A Hyper-parameter Inference for Radon Transformed Image Reconstruction Using Bayesian Inference

2010 ◽  
pp. 26-33 ◽  
Author(s):  
Hayaru Shouno ◽  
Masato Okada
Keyword(s):  
Bayesian Inference ◽  
Image Reconstruction ◽  
Parameter Inference

Low-count PET image reconstruction with Bayesian inference over a Deep Prior

2021 ◽  
Author(s):  
Hernan Camilo Carrillo Lindado ◽  
Maël Millardet ◽  
Thomas Carlier ◽  
Diana Mateus
Keyword(s):  
Bayesian Inference ◽  
Image Reconstruction ◽  
Pet Image Reconstruction

scholarly journals A Bayesian Hyperparameter Inference for Radon-Transformed Image Reconstruction

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Hayaru Shouno ◽  
Madomi Yamasaki ◽  
Masato Okada
Keyword(s):  
Bayesian Inference ◽  
Image Reconstruction ◽  
Prior Information ◽  
Additive White Gaussian Noise ◽  
Estimation Accuracy ◽  
Reconstruction Method ◽  
Model Framework ◽  
Poissonian Noise ◽  
Observation Noise

We develop a hyperparameter inference method for image reconstruction from Radon transform which often appears in the computed tomography, in the manner of Bayesian inference. Hyperparameters are often introduced in Bayesian inference to control the strength ratio between prior information and the fidelity to the observation. Since the quality of the reconstructed image is controlled by the estimation accuracy of these hyperparameters, we apply Bayesian inference into the filtered back-projection (FBP) reconstruction method with hyperparameters inference and demonstrate that the estimated hyperparameters can adapt to the noise level in the observation automatically. In the computer simulation, at first, we show that our algorithm works well in the model framework environment, that is, observation noise is an additive white Gaussian noise case. Then, we also show that our algorithm works well in the more realistic environment, that is, observation noise is Poissonian noise case. After that, we demonstrate an application for the real chest CT image reconstruction under the Gaussian and Poissonian observation noises.

scholarly journals Evaluation of a new image reconstruction method for digital breast tomosynthesis: effects on the visibility of breast lesions and breast density

2019 ◽  
Vol 92 (1103) ◽  
pp. 20190345 ◽  
Author(s):  
Julia Krammer ◽  
Sergei Zolotarev ◽  
Inge Hillman ◽  
Konstantinos Karalis ◽  
Dzmitry Stsepankou ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Image Reconstruction ◽  
Image Quality ◽  
Breast Density ◽  
Breast Imaging ◽  
Reconstruction Method ◽  
Back Projection ◽  
Filtered Back Projection ◽  
Breast Tomosynthesis

Objective: To compare image quality and breast density of two reconstruction methods, the widely-used filtered-back projection (FBP) reconstruction and the iterative heuristic Bayesian inference reconstruction (Bayesian inference reconstruction plus the method of total variation applied, HBI). Methods: Thirty-two clinical DBT data sets with malignant and benign findings, n = 27 and 17, respectively, were reconstructed using FBP and HBI. Three experienced radiologists evaluated the images independently using a 5-point visual grading scale and classified breast density according to the American College of Radiology Breast Imaging-Reporting And Data System Atlas, fifth edition. Image quality metrics included lesion conspicuity, clarity of lesion borders and spicules, noise level, artifacts surrounding the lesion, visibility of parenchyma and breast density. Results: For masses, the image quality of HBI reconstructions was superior to that of FBP in terms of conspicuity,clarity of lesion borders and spicules (p < 0.01). HBI and FBP were not significantly different in calcification conspicuity. Overall, HBI reduced noise and supressed artifacts surrounding the lesions better (p < 0.01). The visibility of fibroglandular parenchyma increased using the HBI method (p < 0.01). On average, five cases per radiologist were downgraded from BI-RADS breast density category C/D to A/B. Conclusion: HBI significantly improves lesion visibility compared to FBP. HBI-visibility of breast parenchyma increased, leading to a lower breast density rating. Applying the HBIR algorithm should improve the diagnostic performance of DBT and decrease the need for additional imaging in patients with dense breasts. Advances in knowledge: Iterative heuristic Bayesian inference (HBI) image reconstruction substantially improves the image quality of breast tomosynthesis leading to a better visibility of breast carcinomas and reduction of the perceived breast density compared to the widely-used filtered-back projection (FPB) reconstruction. Applying HBI should improve the accuracy of breast tomosynthesis and reduce the number of unnecessary breast biopsies. It may also reduce the radiation dose for the patients, which is especially important in the screening context.

scholarly journals Two case studies detailing Bayesian parameter inference for dynamic energy budget models

2018 ◽  
Author(s):  
Philipp H. Boersch-Supan ◽  
Leah R. Johnson
Keyword(s):  
Bayesian Inference ◽  
Case Studies ◽  
Energy Budget ◽  
Open Source Software ◽  
Prior Information ◽  
Model Parameters ◽  
Parameter Inference ◽  
Dynamic Energy Budget ◽  
Full Life Cycle ◽  
Open Source Software Package

