Bayesian Reconstruction Method Research Articles

SBL-LCGL: sparse Bayesian learning based on Laplace distribution for robust cone-beam x-ray luminescence computed tomography

Objective. To address the quality and accuracy issues in the distribution of nanophosphors (NPs) using Cone-beam x-ray luminescence computed tomography (CB-XLCT) by proposing a novel reconstruction strategy.Approach. This paper introduces a sparse Bayesian learning reconstruction method termed SBL-LCGL, which is grounded in the Lipschitz continuous gradient condition and the Laplace prior to overcome the ill-posed inverse problem inherent in CB-XLCT.Main results. The SBL-LCGL method has demonstrated its effectiveness in capturing the sparse features of NPs and mitigating the computational complexity associated with matrix inversion. Both numerical simulation andin vivoexperiments confirm that the method yields satisfactory imaging results regarding the position and shape of the targets.Significance. The advancements presented in this work are expected to enhance the clinical applicability of CB-XLCT, contributing to its broader adoption in medical imaging and diagnostics.

Bayesian reconstruction of 3D particle positions in high-seeding density flows

Abstract Measuring particles' three-dimensional (3D) positions using multi-camera images in fluid dynamics is critical for resolving spatiotemporally complex flows like turbulence and mixing. However, current methods are prone to errors due to camera noise, optical configuration and experimental setup limitations, and high seeding density, which compound to create fake measurements (ghost particles) and add noise and error to velocity estimations. We introduce a Bayesian Volumetric Reconstruction (BVR) method, addressing these challenges by using probability theory to estimate uncertainties in particle position predictions. Our method assumes a uniform distribution of particles within the reconstruction volume and employs a model mapping particle positions to observed camera images. We utilize variational inference with a modified loss function to determine the posterior distribution over particle positions. Key features include a penalty term to reduce ghost particles, provision of uncertainty bounds, and scalability through subsampling. In tests with synthetic data and four cameras, BVR achieved 95% accuracy with less than 3% ghost particles and an RMS error under 0.3 pixels at a density of 0.1 particles per pixel (ppp). This shows 57% to 97% less ghost particles and 1.3 to 2 times lower RMS error than standard MART and IPR reconstructions. In an experimental Poiseuille flow measurement, our method closely matched the theoretical solution. Additionally, in a complex cerebral aneurysm basilar tip geometry flow experiment, our reconstructions were dense and consistent with observed flow patterns. Our BVR method effectively reconstructs particle positions in complex 3D flows, particularly in situations with high particle image densities and camera distortions. It distinguishes itself by providing quantifiable uncertainty estimates and scaling efficiently for larger image dimensions, making it applicable across a range of fluid flow scenarios.

A data-driven approach for the partial reconstruction of individual human molar teeth using generative deep learning.

Due to the high prevalence of dental caries, fixed dental restorations are regularly required to restore compromised teeth or replace missing teeth while retaining function and aesthetic appearance. The fabrication of dental restorations, however, remains challenging due to the complexity of the human masticatory system as well as the unique morphology of each individual dentition. Adaptation and reworking are frequently required during the insertion of fixed dental prostheses (FDPs), which increase cost and treatment time. This article proposes a data-driven approach for the partial reconstruction of occlusal surfaces based on a data set that comprises 92 3D mesh files of full dental crown restorations. A Generative Adversarial Network (GAN) is considered for the given task in view of its ability to represent extensive data sets in an unsupervised manner with a wide variety of applications. Having demonstrated good capabilities in terms of image quality and training stability, StyleGAN-2 has been chosen as the main network for generating the occlusal surfaces. A 2D projection method is proposed in order to generate 2D representations of the provided 3D tooth data set for integration with the StyleGAN architecture. The reconstruction capabilities of the trained network are demonstrated by means of 4 common inlay types using a Bayesian Image Reconstruction method. This involves pre-processing the data in order to extract the necessary information of the tooth preparations required for the used method as well as the modification of the initial reconstruction loss. The reconstruction process yields satisfactory visual and quantitative results for all preparations with a root mean square error (RMSE) ranging from 0.02 mm to 0.18 mm. When compared against a clinical procedure for CAD inlay fabrication, the group of dentists preferred the GAN-based restorations for 3 of the total 4 inlay geometries. This article shows the effectiveness of the StyleGAN architecture with a downstream optimization process for the reconstruction of 4 different inlay geometries. The independence of the reconstruction process and the initial training of the GAN enables the application of the method for arbitrary inlay geometries without time-consuming retraining of the GAN.

