Inclusion Of Prior Information Research Articles

Pie-Net: Prior-information-enabled deep learning noise reduction for coronary CT angiography acquired with a photon counting detector CT.

Photon-counting-detector CT (PCD-CT) enables the production of virtual monoenergetic images (VMIs) at a high spatial resolution (HR) via simultaneous acquisition of multi-energy data. However, noise levels in these HR VMIs are markedly increased. To develop a deep learning technique that utilizes a lower noise VMI as prior information to reduce image noise in HR, PCD-CT coronary CT angiography (CTA). Coronary CTA exams of 10 patients were acquired using PCD-CT (NAEOTOM Alpha, Siemens Healthineers). A prior-information-enabled neural network (Pie-Net) was developed, treating one lower-noise VMI (e.g., 70keV) as a prior input and one noisy VMI (e.g., 50keV or 100keV) as another. For data preprocessing, noisy VMIs were reconstructed by filtered back-projection (FBP) and iterative reconstruction (IR), which were then subtracted to generate "noise-only" images. Spatial decoupling was applied to the noise-only images to mitigate overfitting and improve randomization. Thicker slice averaging was used for the IR and prior images. The final training inputs for the convolutional neural network (CNN) inside the Pie-Net consisted of thicker-slice signal images with the reinsertion of spatially decoupled noise-only images and the thicker-slice prior images. The CNN training labels consisted of the corresponding thicker-slice label images without noise insertion. Pie-Net's performance was evaluated in terms of image noise, spatial detail preservation, and quantitative accuracy, and compared to a U-net-based method that did not include prior information. Pie-Net provided strong noise reduction, by 95±1% relative to FBP and by 60±8% relative to IR. For HR VMIs at different keV (e.g., 50keV or 100keV), Pie-Net maintained spatial and spectral fidelity. The inclusion of prior information from the PCD-CT data in the spectral domain was able to improve a robust deep learning-based denoising performance compared to the U-net-based method, which caused some loss of spatial detail and introduced some artifacts. The proposed Pie-Net achieved substantial noise reduction while preserving HR VMI's spatial and spectral properties.

Bayesian models for aggregate and individual patient data component network meta-analysis.

Network meta‐analysis can synthesize evidence from studies comparing multiple treatments for the same disease. Sometimes the treatments of a network are complex interventions, comprising several independent components in different combinations. A component network meta‐analysis (CNMA) can be used to analyze such data and can in principle disentangle the individual effect of each component. However, components may interact with each other, either synergistically or antagonistically. Deciding which interactions, if any, to include in a CNMA model may be difficult, especially for large networks with many components. In this article, we present two Bayesian CNMA models that can be used to identify prominent interactions between components. Our models utilize Bayesian variable selection methods, namely the stochastic search variable selection and the Bayesian LASSO, and can benefit from the inclusion of prior information about important interactions. Moreover, we extend these models to combine data from studies providing aggregate information and studies providing individual patient data (IPD). We illustrate our models in practice using three real datasets, from studies in panic disorder, depression, and multiple myeloma. Finally, we describe methods for developing web‐applications that can utilize results from an IPD‐CNMA, to allow for personalized estimates of relative treatment effects given a patient's characteristics.

