Bayesian Reconstruction Algorithm Research Articles

Contributed Session II: Computational modeling of shift in unique yellow for small stimuli.

Unique yellow (UY) is largely invariant to L:M cone proportion for spatially-extended stimuli in healthy trichromats. However, a recent adaptive-optics-based study by Boehm et al. reveals that when stimulus size is reduced to a few arcmin, color appearance depends on the local L:M proportion in the patch of the retina on which the stimulus was imaged. We aimed to determine if such findings are consistent with a normative account of visual processing. A series of 3.5 and 10 arcmin stimuli were simulated as isoluminant mixtures of 540 and 680 nm primaries. We modeled sensory encoding under adaptive-optics conditions using the open-source software ISETBio, for simulated retinal cone mosaics with varying local L:M proportions. The resultant cone excitations were decoded using a Bayesian image reconstruction algorithm (Zhang et al., 2022). For the 3.5 arcmin stimuli, as local L:M proportion decreased, the 540 nm component of the reconstructions increased relative to the 680 nm component. This is qualitatively consistent with the experimental observations of Boehm et al. For 10 arcmin stimuli, in contrast, reconstructions were stable across variation in local L:M cone proportion. Notably, reconstructions depend not only on the local L:M cone proportion, but also on the proportion in the immediately surrounding retina, leading to a testable prediction. The computational observations frame the experimental results as a normative consequence of visual processing.

Bayesian Reconstruction Algorithms for Low-Dose Computed Tomography Are Not Yet Suitable in Clinical Context.

Computed tomography (CT) is a widely used examination technique that usually requires a compromise between image quality and radiation exposure. Reconstruction algorithms aim to reduce radiation exposure while maintaining comparable image quality. Recently, unsupervised deep learning methods have been proposed for this purpose. In this study, a promising sparse-view reconstruction method (posterior temperature optimized Bayesian inverse model; POTOBIM) is tested for its clinical applicability. For this study, 17 whole-body CTs of deceased were performed. In addition to POTOBIM, reconstruction was performed using filtered back projection (FBP). An evaluation was conducted by simulating sinograms and comparing the reconstruction with the original CT slice for each case. A quantitative analysis was performed using peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM). The quality was assessed visually using a modified Ludewig's scale. In the qualitative evaluation, POTOBIM was rated worse than the reference images in most cases. A partially equivalent image quality could only be achieved with 80 projections per rotation. Quantitatively, POTOBIM does not seem to benefit from more than 60 projections. Although deep learning methods seem suitable to produce better image quality, the investigated algorithm (POTOBIM) is not yet suitable for clinical routine.

Bayesian reconstruction of dark matter distribution from peculiar velocities: accounting for inhomogeneous Malmquist bias

ABSTRACT We present a Bayesian velocity field reconstruction algorithm that performs the reconstruction of the mass density field using only peculiar velocity data. Our method consistently accounts for the inhomogeneous Malmquist (IHM) bias using analytical integration along the line of sight. By testing our method on a simulation, we show that our method gives an unbiased reconstruction of the velocity field. We show that not accounting for the IHM bias can lead to significant biases in the Bayesian reconstructions. We applied our method to a peculiar velocity data set consisting of the SFI++ and 2MTF Tully–Fisher catalogues and the A2 supernovae compilation, thus obtaining a novel velocity reconstruction in the local Universe. Our velocity reconstructions have a cosmological power spectrum consistent with the theoretical expectation. Furthermore, we obtain a full description of the uncertainties on reconstruction through samples of the posterior distribution. We validate our velocity reconstruction of the local Universe by comparing it to an independent reconstruction using the 2M++ galaxy catalogue, obtaining good agreement between the two reconstructions. Using Bayesian model comparison, we find that our velocity model performs better than the adaptive kernel smoothed velocity with the same peculiar velocity data. However, our velocity model does not perform as well as the velocity reconstruction from the 2M++ galaxy catalogue, due to the sparse and noisy nature of the peculiar velocity tracer samples. The method presented here provides a way to include peculiar velocity data in initial condition reconstruction frameworks.

