison to existing partial volume estimation techniques without a noise reduction step

Approche variationnelle pour le calcul bay\'esien dans les probl\`emes inverses en imagerie

In a non supervised Bayesian estimation approach for inverse problems in imaging systems, one tries to estimate jointly the unknown image pixels $f$ and the hyperparameters $\theta$ given the observed data $g$ and a model $M$ linking these quantities. This is, in general, done through the joint posterior law $p(f,\theta|g;M)$. The expression of this joint law is often very complex and its exploration through sampling and computation of the point estimators such as MAP and posterior means need either optimization of or integration of multivariate probability laws. In any of these cases, we need to do approximations. Laplace approximation and sampling by MCMC are two approximation methods, respectively analytical and numerical, which have been used before with success for this task. In this paper, we explore the possibility of approximating this joint law by a separable one in $f$ and in $\theta$. This gives the possibility of developing iterative algorithms with more reasonable computational cost, in particular, if the approximating laws are choosed in the exponential conjugate families. The main objective of this paper is to give details of different algorithms we obtain with different choices of these families. To illustrate more in detail this approach, we consider the case of image restoration by simple or myopic deconvolution with separable, simple markovian or hidden markovian models.Comment: 31 pages, 2 figures, had been submitted to "Revue Traitement du signal", but not accepte

Combining spatial priors and anatomical information for fMRI detection

In this paper, we analyze Markov Random Field (MRF) as a spatial regularizer in fMRI detection. The low signal-to-noise ratio (SNR) in fMRI images presents a serious challenge for detection algorithms, making regularization necessary to achieve good detection accuracy. Gaussian smoothing, traditionally employed to boost SNR, often produces over-smoothed activation maps. Recently, the use of MRF priors has been suggested as an alternative regularization approach. However, solving for an optimal configuration of the MRF is NP-hard in general. In this work, we investigate fast inference algorithms based on the Mean Field approximation in application to MRF priors for fMRI detection. Furthermore, we propose a novel way to incorporate anatomical information into the MRF-based detection framework and into the traditional smoothing methods. Intuitively speaking, the anatomical evidence increases the likelihood of activation in the gray matter and improves spatial coherency of the resulting activation maps within each tissue type. Validation using the receiver operating characteristic (ROC) analysis and the confusion matrix analysis on simulated data illustrates substantial improvement in detection accuracy using the anatomically guided MRF spatial regularizer. We further demonstrate the potential benefits of the proposed method in real fMRI signals of reduced length. The anatomically guided MRF regularizer enables significant reduction of the scan length while maintaining the quality of the resulting activation maps.National Institutes of Health (U.S.) (National Institute for Biomedical Imaging and Bioengineering (U.S.)/National Alliance for Medical Image Computing (U.S.) Grant U54-EB005149)National Science Foundation (U.S.) (Grant IIS 9610249)National Institutes of Health (U.S.) (National Center for Research Resources (U.S.)/Biomedical Informatics Research Network Grant U24-RR021382)National Institutes of Health (U.S.) (National Center for Research Resources (U.S.)/Neuroimaging Analysis Center (U.S.) Grant P41-RR13218)National Institutes of Health (U.S.) (National Institute of Neurological Disorders and Stroke (U.S.) Grant R01-NS051826)National Science Foundation (U.S.) (CAREER Grant 0642971)National Science Foundation (U.S.). Graduate Research FellowshipNational Center for Research Resources (U.S.) (FIRST-BIRN Grant)Neuroimaging Analysis Center (U.S.