The role of biomarkers in cell counting with U‐Net CNN

AbstractBackgroundImaging methods that are non‐destructive preserve tissue integrity and lead to improved topography analysis for the study of neurodegenerative diseases like Alzheimer’s Disease (AD). Immunofluorescence (IF) staining methods facilitate such investigations by addressing a gradient of intensity variations relevant for in situ cell detection [1] and morphology quantification. This paper reports on the colocalization of proteins and cell structures from human post‐mortem tissue by evaluating IF expression by means of TBR1 and NeuN biomarkers. We compare different U‐Net‐based models by exploring image representations obtained by combining image channels with different biomarkers.MethodFrom an image dataset with 21 full‐size IF micrographs, we augment it by creating a cropping mechanism resulting in 40 to 60 image crops from each micrograph, each crop with 128x128 pixels. Later, we enhance the resulting 1,200 cropped images, and construct 3‐channel (x,y,z) image inputs of dimensions 128x128x3 for the U‐Net model in a two‐fold process: (I) stack all 3 channels with single‐channel IF cropped images corresponding to NeuN biomarkers (NeuN, NeuN, NeuN); (II) stack the single channel images of TBR1, NeuN, and a single image representing the maximum pixel intensities from TBR1 and NeuN images (TBR1, NeuN, max (TBR1, NeuN)). With a test‐train split of 70% ‐ 30%, and parameter tuning, we compare the two models via metrics such as neuron areas, counts, accuracy and recall.ResultThe model trained with channel stacking (II) outperforms the model trained with (I) with an accuracy and recall of 0.96 and 0.5, as opposed to 0.95 and 0.4. We also found a great variation in neuron area and counts as depicted in the images below.ConclusionWhile this is the first step in accelerating the quantification of neurons for the pathophysiology studies necessary for drug development, there is a need in establishing protocols for the generation of datasets with manual segmentation to further train our models. The inclusion of prior information about the expected neuron morphology increases the performance of our networks, and successfully deploy a foreseen automated pipeline. Reference: [1] Ehrenberg et al. A manual multiplex immunofluorescence method for investigating neurodegenerative diseases. Journal of Neuroscience Methods, June, 2020.

The role of biomarkers in cell counting with U‐Net CNN

AbstractBackgroundImaging methods that are non‐destructive preserve tissue integrity and lead to improved topography analysis for the study of neurodegenerative diseases like Alzheimer’s Disease (AD). Immunofluorescence (IF) staining methods facilitate such investigations by addressing a gradient of intensity variations relevant for in situ cell detection [1] and morphology quantification. This paper reports on the colocalization of proteins and cell structures from human post‐mortem tissue by evaluating IF expression by means of TBR1 and NeuN biomarkers. We compare different U‐Net‐based models by exploring image representations obtained by combining image channels with different biomarkers.MethodFrom an image dataset with 21 full‐size IF micrographs, we perform data augmentation by creating a cropping mechanism resulting in 40 to 60 image crops from each micrograph, each crop with 128x128 pixels. Later, we enhance the resulting 1,200 cropped images, and construct 3‐channel (X,Y,Z) image inputs of dimensions 128x128x3 for the U‐Net model in a two‐fold process: (I) stack all 3 channels with single‐channel IF cropped images corresponding to NeuN biomarkers (NeuN, NeuN, NeuN); (II) stack the single channel images of TBR1, NeuN, and a single image representing the maximum pixel intensities from TBR1 and NeuN images (TBR1, NeuN, max (TBR1, NeuN)). With a test‐train split of 70% ‐ 30%, and parameter tuning, we compare the two models via metrics such as neuron areas, counts, accuracy and recall.ResultThe model trained with channel stacking (II) outperforms the model trained with (I) with an accuracy and recall of 0.96 and 0.5, as opposed to 0.95 and 0.4. We also found a great variation in neuron area and counts as depicted in the images below.ConclusionWhile this is the first step in accelerating the quantification of neurons for the pathophysiology studies necessary for drug development, there is a need in establishing protocols for the generation of datasets with manual segmentation to further train our models. The inclusion of prior information about the expected neuron morphology increases the performance of our networks, and can successfully deploy a foreseen automated pipeline. [1] Ehrenberg et al. A manual multiplex immunofluorescence method for investigating neurodegenerative diseases. Journal of Neuroscience Methods,June, 2020.