Uncertainty and source term reconstruction with environmental air samples

Environmental air sampling is one of the principal monitoring technologies employed for the verification of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). By combining the analysis of environmental samples with Atmospheric Transport and Dispersion Modelling (ATDM), and using a Bayesian source reconstruction algorithm, an estimate of the release location, duration, and quantity can be computed.Bayesian source reconstruction uses an uncertainty distribution of the input parameters, or priors, in a statistical framework to produce posterior probability estimates of the event parameters. The quality of the event reconstruction directly depends on the accuracy of the prior uncertainty distribution. With many of the input parameters, the selection of the uncertainty distribution is not difficult. However, with environmental samples, there is one component of the uncertainty at the interface between sample measurements and the ATDM that has been overlooked. Typically, a much smaller volume or quantity of material is sampled from the much larger domain represented in the ATDM. By examining the response of a dense network of radionuclide detectors on the West Coast of Canada during the passage of the Fukushima debris plume, an initial estimate of this uncertainty was determined to be between 20% and 30% depending on sample integration time.

Flat-field multiplexed multifocal structured illumination super-resolution microscopy

Multifocal structured illumination microscopy (MSIM) can achieve optically sectioned images with twice the diffraction limited resolution at an imaging speed of 1 Hz and an imaging depth of up to 50 μm. Compared with the traditional wide-field SIM, the MSIM has greater imaging depth and optical sectionning ability, and it is more suitable for long-term three-dimensional (3D) super-resolution imaging of living thick samples. However, the MSIM has some problems, such as slow imaging speed and complex image post-processing process. In this work, a fast super-resolution imaging method and system based on the flat-field multiplexed MSIM (FM-MSIM) is proposed. By inserting a beam shaping device into the illumination light path, the Gaussian beam is reshaped into a uniform flat-top profile, thereby improving the intensity uniformity of excitation multi-spot focal array and expanding the field of view. By elongating each diffraction limited excitation focal point four times along the <i>Y</i> direction to form a new multiplexed multifocal array pattern, the number of scanning steps is reduced, the energy utilization is improved, and then the imaging speed and signal-to-noise ratio are improved. Combined with the sparse Bayesian learning image reconstruction algorithm based on multiple measurement vector model, the image reconstruction steps are simplified, the imaging speed can be improved at least 4 times while ensuring the spatial resolution of MSIM. On this basis, the established FM-MSIM system is used to carry out the super-resolution imaging experiments on the BSC cell microtubule samples and mouse kidney slices. The experimental results prove the fast three-dimensional super-resolution imaging ability of the system, which is of great significance in developing the fast MSIM.

CodEx: A Modular Framework for Joint Temporal De-Blurring and Tomographic Reconstruction

In many computed tomography (CT) imaging applications, it is important to rapidly collect data from an object that is moving or changing with time. Tomographic acquisition is generally assumed to be step-and-shoot, where the object is rotated to each desired angle, and a view is taken. However, step-and-shoot acquisition is slow and can waste photons, so in practice fly-scanning is done where the object is continuously rotated while collecting data. However, this can result in motion-blurred views and consequently reconstructions with severe motion artifacts. In this paper, we introduce CodEx, a modular framework for joint de-blurring and tomographic reconstruction that can effectively invert the motion blur introduced in sparse view fly-scanning. The method is a synergistic combination of a novel acquisition method with a novel non-convex Bayesian reconstruction algorithm. CodEx works by encoding the acquisition with a known binary code that the reconstruction algorithm then inverts. Using a well chosen binary code to encode the measurements can improve the accuracy of the inversion process. The CodEx reconstruction method uses the alternating direction method of multipliers (ADMM) to split the inverse problem into iterative deblurring and reconstruction sub-problems, making reconstruction practical to implement. We present reconstruction results on both simulated and binned experimental data to demonstrate the effectiveness of our method.