A Bayesian approach for CT reconstruction with defect detection for subsea pipelines

Subsea pipelines can be inspected via 2D cross-sectional x-ray computed tomography (CT). Traditional reconstruction methods produce an image of the pipe’s interior that can be post-processed for detection of possible defects. In this paper we propose a novel Bayesian CT reconstruction method with built-in defect detection. We decompose the reconstruction into a sum of two images; one containing the overall pipe structure, and one containing defects, and infer the images simultaneously in a Gibbs scheme. Our method requires that prior information about the two images is very distinct, i.e. the first image should contain the large-scale and layered pipe structure, and the second image should contain small, coherent defects. We demonstrate our methodology with numerical experiments using synthetic and real CT data from scans of subsea pipes in cases with full and limited data. Experiments demonstrate the effectiveness of the proposed method in various data settings, with reconstruction quality comparable to existing techniques, while also providing defect detection with uncertainty quantification.

Testing Bayesian reconstruction methods from peculiar velocities

ABSTRACT Reconstructing the large-scale density and velocity fields from surveys of galaxy distances is a major challenge for cosmography. The data are very noisy and sparse. Estimated distances, and thereby peculiar velocities, are strongly affected by the Malmquist-like lognormal bias. Two algorithms have been recently introduced to perform reconstructions from such data: the Bias Gaussian correction coupled with the Wiener filter (BGc/WF) and the Hamlet implementation of the Hamiltonian Monte Carlo forward modelling. The two methods are tested here against mock catalogues that mimic the Cosmicflows-3 data. Specifically the reconstructed cosmography and moments of the velocity field (monopole, dipole) are examined. A comparison is made to the ‘exact’ WF as well, namely, the WF in the unrealistic case of zero observational errors. This is to understand the limits of the WF method. The following is found. In the nearby regime ($d \lesssim 40 \, \mathrm{ \mathit{ h}}^{-1}\, {\rm Mpc}$), the two methods perform roughly equally well. Hamlet shows more contrast in the intermediate regime ($40 \lesssim d \lesssim 120 \, h^{-1}\, {\rm Mpc}$). The main differences between the two appear in the most distant regime ($d \gtrsim 120 \, h^{-1}\, {\rm Mpc}$), close to the edge of the data. Hamlet outperforms the BGc/WF in terms of contrast and tighter correlations of the density and velocity fields. Yet, close to the edge of the data, Hamlet yields a slightly biased reconstruction, which affects the multipoles of the velocity field. Such biases are missing from the BGc/WF reconstruction. In sum, both methods perform well and create reliable reconstructions with significant differences apparent when details are examined.

Bayesian inference of real-time dynamics from lattice QCD

The computation of dynamical properties of nuclear matter, ranging from parton distribution functions of nucleons and nuclei to transport properties in the quark-gluon plasma, constitutes a central goal of modern theoretical physics. This real-time physics often defies a perturbative treatment and the most successful strategy so far is to deploy lattice QCD simulations. These numerical computations are based on Monte-Carlo sampling and formulated in an artificial Euclidean time. Real-time physics is most conveniently formulated in terms of spectral functions, which are hidden in lattice QCD behind an ill-posed inverse problem. I will discuss state-of-the art methods in the extraction of spectral functions from lattice QCD simulations, based on Bayesian inference and emphasize the importance of prior domain knowledge, vital to regularizing the otherwise ill-posed extraction task. With Bayesian inference allowing us to make explicit the uncertainty in both observations and in our prior knowledge, a systematic estimation of the total uncertainties in the extracted spectral functions is nowadays possible. Two implementations of the Bayesian Reconstruction (BR) method for spectral function extraction, one for MAP point estimates and one based on an open access Monte-Carlo sampler are provided. I will briefly touch on the use of machine learning for spectral function reconstruction and discuss some new insight it has brought to the Bayesian community.

A Bayesian level set method for the shape reconstruction of inverse scattering problems in elasticity

This paper is concerned with recovering the shape of the scatterer for the two-dimensional time-harmonic inverse scattering problem in elasticity. The level set method is used for representing the geometry shape of the scatterer. The Bayesian inference approach provides a natural framework in which we are able to formulate the inverse problem as a statistical inference problem. The priors for the level set functions are achieved via the Whittle-Matérn Gaussian random fields, and the Markov chain Monte Carlo (MCMC) method is applied to extract the information of the posterior distribution whose well-posedness would be discussed as well. Numerical experiments demonstrate the effectiveness of the proposed approach.