Legacy of historic land cover changes on sediment provenance tracked with isotopic tracers in a Mediterranean agroforestry catchment

A Compound Specific Stable Isotope (CSSI) sediment tracing approach is applied for the first time in a Mediterranean mountain agroforestry catchment subjected to intense land use changes in the past decades. Many Mediterranean mountain environments underwent conversion of rangelands into croplands during the previous centuries to increase agricultural production. Converted land has increased the risk of erosion and in some cases has led to loss of the entire fertile topsoil. After land abandonment the process was gradually reversed during the middle of the 20th century, allowing the recovery of natural land cover and reduction of soil erosion rates.The 13C abundance of long chain fatty acids was used as tracer to assess the contribution of soil under different vegetation covers in complex landscapes subjected to land use changes after land abandonment in a medium-sized Mediterranean catchment. A Bayesian mixing model (MixSIAR) was used for estimating the contribution of different land use types to suspended sediments. To this purpose, composite samples were collected over the four main land covers existing in the study area: cropland, Mediterranean forest, pine forest, scrubland, and two main geomorphic elements: highly disturbed areas such as exposed subsoil and channel banks. Suspended sediment traps were installed at three locations in the catchment to assess the variability of source contributions from the headwaters to the outlet of the catchment. At every sampling point three replicating traps integrated the suspended sediment per climatologic season during a one hydrological year. The fatty acids (FAs) content was significantly higher at the catchment outlet than at the headwaters. The δ13C signatures of the FAs were successful in discriminating between Mediterranean forest, scrubland, pine forest and both geomorphic elements. Overall, the model identified agricultural land as the largest contributing source for most of the sampled seasons. The inclusion of prior information with different informativeness produced variations in the model outputs and could represent an advantage as much as a disadvantage if priors are not used with caution and supported by robust evidence. The results of this study suggest that CSSI tracers are needed to correctly assess land use related sediment sources, while channel bank and subsoil contributions require geochemical tracers. The high agricultural apportionment despite its small coverage (16%) point out to the impact of human activities and the agriculture cycle on soil loss in these mountain agroforestry systems.

Improved ptychographic inspection of EUV reticles via inclusion of prior information.

The development of actinic mask metrology tools represents one of the major challenges to be addressed on the roadmap of extreme ultraviolet (EUV) lithography. Technological advancements in EUV lithography result in the possibility to print increasingly fine and highly resolved structures on a silicon wafer; however, the presence of fine-scale defects, interspersed in the printable mask layout, may lead to defective wafer prints. Hence, the development of actinic methods for review of potential defect sites becomes paramount. Here, we report on a ptychographic algorithm that makes use of prior information about the object to be retrieved, generated by means of rigorous computations, to improve the detectability of defects whose dimensions are of the order of the wavelength. The comprehensive study demonstrates that the inclusion of prior information as a regularizer in the ptychographic optimization problem results in a higher reconstruction quality and an improved robustness to noise with respect to the standard ptychographic iterative engine (PIE). We show that the proposed method decreases the number of scan positions necessary to retrieve a high-quality image and relaxes requirements in terms of signal-to-noise ratio (SNR). The results are further compared with state-of-the-art total variation-based ptychographic imaging.

A bayesian approach to the spectral F-Test: Application to auditory steady-state responses

Background and ObjectiveAuditory steady-state responses (ASSRs) represent an objective method used in clinical practice to assess hearing thresholds. The steady-state nature of these signals allows response detection by means of statistical techniques in the frequency domain as spectral F-test. This objective response detection (ORD) compares the power of the response bin against the power of the neighboring frequency noise bins. Most ORD algorithms are based on the Neyman-Pearson approach to the hypothesis test provided that the likelihood ratio test is the most powerful test for a given significance level alpha (also called Type I error). On the other hand, the Bayesian approach allows the inclusion of prior information in the model and enables the updating of this information with posterior knowledge. This approach, however, has not been explored with respect to ORD techniques, thus enabling the exploration of new paradigms, which may contribute to this field of study, especially in terms of the time required for response detection. The aim of this study is to use the Bayesian approach in the implementation of the spectral F-test for application to ASSRs. MethodsMonte Carlo simulations were performed to evaluate Neyman-Pearson and Bayesian detectors’ performances with the spectral F-test as a function of the signal-to-noise ratio. Then, the two detectors were applied to ASSR recordings of nine normal-hearing individuals subjected to amplitude-modulated tones of various intensities. ResultsBoth simulation and ASSR data analyses showed that among the scenarios analyzed, the most promising case was that in which the lowest possible values for the a priori probability were selected for the null hypothesis (H0), allowing detection at low signal-to-noise ratios. The worst performance occurred when the a priori probabilities for both hypotheses were equal. The ASSR data also showed that higher stimulus intensity led to better performance and faster detection due to improvements in the signal-to-noise ratio. ConclusionsThe a priori probabilities can affect the Bayesian detector's performance, directly impacting the time needed to identify responses. The parallel behaviors observed between the performances of both approaches showed that the Bayesian detector can achieve its ideal performance at lower signal-to-noise ratios compared to the optimal performance of the Neyman-Pearson detector, reflecting the promising applicability of the Bayesian approach to evoked potentials.