AbstractMechanistic representations of individual life-history trajectories are powerful tools for the prediction of organismal growth, reproduction and survival under novel environmental conditions. Dynamic energy budget (DEB) theory provides compact models to describe the acquisition and allocation of energy by organisms over their full life cycle. However, estimating DEB model parameters, and their associated uncertainties and covariances, is not trivial. Bayesian inference provides a coherent way to estimate parameter uncertainty, and propagate it through the model, while also making use of prior information to constrain the parameter space. We outline a Bayesian inference approach for energy budget models and provide two case studies – based on a simplified DEBkiss model, and the standard DEB model – detailing the implementation of such inference procedures using the open-source software package deBInfer. We demonstrate how DEB and DEBkiss parameters can be estimated in a Bayesian framework, but our results also highlight the difficulty of identifying DEB model parameters which serves as a reminder that fitting these models requires statistical caution.

scholarly journals Evidence for the null hypothesis in functional magnetic resonance imaging using group-level Bayesian inference

2021 ◽  
Author(s):  
Ruslan Masharipov ◽  
Yaroslav Nikolaev ◽  
Alexander Korotkov ◽  
Michael Didur ◽  
Denis Cherednichenko ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Sample Size ◽  
Null Hypothesis ◽  
Bayesian Model ◽  
Significance Testing ◽  
Large Sample Size ◽  
Null Hypothesis Significance Testing ◽  
Parameter Inference ◽  
Effect Assessment ◽  
Null Effect

Classical null hypothesis significance testing is limited to the rejection of the point-null hypothesis; it does not allow the interpretation of non-significant results. Moreover, studies with a sufficiently large sample size will find statistically significant results even when the effect is negligible and may be considered practically equivalent to the null effect. This leads to a publication bias against the null hypothesis. There are two main approaches to assess null effects: shifting from the point-null to the interval-null hypothesis and considering the practical significance in the frequentist approach; using the Bayesian parameter inference based on posterior probabilities, or the Bayesian model inference based on Bayes factors. Herein, we discuss these statistical methods with particular focus on the application of the Bayesian parameter inference, as it is conceptually connected to both frequentist and Bayesian model inferences. Although Bayesian methods have been theoretically elaborated and implemented in commonly used neuroimaging software, they are not widely used for null effect assessment. To demonstrate the advantages of using the Bayesian parameter inference, we compared it with classical null hypothesis significance testing for fMRI data group analysis. We also consider the problem of choosing a threshold for a practically significant effect and discuss possible applications of Bayesian parameter inference in fMRI studies. We argue that Bayesian inference, which directly provides evidence for both the null and alternative hypotheses, may be more intuitive and convenient for practical use than frequentist inference, which only provides evidence against the null hypothesis. Moreover, it may indicate that the obtained data are not sufficient to make a confident inference. Because interim analysis is easy to perform using Bayesian inference, one can evaluate the data as the sample size increases and decide to terminate the experiment if the obtained data are sufficient to make a confident inference. To facilitate the application of the Bayesian parameter inference to null effect assessment, scripts with a simple GUI were developed.

Holographic SAR Tomography Image Reconstruction by Combination of Adaptive Imaging and Sparse Bayesian Inference

2017 ◽  
Vol 14 (8) ◽  
pp. 1248-1252 ◽  
Author(s):  
Qian Bao ◽  
Yun Lin ◽  
Wen Hong ◽  
Wenjie Shen ◽  
Yue Zhao ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Image Reconstruction ◽  
Adaptive Imaging ◽  
Tomography Image

scholarly journals Comparing inclination-dependent analyses of kilonova transients

2021 ◽  
Vol 502 (2) ◽  
pp. 3057-3065
Author(s):  
J Heinzel ◽  
M W Coughlin ◽  
T Dietrich ◽  
M Bulla ◽  
S Antier ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Neutron Star ◽  
Gravitational Wave ◽  
Inclination Angle ◽  
Soft Constraints ◽  
Parameter Inference ◽  
Binary Neutron Star ◽  
Wave Measurements ◽  
Inclination Angles ◽  
Optical Transient

ABSTRACT The detection of the optical transient AT2017gfo proved that binary neutron star mergers are progenitors of kilonovae (KNe). Using a combination of numerical-relativity and radiative-transfer simulations, the community has developed sophisticated models for these transients for a wide portion of the expected parameter space. Using these simulations and surrogate models made from them, it has been possible to perform Bayesian inference of the observed signals to infer properties of the ejected matter. It has been pointed out that combining inclination constraints derived from the KN with gravitational-wave measurements increases the accuracy with which binary parameters can be estimated, in particular breaking the distance-inclination degeneracy from gravitational wave inference. To avoid bias from the unknown ejecta geometry, constraints on the inclination angle for AT2017gfo should be insensitive to the employed models. In this work, we compare different assumptions about the ejecta and radiative reprocesses used by the community and we investigate their impact on the parameter inference. While most inferred parameters agree, we find disagreement between posteriors for the inclination angle for different geometries that have been used in the current literature. According to our study, the inclusion of reprocessing of the photons between different ejecta types improves the modeling fits to AT2017gfo and, in some cases, affects the inferred constraints. Our study motivates the inclusion of large ∼ 1-mag uncertainties in the KN models employed for Bayesian analysis to capture yet unknown systematics, especially when inferring inclination angles, although smaller uncertainties seem appropriate to capture model systematics for other intrinsic parameters. We can use this method to impose soft constraints on the ejecta geometry of the KN AT2017gfo.

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