A Bayesian ILC Method for CMB B-mode Posterior Estimation and Reconstruction of Primordial Gravity Wave Signal

Abstract The cosmic microwave background (CMB) radiation B-mode polarization signal contains the unique signature of primordial metric perturbations produced during the inflation. The separation of the weak CMB B-mode signal from strong foreground contamination in observed maps is a complex task, and proposed new-generation low-noise satellite missions compete with the weak signal level of this gravitational background. In this paper, for the first time, we employ a foreground model-independent internal linear combination (ILC) method to reconstruct the CMB B-mode signal using simulated observations over large angular scales of the sky of six frequency bands of the future-generation CMB mission Probe of Inflation and Cosmic Origins (PICO). We estimate the joint CMB B-mode posterior density following the interleaving Gibbs steps of the B-mode angular power spectrum and cleaned map samples using the ILC method. We extend and improve the earlier reported Bayesian ILC method to analyze weak CMB B-mode reconstruction by introducing noise-bias corrections at two stages during the ILC weight estimation. By performing 200 Monte Carlo simulations of the Bayesian ILC method, we find that our method can reconstruct the CMB signals and the joint posterior density accurately over large angular scales of the sky. We estimate the Blackwell–Rao statistics of the marginal density of the CMB B-mode angular power spectrum and use them to estimate the joint density of the tensor-to-scalar ratio r and a lensing power spectrum amplitude A lens . Using 200 Monte Carlo simulations of the delensing approach, we find that our method can achieve an unbiased detection of the primordial gravitational-wave signal r with more than 8σ significance for levels of r ≥ 0.01 for input frequency maps with realistic lensing and foregrounds with constant spectral indices.

Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

Quantitative bone SPECT/CT reconstruction utilizing anatomical information

BackgroundBone SPECT/CT has been shown to offer superior sensitivity and specificity compared to conventional whole-body planar scanning. Furthermore, bone SPECT/CT allows quantitative imaging, which is challenging with planar methods. In order to gain better quantitative accuracy, Bayesian reconstruction algorithms, including both image derived and anatomically guided priors, have been utilized in reconstruction in PET/CT scanning, but they have not been widely used in SPECT/CT studies. Therefore, the aim of this work was to evaluate the performance of CT-guided reconstruction in quantitative bone SPECT.MethodsThree Bayesian reconstruction methods were evaluated against the conventional ordered subsets expectation maximization (OSEM) reconstruction method. One of the studied Bayesian methods was the relative difference prior (RDP), which has recently gained popularity in PET reconstruction. The other two methods, anatomically guided smoothing prior (AMAP-S) and anatomically guided relative difference prior (AMAP-R), utilized anatomical information from the CT scan. The reconstruction methods were evaluated in terms of quantitative accuracy with artificial lesions inserted in clinical patient studies and with 20 real clinical patients. Maximum and mean standardized uptake values (SUVs) of the lesions were defined.ResultsThe analyses showed that all studied Bayesian methods performed better than OSEM and the anatomical priors also outperformed RDP. The average relative error in mean SUV for the artificial lesion study for OSEM, RDP, AMAP-S, and AMAP-R was − 53%, − 35%, − 15%, and − 10%, when the CT study had matching lesions. In the patient study, the RDP method gave 16 ± 9% higher maximum SUV values than OSEM, while AMAP-S and AMAP-R offered increases of 36 ± 8% and 36 ± 9%, respectively. Mean SUV increased for RDP, AMAP-S, and AMAP-R by 18 ± 9%, 26 ± 5%, and 33 ± 5% when compared to OSEM.ConclusionsThe Bayesian methods with anatomical prior, especially the relative difference prior-based method (AMAP-R), outperformed OSEM and reconstruction without anatomical prior in terms of quantitative accuracy.

Iterative versus non-iterative image reconstruction methods for sparse magnetic resonance imaging.

Magnetic resonance imaging (MRI) using under-sampled k-space data is a common method to shorten the imaging time. Iterative Bayesian algorithms are usually used for its image reconstruction. This paper compares an iterative Bayesian image reconstruction method that uses both spatial and temporal constraints and a non-iterative reconstruction algorithm that does not use temporal constraints. Three patient studies are performed. It is interesting to notice that the images reconstructed by the iterative Bayesian algorithm may introduce more bias than the non-iterative algorithm, even though the images provided by the iterative Bayesian algorithm look less noisy. The bias can be reduced by decreasing the influence of the temporal constraints.