Improved time-censored reliability test plans for k-out-of-n gamma systems

Relevant prior knowledge supported by historical data and expert judgments is common in many manufacturing processes. The classical viewpoint to the determination of acceptance sampling plans for k-out-of-n gamma systems is generalized to those situations in which the available previous information is appreciable. A beta distribution with a reduced parameter space is adopted to describe the stochastic behavior of the fraction of defective systems. An integer nonlinear programming problem is stated to find the inspection scheme that minimizes the required number of components to test and keeps the average producer and consumer risks below specified thresholds. First, lower and upper bounds, as well as an approximate solution, are derived. Then, an efficient step-by-step procedure, which finds the best acceptance sampling plan in a finite number of iterations, is provided. The inclusion of prior information into the decision process provides substantial savings in the sample size required for demonstrating system reliability, and also more accurate assessments of the actual producer and consumer risks. A system of five water pumps for cooling a reactor is analyzed for illustrative and comparative purposes.

Bayesian forecast combination in VAR-DSGE models

We evaluate the performance of individual and combination forecasts produced by Bayesian vector autoregressions (Bayesian VARs) with economic and/or non-economic information. In particular, we conduct an out-of-sample forecasting experiment using Bayesian VARs with statistical and/or DSGE prior(s) over two subsamples, representing the so-called “Great Inflation” and “Great Moderation” periods, respectively. Our main findings are summarized as follows. First, in most cases, the inclusion of prior information, either statistical or economic prior(s), improves the accuracy of point forecasts produced by the Bayesian VARs, relative to the ARMA(1,1) benchmark. Second, forecast combination helps to produce unbiased forecasts in most cases. Moreover, it significantly improves the forecast accuracy of the macro-econometric models, especially during the “Great Moderation” period. Third, the selection of the weighting scheme in forecast combination, simple averaging or Bayesian model averaging (BMA), does not affect the conclusions made above. Finally, partially in line with the recent literature, we find a positive relationship between the persistence of inflation and its relative forecast accuracy at the four-quarter horizon.

Scaling marine fish movement behavior from individuals to populations.

Understanding how, where, and when animals move is a central problem in marine ecology and conservation. Key to improving our knowledge about what drives animal movement is the rising deployment of telemetry devices on a range of free‐roaming species. An increasingly popular way of gaining meaningful inference from an animal's recorded movements is the application of hidden Markov models (HMMs), which allow for the identification of latent behavioral states in the movement paths of individuals. However, the use of HMMs to explore the population‐level consequences of movement is often limited by model complexity and insufficient sample sizes. Here, we introduce an alternative approach to current practices and provide evidence of how the inclusion of prior information in model structure can simplify the application of HMMs to multiple animal movement paths with two clear benefits: (a) consistent state allocation and (b) increases in effective sample size. To demonstrate the utility of our approach, we apply HMMs and adapted HMMs to over 100 multivariate movement paths consisting of conditionally dependent daily horizontal and vertical movements in two species of demersal fish: Atlantic cod (Gadus morhua; n = 46) and European plaice (Pleuronectes platessa; n = 61). We identify latent states corresponding to two main underlying behaviors: resident and migrating. As our analysis considers a relatively large sample size and states are allocated consistently, we use collective model output to investigate state‐dependent spatiotemporal trends at the individual and population levels. In particular, we show how both species shift their movement behaviors on a seasonal basis and demonstrate population space use patterns that are consistent with previous individual‐level studies. Tagging studies are increasingly being used to inform stock assessment models, spatial management strategies, and monitoring of marine fish populations. Our approach provides a promising way of adding value to tagging studies because inferences about movement behavior can be gained from a larger proportion of datasets, making tagging studies more relevant to management and more cost‐effective.

