182 research outputs found

    Bayesian model comparison for compartmental models with applications in positron emission tomography

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    We develop strategies for Bayesian modelling as well as model comparison, averaging and selection for compartmental models with particular emphasis on those that occur in the analysis of positron emission tomography (PET) data. Both modelling and computational issues are considered. Biophysically inspired informative priors are developed for the problem at hand, and by comparison with default vague priors it is shown that the proposed modelling is not overly sensitive to prior specification. It is also shown that an additive normal error structure does not describe measured PET data well, despite being very widely used, and that within a simple Bayesian framework simultaneous parameter estimation and model comparison can be performed with a more general noise model. The proposed approach is compared with standard techniques using both simulated and real data. In addition to good, robust estimation performance, the proposed technique provides, automatically, a characterisation of the uncertainty in the resulting estimates which can be considerable in applications such as PET

    Singular value decomposition analysis of back projection operator of maximum likelihood expectation maximization PET image reconstruction.

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    Background In emission tomography maximum likelihood expectation maximization reconstruction technique has replaced the analytical approaches in several applications. The most important drawback of this iterative method is its linear rate of convergence and the corresponding computational burden. Therefore, simplifications are usually required in the Monte Carlo simulation of the back projection step. In order to overcome these problems, a reconstruction code has been developed with graphical processing unit based Monte Carlo engine which enabled full physical modelling in the back projection. Materials and methods Code performance was evaluated with simulations on two geometries. One is a sophisticated scanner geometry which consists of a dodecagon with inscribed circle radius of 8.7 cm, packed on each side with an array of 39 × 81 LYSO detector pixels of 1.17 mm sided squares, similar to a Mediso nanoScan PET/CT scanner. The other, simplified geometry contains a 38,4mm long interval as a voxel space, detector pixels are assigned in two parallel sections each containing 81 crystals of a size 1.17×1.17 mm. Results We have demonstrated that full Monte Carlo modelling in the back projection step leads to material dependent inhomogeneities in the reconstructed image. The reasons behind this apparently anomalous behaviour was analysed in the simplified system by means of singular value decomposition and explained by different speed of convergence. Conclusions To still take advantage of the higher noise stability of the full physical modelling, a new filtering technique is proposed for convergence acceleration. Some theoretical considerations for the practical implementation and for further development are also presented

    Postreconstruction filtering of 3D PET images by using weighted higher-order singular value decomposition

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    Additional file 1. Original 3D PET images data used in this work to generate the results

    Toward Automatic Model Comparison: An Adaptive Sequential Monte Carlo Approach

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    Model comparison for the purposes of selection, averaging, and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a particular class. Substantial progress has been made in recent years, but difficulties remain in the implementation of existing schemes. This article presents adaptive sequential Monte Carlo (SMC) sampling strategies to characterize the posterior distribution of a collection of models, as well as the parameters of those models. Both a simple product estimator and a combination of SMC and a path sampling estimator are considered and existing theoretical results are extended to include the path sampling variant. A novel approach to the automatic specification of distributions within SMC algorithms is presented and shown to outperform the state of the art in this area. The performance of the proposed strategies is demonstrated via an extensive empirical study. Comparisons with state-of-the-art algorithms show that the proposed algorithms are always competitive, and often substantially superior to alternative techniques, at equal computational cost and considerably less application-specific implementation effort. Supplementary materials for this article are available online.AJ was supported by EPSRC grant EP/I017984/1; JA by EPSRC grant EP/K021672/1 and the EPSRC/HEFCE CRiSM grant

    Segmentation of skin lesions in 2D and 3D ultrasound images using a spatially coherent generalized Rayleigh mixture model

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    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

    The node-wise pseudo-marginal method : model selection with spatial dependence on latent graphs

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    Motivated by problems from neuroimaging in which existing approaches make use of “mass univariate” analysis which neglects spatial structure entirely, but the full joint modelling of all quantities of interest is computationally infeasible, a novel method for incorporating spatial dependence within a (potentially large) family of model-selection problems is presented. Spatial dependence is encoded via a Markov random field model for which a variant of the pseudo-marginal Markov chain Monte Carlo algorithm is developed and extended by a further augmentation of the underlying state space. This approach allows the exploitation of existing unbiased marginal likelihood estimators used in settings in which spatial independence is normally assumed thereby facilitating the incorporation of spatial dependence using non-spatial estimates with minimal additional development effort. The proposed algorithm can be realistically used for analysis of moderately sized data sets such as 2D slices of whole 3D dynamic PET brain images or other regions of interest. Principled approximations of the proposed method, together with simple extensions based on the augmented spaces, are investigated and shown to provide similar results to the full pseudo-marginal method. Such approximations and extensions allow the improved performance obtained by incorporating spatial dependence to be obtained at negligible additional cost. An application to measured PET image data shows notable improvements in revealing underlying spatial structure when compared to current methods that assume spatial independence

    Markov random field image modelling

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    Includes bibliographical references.This work investigated some of the consequences of using a priori information in image processing using computer tomography (CT) as an example. Prior information is information about the solution that is known apart from measurement data. This information can be represented as a probability distribution. In order to define a probability density distribution in high dimensional problems like those found in image processing it becomes necessary to adopt some form of parametric model for the distribution. Markov random fields (MRFs) provide just such a vehicle for modelling the a priori distribution of labels found in images. In particular, this work investigated the suitability of MRF models for modelling a priori information about the distribution of attenuation coefficients found in CT scans
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