Towards the nucleon hadronic tensor from lattice QCD

We present the first calculation of the hadronic tensor on the lattice for the nucleon. The hadronic tensor can be used to extract the structure functions in deep inelastic scatterings and also provide information for the neutrino-nucleon scattering which is crucial to the neutrino-nucleus scattering experiments at low energies. The most challenging part in the calculation is to solve an inverse problem. We have implemented and tested three algorithms using mock data, showing that the Bayesian Reconstruction method has the best resolution in extracting peak structures while the Backus-Gilbert and Maximum Entropy methods are somewhat more stable for the flat spectral function. Numerical results are presented for both the elastic case (clover fermions on domain wall configuration with $m_\pi\sim$ 370 MeV and $a\sim$ 0.06 fm) and a case (anisotropic clover lattice with $m_\pi\sim$ 380 MeV and $a_t\sim$ 0.035 fm) with large momentum transfer. For the former case, the reconstructed Minkowski hadronic tensor gives precisely the vector charge which proves the feasibility of the approach. While for the latter case, the nucleon resonances and possibly shallow inelastic scattering contributions around $\nu=1$ GeV are clearly observed but no information is obtained for higher excited states with $\nu>2$ GeV. A check of the effective masses of $\rho$ meson with different lattice setups indicates that, in order to reach higher energy transfers, using lattices with smaller lattice spacings is essential.

Bayesian reconstruction method for underwater 3D range-gated imaging enhancement.

We investigate a systematic improvement for 3D range-gated imaging in scattering environments. Drawbacks including absorption, ambient light, and scattering effect are studied. The former two are compensated through parameter estimation and preprocessing. With regard to the scattering effect, we propose a new 3D reconfiguration algorithm using a Bayesian approach that incorporates spatial constraints through a general Gaussian Markov random field. The model takes both scene depth and albedo into account, which provides a more informative and accurate restoration result. Hyper-parameters for the statistical mechanism are evaluated adaptively in the procedure and an iterated conditional mode optimization algorithm is employed to find an optimum solution. The performance of our method was assessed via conducting various experiments and the results also indicate that the proposed method is helpful for restoring the 2D image of a scene with improved visibility.

Noise source identification of high-speed motion mechanism of textile equipment based on equivalent source method

In order to accurately identify the noise sources of high-end textile equipment and achieve noise control, this paper takes warp knitting machine as an example to accurately locate the main voice mechanism. Firstly, the stability and accuracy of traditional equivalent source method (TRESM) and Bayesian regularization criterion method for acoustic field reconstruction in different frequency bands are simulated and verified. Secondly, the accuracy of iterative reweighted least squares (IRLS) and steepest descent iteration equivalent source method (SDIESM) in medium- and high-frequency bands is verified. The results show that TRESM and Bayesian methods are suitable for the identification of medium- and low-frequency noise sources, and IRLS and SDIESM algorithms have better adaptability to complex sound fields. Bayesian method, IRLS and SDIESM algorithm can be used to identify the noise sources of broadband warp knitting machine. The main noise sources are spindle motor, pulling roller, spindle of loop forming mechanism and push rod of comb bar transverse mechanism, which provide theoretical support for active noise reduction of loom.

Jointly super-resolved and optically sectioned Bayesian reconstruction method for structured illumination microscopy.

Structured Illumination Microscopy (SIM) is an imaging technique for achieving both super-resolution (SR) and optical sectioning (OS) in wide-field microscopy. It consists in illuminating the sample with periodic patterns at different orientations and positions. The resulting images are then processed to reconstruct the observed object with SR and/or OS. In this work, we present BOSSA-SIM, a general-purpose SIM reconstruction method, applicable to moving objects such as encountered in in vivo retinal imaging, that enables SR and OS jointly in a fully unsupervised Bayesian framework. By modeling a 2-layer object composed of an in-focus layer and a defocused layer, we show that BOSSA-SIM is able to jointly reconstruct them so as to get a super-resolved and optically sectioned in-focus layer. The achieved performance, assessed quantitatively by simulations for several noise levels, compares favorably with a state-of-the-art method. Finally, we validate our method on open-access experimental microscopy data.

A diverse assemblage of RNA and DNA viruses found in mosquitoes collected in southern Portugal

This work describes the detection and partial characterization of mosquito-borne virus genomic sequences, based on the analysis of mosquitoes collected from the Spring to Fall of 2018 in the Algarve (southern Portugal). The viral survey that was carried out using multiple primer sets disclosed the presence of both RNA and DNA viral sequences in these mosquitoes, which were subsequently analysed using maximum likelihood and Bayesian phylogenetic reconstruction methods. The obtained results brought to light three lineages of insect-specific flaviviruses, a monophyletic cluster of bunyaviruses from an unassigned group within the Phenuiviridae family, as well as brevidensoviruses (Parvoviridae, Densovirinae:). The latter two groups of viruses were here described for the first time in mosquitoes from Portugal. Results relating to the tentative isolation of the putative viruses identified in C6/36 cells are also shown, and the serendipitous, although not unexpected, isolation a Negev-like Nelorpivirus from Culex laticinctcus mosquitoes is reported.