Changes of [18F]FDG-PET/CT quantitative parameters in tumor lesions by the Bayesian penalized-likelihood PET reconstruction algorithm and its influencing factors

BackgroundTo compare the changes in quantitative parameters and the size and degree of 18F-fluorodeoxyglucose ([18F]FDG) uptake of malignant tumor lesions between Bayesian penalized-likelihood (BPL) and non-BPL reconstruction algorithms.MethodsPositron emission tomography/computed tomography images of 86 malignant tumor lesions were reconstructed using the algorithms of ordered subset expectation maximization (OSEM), OSEM + time of flight (TOF), OSEM + TOF + point spread function (PSF), and BPL. [18F]FDG parameters of maximum standardized uptake value (SUVmax), SUVmean, metabolic tumor volume (MTV), total lesion glycolysis (TLG), and signal-to-background ratio (SBR) of these lesions were measured. Quantitative parameters between the different reconstruction algorithms were compared, and correlations between parameter variation and lesion size or the degree of [18F]FDG uptake were analyzed.ResultsAfter BPL reconstruction, SUVmax, SUVmean, and SBR were significantly increased, MTV was significantly decreased. The difference values of %ΔSUVmax, %ΔSUVmean, %ΔSBR, and the absolute value of %ΔMTV between BPL and OSEM + TOF were 40.00%, 38.50%, 33.60%, and 33.20%, respectively, which were significantly higher than those between BPL and OSEM + TOF + PSF. Similar results were observed in the comparison of OSEM and OSEM + TOF + PSF with BPL. The %ΔSUVmax, %ΔSUVmean, and %ΔSBR were all significantly negatively correlated with the size and degree of [18F]FDG uptake in the lesions, whereas significant positive correlations were observed for %ΔMTV and %ΔTLG.ConclusionThe BPL reconstruction algorithm significantly increased SUVmax, SUVmean, and SBR and decreased MTV of tumor lesions, especially in small or relatively hypometabolic lesions.

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.

Robust estimation of noise for electromagnetic brain imaging with the champagne algorithm

Robust estimation of the number, location, and activity of multiple correlated brain sources has long been a challenging task in electromagnetic brain imaging from M/EEG data, one that is significantly impacted by interference from spontaneous brain activity, sensor noise, and other sources of artifacts. Recently, we introduced the Champagne algorithm, a novel Bayesian inference algorithm that has shown tremendous success in M/EEG source reconstruction. Inherent to Champagne and most other related Bayesian reconstruction algorithms is the assumption that the noise covariance in sensor data can be estimated from “baseline” or “control” measurements. However, in many scenarios, such baseline data is not available, or is unreliable, and it is unclear how best to estimate the noise covariance. In this technical note, we propose several robust methods to estimate the contributions to sensors from noise arising from outside the brain without the need for additional baseline measurements. The incorporation of these methods for diagonal noise covariance estimation improves the robust reconstruction of complex brain source activity under high levels of noise and interference, while maintaining the performance features of Champagne. Specifically, we show that the resulting algorithm, Champagne with noise learning, is quite robust to initialization and is computationally efficient. In simulations, performance of the proposed noise learning algorithm is consistently superior to Champagne without noise learning. We also demonstrate that, even without the use of any baseline data, Champagne with noise learning is able to reconstruct complex brain activity with just a few trials or even a single trial, demonstrating significant improvements in source reconstruction for electromagnetic brain imaging.

Characterization of tissue-specific pre-log Bayesian CT reconstruction by texture-dose relationship.

Tissue textures have been recognized as biomarkers for various clinical tasks. In computed tomography (CT) image reconstruction, it is important but challenging to preserve the texture when lowering x-ray exposure from full- toward low-/ultra-low dose level. Therefore, this paper aims to explore the texture-dose relationship within one tissue-specific pre-log Bayesian CT reconstruction algorithm. To enhance the texture in ultra-low dose CT (ULdCT) reconstruction, this paper presents a Bayesian type algorithm. A shifted Poisson model is adapted to describe the statistical properties of pre-log data, and a tissue-specific Markov random field prior (MRFt) is used to incorporate tissue texture from previous full-dose CT, thus called SP-MRFt algorithm. Utilizing the SP-MRFt algorithm, we investigated tissue texture degradation as a function of x-ray dose levels from full dose (100mAs/120kVp) to ultralow dose (1mAs/120kVp) by using quantitative texture-based evaluation metrics. Experimental results show the SP-MRFt algorithm outperforms conventional filtered back projection (FBP) and post-log domain penalized weighted least square MRFt (PWLS-MRFt) in terms of noise suppression and texture preservation. Comparable results are also obtained with shifted Poisson model with 7×7 Huber MRF weights (SP-Huber7). The investigation on texture-dose relationship shows that the quantified texture measures drop monotonically as dose level decreases, and interestingly a turning point is observed on the texture-dose response curve. This important observation implies that there exists a minimum dose level, at which a given CT scanner (hardware configuration and image reconstruction software) can achieve without compromising clinical tasks. Moreover, the experiment results show that the variance of electronic noise has higher impact than the mean to the texture-dose relationship.