On model order priors for Bayesian identification of SISO linear systems

ABSTRACTA method for the identification of single input single output linear systems is presented. The method employs a Bayesian approach to compute the posterior distribution of the model parameters given the data-set. Since this distribution is often unavailable in closed form, a Metropolis Hastings algorithm is implemented to draw samples from it. To implement the sampler, the inclusion of prior information regarding the model order of the identified system is discussed. As one of the main contributions of this work, a prior over the Hankel singular values of the model is imposed. Numerical examples illustrate the method.

A Maximum-Caliber Approach to Predicting Perturbed Folding Kinetics Due to Mutations.

We present a maximum-caliber method for inferring transition rates of a Markov state model (MSM) with perturbed equilibrium populations given estimates of state populations and rates for an unperturbed MSM. It is similar in spirit to previous approaches, but given the inclusion of prior information, it is more robust and simple to implement. We examine its performance in simple biased diffusion models of kinetics and then apply the method to predicting changes in folding rates for several highly nontrivial protein folding systems for which non-native interactions play a significant role, including (1) tryptophan variants of the GB1 hairpin, (2) salt-bridge mutations of the Fs peptide helix, and (3) MSMs built from ultralong folding trajectories of FiP35 and GTT variants of the WW domain. In all cases, the method correctly predicts changes in folding rates, suggesting the wide applicability of maximum-caliber approaches to efficiently predict how mutations perturb protein conformational dynamics.

Improving estimation in genetic models using prior information

Statistical models used to investigate research questions in behavioral genetics often require large amountsof data. This paper introduces some key concepts of Bayesian analysis and illustrates how these methodscan aid model estimation when the data does not provide enough information to reliably answer researchquestions. The use of informative prior distributions is discussed as a method of incorporating informationfrom other sources than the data at hand. The procedure is illustrated with an ACE model decomposition ofthe variance of antisocial personality disorder. The data originates from the Norwegian Twin Registry, andincludes adult twins assessed with the Structured Interview for DSM Personality (SIDP-IV). Inclusion ofprior information lead to a shift with respect to conclusions about the presence of shared environmentaleffects compared to a traditional analysis. Small and medium sized studies should consider use of priorinformation to aid estimation of population parameters.

Uncertainty estimates of psychoacoustic thresholds obtained from group test

Adaptive psychoacoustic test methods, in which the next signal level depends on the response to the previous signal, are the most efficient for determining psychoacoustic thresholds of individual subjects. In many tests conducted in the NASA psychoacoustic labs, the goal is to determine thresholds representative of the general population. To do this economically, non-adaptive testing methods are used in which three or four subjects are tested at the same time with predetermined signal levels. This approach requires us to identify techniques for assessing the uncertainty in resulting group-average psychoacoustic thresholds. In this presentation we examine the Delta Method of frequentist statistics, the Generalized Linear Model (GLM), the Nonparametric Bootstrap, a frequentist method, and Markov Chain Monte Carlo Posterior Estimation and a Bayesian approach. Each technique is exercised on a manufactured, theoretical dataset and then on datasets from two psychoacoustics facilities at NASA. The Delta Method is the simplest to implement and accurate for the cases studied. The GLM is found to be the least robust, and the Bootstrap takes the longest to calculate. The Bayesian Posterior Estimate is the most versatile technique examined because it allows the inclusion of prior information.