Auditory entrainment of motor responses in older adults with and without Parkinson’s disease: An MEG study

Medical therapies applied to Parkinson’s disease (PD) have advanced tremendously since the 1960’s based on advances in our understanding of the underlying neurophysiology. Behavioral therapies, such as rhythmic auditory stimulation (RAS), have been developed more recently and demonstrated efficacy. However, the neural mechanisms of RAS are only vaguely understood. In this study, we examined the neurophysiology of RAS using magnetoencephalography (MEG) in a sample of older adults with (21 people) and without PD (23 participants). All participants underwent high-density MEG during a beat-based cued tapping task with rhythmic and non-rhythmic patterns, and the resulting data were analyzed using a Bayesian image reconstruction method. Complex wavelet based time-frequency decomposition was used to compute inter-trial phase locking factor (PLF) to auditory stimuli for left and right signal space projection vectors. Tapping with a rhythm compared to a non-rhythmic sequence resulted in differential brain activity in each group: (i) a greater activation of temporal, motor and parietal areas was found in healthy adults; (ii) a greater reliance on parietal and frontal gyri was found in PD participants. During rhythmic tapping, older adults without PD had significantly stronger neural activity in bilateral frontal, supplementary and primary motor areas compared to those with PD. Conversely, older adults with PD exhibited significantly stronger activity in the bilateral parietal regions, as well as the rolandic operculum and bilateral supramarginal gyri, relative to their healthy peers. These data suggest that RAS mobilizes diverse oscillatory networks; Healthy controls may shift to frontal areas mobilization whereas PD patients rely on parietal areas to a greater extent, which may reflect frontal network dysfunction with compensation in PD, and could serve as specific regions of interest for further RAS studies.

A non-negative Bayesian learning method for impact force reconstruction

Detecting and identifying impact events, which may cause severe damages, is important in assessment of the integrity of many engineering structures. This paper presents a new approach for reconstructing the impact forces applied on engineering structures (e.g., composites) using sensor recordings of the structural responses. The problem is firstly formulated as a discretized deconvolution problem in the time domain with the impact force vector as the unknown. Then with consideration of the physical property of the impact force, an inverse analysis approach of Bayesian learning with non-negative regularization constraints is employed to solve the ill-posed deconvolution problem. The newly proposed impact force reconstruction approach is illustrated by experimental examples performed on a sandwich composite structure. Results have demonstrated the effectiveness and applicability of the proposed approach to reconstruct impact forces.

Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain.

In this paper, a hierarchical prior model based on the Haar transformation and an appropriate Bayesian computational method for X-ray CT reconstruction are presented. Given the piece-wise continuous property of the object, a multilevel Haar transformation is used to associate a sparse representation for the object. The sparse structure is enforced via a generalized Student-t distribution (), expressed as the marginal of a normal-inverse Gamma distribution. The proposed model and corresponding algorithm are designed to adapt to specific 3D data sizes and to be used in both medical and industrial Non-Destructive Testing (NDT) applications. In the proposed Bayesian method, a hierarchical structured prior model is proposed, and the parameters are iteratively estimated. The initialization of the iterative algorithm uses the parameters of the prior distributions. A novel strategy for the initialization is presented and proven experimentally. We compare the proposed method with two state-of-the-art approaches, showing that our method has better reconstruction performance when fewer projections are considered and when projections are acquired from limited angles.

Transversal and Longitudinal Gluon Spectral Functions from Twisted Mass Lattice QCD with Nf = 2 + 1 + 1 Flavors

I report on the first application of a novel, generalized Bayesian reconstruction (BR) method for spectral functions to the characterization of QCD constituents. These spectral functions find applications in off-shell kinetics of the quark-gluon plasma and in calculations of transport coefficients. The new BR method is applied to Euclidean propagator data, obtained in Landau gauge on lattices with $N_f=2+1+1$ dynamical flavors by the "twisted mass at finite temperature" (tmfT) collaboration. The deployed reconstruction method is designed for spectral functions that can exhibit positivity violation (opposed to that of hadronic bound states). The transversal and longitudinal gluon spectral functions show a robust structure composed of quasiparticle peak and a negative trough. Characteristic differences between the hadronic and the plasma phase and between the two channels become visible. We obtain the temperature dependence of the transversal and longitudinal gluon masses.