Parametric Reconstruction Method Research Articles

Human body construction based on combination of parametric and nonparametric reconstruction methods

Human body construction based on combination of parametric and nonparametric reconstruction methods

3D dynamic observation of human sperm by parallel phase-shifting digital holographic microscopy based on pixelated polarization

Morphology and motility are essential criteria for assessing sperm viability. However, the human sperm head is small (∼3–4 μm) and requires a relatively high-magnification microscope objective, while the sperm flagella (∼45 μm) are poorly visible with complex 3D properties. Microscopic dynamic observation of intact sperm in 3D is challenging. Conventional inspection methods with a limited depth of field are inadequate for this issue. To provide a solution to this critical need, we develop pixelated polarization-based parallel phase-shifting digital holographic microscopy for the 3D dynamic observation of human sperm. Compared to conventional holographic imaging, this approach can effectively separate the object wavefront and avoid image quality degradation while fully exploiting the spatial bandwidth of the camera. We propose the use of the Stokes parameter reconstruction method to reconstruct the object wavefront and investigate the effect of the sampling interval on the system resolution by spectral analysis. The methodology achieves the retrieval of the 3D trajectory and motion parameters of sperm and reconstructs the sperm head orientation and the thin, highly-dynamic flagellum. The system allows for more comprehensive information on sperm motility and morphology, which is significant for male reproductive research. It also has significant potential for 3D dynamic observation of micro-organisms.

IVIM-DKI with parametric reconstruction method for lymph node evaluation and characterization in lymphoma: A preliminary study comparison with FDG-PET/CT

To investigate IVIM-DKI in diagnosing benign and malignant lymph nodes in lymphoma and its subtypes in comparison to FDG-PET/CT. A total of twenty-one (n = 21) patients diagnosed with biopsy-proven Hodgkin lymphoma(HL: n = 13) and non-Hodgkin lymphoma (NHL: n = 8) were prospectively evaluated. All patients underwent MRI(T1-weighted, Short-Tau-Inversion-Recovery (STIR)), and IVIM-DKI was acquired with 9b-values (0–2000s/mm2) at 1.5T and whole-body FDG-PET/CT. The maximum and average standard uptake values (SUVmax and SUVmean) were calculated using PET images. IVIM-DKI parameters (diffusion coefficient(D), pseudo-diffusion coefficient (D*), perfusion fraction (f), and kurtosis (k)) were estimated using IVIM-DKI model with total variation (TV) method (IDTV model). Area-under-curve from receiver-operating-curve (ROC) analysis was used to examine diagnostic value of IVIM-DKI parameters in differentiation between benign and malignant lymph nodes and HL from NHL. Machine learning-based classification of histogram features were performed using linear classifier model. For malignant vs. benign lymph nodes, apparent diffusion coefficient (ADC), f, and k were significantly (p < 0.05) lower in malignant vs. benign lymph nodes. f (AUC:0.88) and k (AUC:0.83) showed high AUC and histogram features combination of f (variance + skewness + kurtosis) showed highest accuracy of 97.2% and AUC of 1. ADC, D, D*, and f were significantly (p < 0.05) lower in NHL than HL. D* showed highest AUC of 0.85 than D (AUC:0.84), ADC (AUC:0.84), and f (AUC:0.74) in NHL vs. HL. SUVmax (spearman-rho = 0.85), ADC (spearman-rho = 0.50), D (spearman-rho = 0.48), and D* (spearman-rho = 0.49) showed significant (p < 0.05) positive correlation with SUVmean. Multi-b-values IVIM-DKI with histogram analysis helps characterize benign and malignant lymph nodes in lymphomas. IVIM-DKI parameters can differentiate malignant lymph nodes in HL and NHL superior to PET parameters.

Estimation Method of State of Charge of Power Battery of New Energy Vehicle Based on K Nearest Neighbor Regression

In order to improve the power battery state of charge detection ability of new energy vehicles and reduce harmonic interference, a measurement method of power battery state of new energy vehicles based on K-nearest neighbor regression analysis is proposed. Build a charging state parameter collection model of new energy vehicle power battery, consider the unbalanced power of uncertain factors, realize the oscillation and fusion processing of charging state of new energy vehicle power battery through the dynamic matching method of mobile energy storage resources of electric vehicle, extract the microgrid load fluctuation characteristic value of charging state signal of new energy vehicle power battery, and analyze the percentage of remaining electricity to rated capacity. The initial charge and capacity characteristics of the battery of the new energy vehicle power battery are matched. The K-nearest neighbor regression analysis method is used to realize the regression analysis and dynamic estimation of the battery state of charge parameters. According to the state of charge of the new energy vehicle power battery, the steady-state characteristic quantity is output, and the demand response load model parameter reconstruction and load balance matching method are used to realize the state of charge estimation and parameter adaptive evaluation of the new energy vehicle power battery. The simulation results show that the accuracy of measuring the state of charge of the power battery of new energy vehicles is high, and the harmonic suppression ability is strong, which improves the balanced configuration and load balancing scheduling ability of the power system of the power battery of new energy vehicles.