Quantitative inverse modelling of a cylindrical object in the laboratory using ERT: An error analysis

Electrical resistivity tomography (ERT) is a geophysical technique that can be used to obtain three-dimensional images of the bulk electrical conductivity of the subsurface. Because the electrical conductivity is strongly related to properties of the subsurface and the flow of water it has become a valuable tool for visualization in many hydrogeological and environmental applications. In recent years, ERT is increasingly being used for quantitative characterization, which requires more detailed prior information than a conventional geophysical inversion for qualitative purposes. In addition, the careful interpretation of measurement and modelling errors is critical if ERT measurements are to be used in a quantitative way. This paper explores the quantitative determination of the electrical conductivity distribution of a cylindrical object placed in a water bath in a laboratory-scale tank. Because of the sharp conductivity contrast between the object and the water, a standard geophysical inversion using a smoothness constraint could not reproduce this target accurately. Better results were obtained by using the ERT measurements to constrain a model describing the geometry of the system. The posterior probability distributions of the parameters describing the geometry were estimated with the Markov chain Monte Carlo method DREAM(ZS). Using the ERT measurements this way, accurate estimates of the parameters could be obtained. The information quality of the measurements was assessed by a detailed analysis of the errors. Even for the uncomplicated laboratory setup used in this paper, errors in the modelling of the shape and position of the electrodes and the shape of the domain could be identified. The results indicate that the ERT measurements have a high information content which can be accessed by the inclusion of prior information and the consideration of measurement and modelling errors.

Efficacy of population structure analysis with breeding populations and inbred lines

The objective was to assess by simulation the efficacy of population structure analysis in plant breeding. Twelve populations and 300 inbred lines were simulated and genotyped using 100 microsatellite loci. The experimental material included populations with and without admixture, ancestry relationship and linkage disequilibrium, and with distinct levels of genetic differentiation and effective sizes. The analyses were performed using Structure software and employed all available models. For all the group number (K) tested, for both populations and inbred lines, the admixture model with correlated allelic frequencies provided the highest value for the logarithm of the marginal likelihood. Fitting appropriate model and using adequate sample size for individuals and markers, Structure was effective in identifying the correct population structure, migrants and individuals with genome from distinct populations. The linkage model did not result in an improvement in clustering relative to the admixture model with correlated allelic frequencies. The inclusion of prior information did not change the results; for some K values the analyses showed slight higher values of the marginal likelihood. The reduction in the number of individuals and markers negatively affected the results. There was a high variation in the most probable K value between the evaluated methods.

A practical guide to Bayesian group sequential designs

Bayesian approaches to the monitoring of group sequential designs have two main advantages compared with classical group sequential designs: first, they facilitate implementation of interim success and futility criteria that are tailored to the subsequent decision making, and second, they allow inclusion of prior information on the treatment difference and on the control group. A general class of Bayesian group sequential designs is presented, where multiple criteria based on the posterior distribution can be defined to reflect clinically meaningful decision criteria on whether to stop or continue the trial at the interim analyses. To evaluate the frequentist operating characteristics of these designs, both simulation methods and numerical integration methods are proposed, as implemented in the corresponding R package gsbDesign. Normal approximations are used to allow fast calculation of these characteristics for various endpoints. The practical implementation of the approach is illustrated with several clinical trial examples from different phases of drug development, with various endpoints, and informative priors.

Landslide susceptibility mapping along road corridors in the Indian Himalayas using Bayesian logistic regression models

Landslide susceptibility mapping (LSM) along road corridors in the Indian Himalayas is an essential exercise that helps planners and decision makers in determining the severity of probable slope failure areas. Logistic regression is commonly applied for this purpose, as it is a robust and straightforward technique that is relatively easy to handle. Ordinary logistic regression as a data-driven technique, however, does not allow inclusion of prior information. This study presents Bayesian logistic regression (BLR) for landslide susceptibility assessment along road corridors. The methodology is tested in a landslide-prone area in the Bhagirathi river valley in the Indian Himalayas. Parameter estimates from BLR are compared with those obtained from ordinary logistic regression. By means of iterative Markov Chain Monte Carlo simulation, BLR provides a rich set of results on parameter estimation. We assessed model performance by the receiver operator characteristics curve analysis, and validated the model using 50% of the landslide cells kept apart for testing and validation. The study concludes that BLR performs better in posterior parameter estimation in general and the uncertainty estimation in particular.