Impact of the Q.Clear reconstruction algorithm on the interpretation of PET/CT images in patients with lymphoma

BackgroundQ.Clear is a new Bayesian penalized-likelihood PET reconstruction algorithm. It has been documented that Q.Clear increases the SUVmax values of different malignant lesions.PurposeSUVmax values are crucial for the interpretation of PET/CT images in patients with lymphoma, particularly when the early and final responses to treatment are evaluated. The aim of the study was to systematically analyse the impact of the use of Q.Clear on the interpretation of PET/CT in patients with lymphoma.MethodsA total of 280 18F-FDG PET/CT scans in patients with lymphoma were performed for staging (sPET), for early treatment response (iPET), after the end of treatment (ePET) and when a relapse of lymphoma was suspected (rPET). Scans were separately reconstructed with two algorithms, Q.Clear and OSEM, and further compared.ResultsThe stage of lymphoma was concordantly diagnosed in 69/70 patients with both algorithms on sPET. Discordant assessment of the Deauville score (p < 0.001) was found in 11 cases (15.7%) of 70 iPET scans and in 11 cases of 70 ePET scans. An upgrade from a negative to a positive scan by Q.Clear occurred in 3 cases (4.3%) of iPET scans and 7 cases (10.0%) of ePET scans. The results of all 70 rPET scans were concordant. The SUVmax values of the target lymphoma lesions measured with Q.Clear were higher than those measured with OSEM in 88.8% of scans.ConclusionAlthough the Q.Clear algorithm may alter the interpretations of PET/CT in only a small proportion of patients, we recommend using standard OSEM reconstruction for the assessment of treatment response.

Process Monitoring of Antisolvent Based Crystallization in Low Conductivity Solutions Using Electrical Impedance Spectroscopy and 2-D Electrical Resistance Tomography

Industrial process monitoring is an important field of research where different chemical processes are monitored and controlled. In this work, electrical impedance spectroscopy (EIS) was used to analyze antisolvent based crystallization of sucrose solutions. The impedance and phase spectra were recorded for four known sucrose concentrations in water, and for each case, four predetermined amounts of ethanol were added. As a result, sixteen different solutions involving sucrose solutions of different concentrations and ethanol to water ratios were analyzed. Significant differences were observed in the magnitude and phase spectra of the solutions in the frequency range of 50 kHz to 300 kHz. The experimentally obtained data from the EIS were converted into frequency response models. Three continuous-time transfer function models of the first-order, second-order, and a second-order with a zero were estimated and compared. In addition, a 2-D electrical resistance tomography (ERT) system with a low conductivity sensor unit was designed and tested with demineralized water, tap water and industrial food grade saturated sucrose solution. Non-conducting phantom and sugar crystals were observed within the saturated sucrose solution using the Bayesian reconstruction algorithm. These demonstrations have the potential to be developed into a multi-frequency ERT systems for monitoring the distribution of the crystals in the reactor. The EIS modality can be a complementary process analytical technology (PAT) tool indicating supersaturation status and provide quality assurance.

Bayesian High Resolution Range Profile Reconstruction of High-speed Moving Target from Under-sampled Data.

Obtained by wide band radar system, high resolution range profile (HRRP) is the projection of scatterers of target to the radar line-of-sight (LOS). HRRP reconstruction is unavoidable for inverse synthetic aperture radar (ISAR) imaging, and of particular usage for target recognition, especially in cases that the ISAR image of target is not able to be achieved. For the high-speed moving target, however, its HRRP is stretched by the high order phase error. To obtain well-focused HRRP, the phase error induced by target velocity should be compensated, utilizing either measured or estimated target velocity. Noting in case of under-sampled data, the traditional velocity estimation and HRRP reconstruction algorithms become invalid, a novel HRRP reconstruction of high-speed target for under-sampled data is proposed. The Laplacian scale mixture (LSM) is used as the sparse prior of HRRP, and the variational Bayesian inference is utilized to derive its posterior, so as to reconstruct it with high resolution from the under-sampled data. Additionally, during the reconstruction of HRRP, the target velocity is estimated via joint constraint of entropy minimization and sparseness of HRRP to compensate the high order phase error brought by the target velocity to concentrate HRRP. Experimental results based on both simulated and measured data validate the effectiveness of the proposed Bayesian HRRP reconstruction algorithm.

