Variational posterior distribution approximation in bayesian emission tomography reconstruction using a gamma mixture prior
نویسندگان
چکیده
Following the Bayesian framework we propose a method to reconstruct emission tomography images which uses gamma mixture prior and variational methods to approximate the posterior distribution of the unknown parameters and image instead of estimating them by using the Evidence Analysis or alternating between the estimation of parameters and image (Iterated Conditional Mode (ICM)) approach. By analyzing the posterior distribution approximation we can examine the quality of the proposed estimates. The method is tested on real Single Positron Emission Tomography (SPECT) images.
منابع مشابه
Joint-MAP Reconstruction/Segmentation for Transmission Tomography Using Mixture-Models as Priors
A Bayesian method, including a pointwise prior comprising mixtures of gamma distributions, is applied to the problem of transmission tomography. A joint MAP (maximum a posteriori) procedure is proposed wherein the reconstruction itself, as well as all pointwise parameters, are calculated simultaneously. It uses an algorithm that successively refines the estimate of the mixture parameters and th...
متن کاملEstimating the periodic components of a biomedical signal through inverse problem modelling and Bayesian inference with sparsity enforcing prior
Abstract : The recent developments in chronobiology need a periodic components (PC) variation analysis for the signals expressing the biological rhythms. A precise estimation of the periodic components vector is required. The classical approaches, based on FFT methods, are inefficient considering the particularities of the data (short length). In this poster we propose a new method, using the s...
متن کاملBayesian Inference Tools for Inverse Problems
In this paper, first the basics of the Bayesian inference for linear inverse problems are presented. The inverse problems we consider are, for example, signal deconvolution, image restoration or image reconstruction in Computed Tomography (CT). The main point to discuss then is the prior modeling of signals and images. We consider two classes of priors: simple or hierarchical with hidden variab...
متن کاملBayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions
In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using variou...
متن کاملBayesian 3D X-ray Computed Tomography image reconstruction with a Scaled Gaussian Mixture prior model
In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is...
متن کامل