Direct 4D parametric imaging for linearized models of reversibly binding PET tracers using generalized AB-EM reconstruction

Due to high noise levels in the voxel kinetics, development of reliable parametric imaging algorithms remains one of most active areas in dynamic brain PET imaging, which in the vast majority of cases involves receptor/transporter studies with reversibly binding tracers. As such, the focus of this work has been to develop a novel direct 4D parametric image reconstruction scheme for such tracers. Based on a relative equilibrium (RE) graphical analysis formulation (Zhou et al 2009b Neuroimage 44 661–70), we developed a closed-form 4D EM algorithm to directly reconstruct distribution volume (DV) parametric images within a plasma input model, as well as DV ratio (DVR) images within a reference tissue model scheme (wherein an initial reconstruction was used to estimate the reference tissue time–activity curves). A particular challenge with the direct 4D EM formulation is that the intercept parameters in graphical (linearized) analysis of reversible tracers (e.g. Logan or RE analysis) are commonly negative (unlike for irreversible tracers, e.g. using Patlak analysis). Subsequently, we focused our attention on the AB-EM algorithm, derived by Byrne (1998, Inverse Problems 14 1455–67) to allow inclusion of prior information about the lower (A) and upper (B) bounds for image values. We then generalized this algorithm to the 4D EM framework, thus allowing negative intercept parameters. Furthermore, our 4D AB-EM algorithm incorporated and emphasized the use of spatially varying lower bounds to achieve enhanced performance. As validation, the means of parameters estimated from 55 human 11C-raclopride dynamic PET studies were used for extensive simulations using a mathematical brain phantom. Images were reconstructed using conventional indirect as well as proposed direct parametric imaging methods. Noise versus bias quantitative measurements were performed in various regions of the brain. Direct 4D EM reconstruction resulted in notable qualitative and quantitative accuracy improvements (over 35% noise reduction, with matched bias, in both plasma and reference-tissue input models). Similar improvements were also observed in the coefficient of variation of the estimated DV and DVR values even for relatively low uptake cortical regions, suggesting the enhanced ability for robust parameter estimation. The method was also tested on a 90 min 11C-raclopride patient study performed on the high-resolution research tomograph wherein the proposed method was shown across a variety of regions to outperform the conventional method in the sense that for a given DVR value, improved noise levels were observed.

Bayesian frequency-domain blind deconvolution of ground-penetrating radar data

Enhancing the resolution and accuracy of surface ground-penetrating radar (GPR) reflection data by inverse filtering to recover a zero-phased band-limited reflectivity image requires a deconvolution technique that takes the mixed-phase character of the embedded wavelet into account. In contrast, standard stochastic deconvolution techniques assume that the wavelet is minimum phase and, hence, often meet with limited success when applied to GPR data. We present a new general-purpose blind deconvolution algorithm for mixed-phase wavelet estimation and deconvolution that (1) uses the parametrization of a mixed-phase wavelet as the convolution of the wavelet's minimum-phase equivalent with a dispersive all-pass filter, (2) includes prior information about the wavelet to be estimated in a Bayesian framework, and (3) relies on the assumption of a sparse reflectivity. Solving the normal equations using the data autocorrelation function provides an inverse filter that optimally removes the minimum-phase equivalent of the wavelet from the data, which leaves traces with a balanced amplitude spectrum but distorted phase. To compensate for the remaining phase errors, we invert in the frequency domain for an all-pass filter thereby taking advantage of the fact that the action of the all-pass filter is exclusively contained in its phase spectrum. A key element of our algorithm and a novelty in blind deconvolution is the inclusion of prior information that allows resolving ambiguities in polarity and timing that cannot be resolved using the sparseness measure alone. We employ a global inversion approach for non-linear optimization to find the all-pass filter phase values for each signal frequency. We tested the robustness and reliability of our algorithm on synthetic data with different wavelets, 1-D reflectivity models of different complexity, varying levels of added noise, and different types of prior information. When applied to realistic synthetic 2-D data and 2-D field data, we obtain images with increased temporal resolution compared to the results of standard processing.