Noise reduction using a Bayesian penalized-likelihood reconstruction algorithm on a time-of-flight PET-CT scanner

PurposeQ.Clear is a block sequential regularized expectation maximization (BSREM) penalized-likelihood reconstruction algorithm for PET. It tries to improve image quality by controlling noise amplification during image reconstruction. In this study, the noise properties of this BSREM were compared to the ordered-subset expectation maximization (OSEM) algorithm for both phantom and patient data acquired on a state-of-the-art PET/CT.MethodsThe NEMA IQ phantom and a whole-body patient study were acquired on a GE DMI 3-rings system in list mode and different datasets with varying noise levels were generated. Phantom data was evaluated using four different contrast ratios. These were reconstructed using BSREM with different β-factors of 300–3000 and with a clinical setting used for OSEM including point spread function (PSF) and time-of-flight (TOF) information. Contrast recovery (CR), background noise levels (coefficient of variation, COV), and contrast-to-noise ratio (CNR) were used to determine the performance in the phantom data. Findings based on the phantom data were compared with clinical data. For the patient study, the SUV ratio, metabolic active tumor volumes (MATVs), and the signal-to-noise ratio (SNR) were evaluated using the liver as the background region.ResultsBased on the phantom data for the same count statistics, BSREM resulted in higher CR and CNR and lower COV than OSEM. The CR of OSEM matches to the CR of BSREM with β = 750 at high count statistics for 8:1. A similar trend was observed for the ratios 6:1 and 4:1. A dependence on sphere size, counting statistics, and contrast ratio was confirmed by the CNR of the ratio 2:1. BSREM with β = 750 for 2.5 and 1.0 min acquisition has comparable COV to the 10 and 5.0 min acquisitions using OSEM. This resulted in a noise reduction by a factor of 2–4 when using BSREM instead of OSEM. For the patient data, a similar trend was observed, and SNR was reduced by at least a factor of 2 while preserving contrast.ConclusionThe BSREM reconstruction algorithm allowed a noise reduction without a loss of contrast by a factor of 2–4 compared to OSEM reconstructions for all data evaluated. This reduction can be used to lower the injected dose or shorten the acquisition time.

Exploiting Block-sparsity for Hyperspectral Kronecker Compressive Sensing: a Tensor-based Bayesian Method.

Bayesian methods are attracting increasing attention in the field of compressive sensing (CS), as they are applicable to recover signals from random measurements. However, these methods have limited use in many tensor-based cases such as hyperspectral Kronecker compressive sensing (HKCS), because they exploit the sparsity in only one dimension. In this paper, we propose a novel Bayesian model for HKCS in an attempt to overcome the above limitation. The model exploits multi-dimensional block-sparsity such that the information redundancies in all dimensions are eliminated. Laplace prior distributions are employed for sparse coefficients in each dimension, and their coupling is consistent with the multi-dimensional block-sparsity model. Based on the proposed model, we develop a tensor-based Bayesian reconstruction algorithm, which decouples the hyperparameters for each dimension via a low-complexity technique. Experimental results demonstrate that the proposed method is able to provide more accurate reconstruction than existing Bayesian methods at a satisfactory speed. Additionally, the proposed method can not only be used for HKCS, it also has the potential to be extended to other multi-dimensional CS applications and to multi-dimensional block-sparse-based data recovery.

Evaluation of a dual signal subspace projection algorithm in magnetoencephalographic recordings from patients with intractable epilepsy and vagus nerve stimulators

Magnetoencephalography (MEG) data is subject to many sources of environmental noise, and interference rejection is a necessary step in the processing of MEG data. Large amplitude interference caused by sources near the brain have been common in clinical settings and are difficult to reject. Artifact from vagal nerve stimulators (VNS) is a prototypical example. In this study, we describe a novel MEG interference rejection algorithm called dual signal subspace projection (DSSP), and evaluate its performance in clinical MEG data from people with epilepsy and implanted VNS. The performance of DSSP was evaluated in a retrospective cohort study of patients with epilepsy and VNS who had MEG scans for source localization of interictal epileptiform discharges. DSSP was applied to the MEG data and compared with benchmark for performance. We evaluated the clinical impact of interference rejection based on human expert detection and estimation of the location and time-course of interictal spikes, using an empirical Bayesian source reconstruction algorithm (Champagne). Clinical recordings, after DSSP processing, became more readable and a greater number of interictal epileptic spikes could be clearly identified. Source localization results of interictal spikes also significantly improved from those achieved before DSSP processing, including meaningful estimates of activity time courses. Therefore, DSSP is a valuable novel interference rejection algorithm that can be successfully deployed for the removal of strong artifacts and interferences in MEG.

Bayesian penalized-likelihood reconstruction algorithm suppresses edge artifacts in PET reconstruction based on point-spread-function

PurposeThe Bayesian penalized-likelihood reconstruction algorithm (BPL), Q.Clear, uses relative difference penalty as a regularization function to control image noise and the degree of edge-preservation in PET images. The present study aimed to determine the effects of suppression on edge artifacts due to point-spread-function (PSF) correction using a Q.Clear. MethodsSpheres of a cylindrical phantom contained a background of 5.3 kBq/mL of [18F]FDG and sphere-to-background ratios (SBR) of 16, 8, 4 and 2. The background also contained water and spheres containing 21.2 kBq/mL of [18F]FDG as non-background. All data were acquired using a Discovery PET/CT 710 and were reconstructed using three-dimensional ordered-subset expectation maximization with time-of-flight (TOF) and PSF correction (3D-OSEM), and Q.Clear with TOF (BPL). We investigated β-values of 200–800 using BPL. The PET images were analyzed using visual assessment and profile curves, edge variability and contrast recovery coefficients were measured. ResultsThe 38- and 27-mm spheres were surrounded by higher radioactivity concentration when reconstructed with 3D-OSEM as opposed to BPL, which suppressed edge artifacts. Images of 10-mm spheres had sharper overshoot at high SBR and non-background when reconstructed with BPL. Although contrast recovery coefficients of 10-mm spheres in BPL decreased as a function of increasing β, higher penalty parameter decreased the overshoot. ConclusionsBPL is a feasible method for the suppression of edge artifacts of PSF correction, although this depends on SBR and sphere size. Overshoot associated with BPL caused overestimation in small spheres at high SBR. Higher penalty parameter in BPL can suppress overshoot more effectively.

The Impact of a Bayesian Penalized-Likelihood Reconstruction Algorithm on a Dual-Time-Point Acquisition Protocol while Performing Ga-68-PSMA PET for Primary Prostate Cancer Detection

The Impact of a Bayesian Penalized-Likelihood Reconstruction Algorithm on a Dual-Time-Point Acquisition Protocol while Performing Ga-68-PSMA PET for Primary Prostate Cancer Detection

Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior

We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm is designed to also work with non-Gaussian posterior distributions which arise, for example, from a non-Gaussian prior distribution. In this work, we use a lognormal prior and compare the reconstruction results to a Gaussian prior in a suite of increasingly realistic tests on mock data. We find that in cases of high noise levels (i.e. for low source galaxy densities and/or high shape measurement uncertainties), both normal and lognormal priors lead to reconstructions of comparable quality, but with the lognormal reconstruction being prone to mass-sheet degeneracy. In the low-noise regime and on small scales, the lognormal model produces better reconstructions than the normal model: The lognormal model 1) enforces non-negative densities, while negative densities are present when a normal prior is employed, 2) better traces the extremal values and the skewness of the true underlying distribution, and 3) yields a higher pixel-wise correlation between the reconstruction and the true density.

L1-Minimization Algorithm for Bayesian Online Compressed Sensing

In this work, we propose a Bayesian online reconstruction algorithm for sparse signals based on Compressed Sensing and inspired by L1-regularization schemes. A previous work has introduced a mean-field approximation for the Bayesian online algorithm and has shown that it is possible to saturate the offline performance in the presence of Gaussian measurement noise when the signal generating distribution is known. Here, we build on these results and show that reconstruction is possible even if prior knowledge about the generation of the signal is limited, by introduction of a Laplace prior and of an extra Kullback–Leibler divergence minimization step for hyper-parameter learning.