Comparison of iterative parametric and indirect deep learning-based reconstruction methods in highly undersampled DCE-MR Imaging of the breast.

To compare the performance of iterative direct and indirect parametric reconstruction methods with indirect deep learning-based reconstruction methods in estimating tracer-kinetic parameters from highly undersampled DCE-MR Imaging breast data and provide a systematic comparison of the same. Estimation of tracer-kinetic parameters using indirect methods from undersampled data requires to reconstruct the anatomical images initially by solving an inverse problem. This reconstructed images gets utilized in turn to estimate the tracer-kinetic parameters. In direct estimation, the parameters are estimated without reconstructing the anatomical images. Both problems are ill-posed and are typically solved using prior-based regularization or using deep learning. In this study, for indirect estimation, two deep learning-based reconstruction frameworks namely, ISTA-Net+ and MODL, were utilized. For direct and indirect parametric estimation, sparsity inducing priors (L1 and Total-Variation) and limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm as solver was deployed. The performance of these techniques were compared systematically in estimation of vascular permeability ( ) from undersampled DCE-MRI breast data using Patlak as pharmaco-kinetic model. The experiments involved retrospective undersampling of the data 20×, 50×, and 100× and compared the results using PSNR, nRMSE, SSIM, and Xydeas metrics. The maps estimated from fully sampled data were utilized as ground truth. The developed code was made available as https://github.com/Medical-Imaging-Group/DCE-MRI-Compare open-source for enthusiastic users. The reconstruction methods performance was evaluated using ten patients breast data (five patients each for training and testing). Consistent with other studies, the results indicate that direct parametric reconstruction methods provide improved performance compared to the indirect parameteric reconstruction methods. The results also indicate that for 20× undersampling, deep learning-based methods performs better or at par with direct estimation in terms of PSNR, SSIM, and nRMSE. However, for higher undersampling rates (50× and 100×) direct estimation performs better in all metrics. For all undersampling rates, direct reconstruction performed better in terms of Xydeas metric, which indicated fidelity in magnitude and orientation of edges. Deep learning-based indirect techniques perform at par with direct estimation techniques for lower undersampling rates in the breast DCE-MR imaging. At higher undersampling rates, they are not able to provide much needed generalization. Direct estimation techniques are able to provide more accurate results than both deep learning- and parametric-based indirect methods in these high undersampling scenarios.

HOLISTIC PARAMETRIC RECONSTRUCTION OF BUILDING MODELS FROM POINT CLOUDS

Abstract. Building models are conventionally reconstructed by building roof points via planar segmentation and then using a topology graph to group the planes together. Roof edges and vertices are then mathematically represented by intersecting segmented planes. Technically, such solution is based on sequential local fitting, i.e., the entire data of one building are not simultaneously participating in determining the building model. As a consequence, the solution is lack of topological integrity and geometric rigor. Fundamentally different from this traditional approach, we propose a holistic parametric reconstruction method which means taking into consideration the entire point clouds of one building simultaneously. In our work, building models are reconstructed from predefined parametric (roof) primitives. We first use a well-designed deep neural network to segment and identify primitives in the given building point clouds. A holistic optimization strategy is then introduced to simultaneously determine the parameters of a segmented primitive. In the last step, the optimal parameters are used to generate a watertight building model in CityGML format. The airborne LiDAR dataset RoofN3D with predefined roof types is used for our test. It is shown that PointNet++ applied to the entire dataset can achieve an accuracy of 83% for primitive classification. For a subset of 910 buildings in RoofN3D, the holistic approach is then used to determine the parameters of primitives and reconstruct the buildings. The achieved overall quality of reconstruction is 0.08 meters for point-surface-distance or 0.7 times RMSE of the input LiDAR points. This study demonstrates the efficiency and capability of the proposed approach and its potential to handle large scale urban point clouds.

Parametric Image Reconstruction for Edge Recovery From Synthetic Aperture Radar Echoes

The edges of a target provide essential geometric information and are extremely important for human visual perception and image recognition. However, due to the coherent superposition of received echoes, the continuous edges of targets are discretized in synthetic aperture radar (SAR) images, i.e., the edges become dispersed points, which seriously affects the extraction of visual and geometric information from SAR images. In this article, we focus on solving the problem of how to recover smooth linear edges (SLEs). By introducing multiangle observations, we propose an SAR parametric image reconstruction method (SPIRM) that establishes a parametric framework to recover SLEs from SAR echoes. At the core of the SPIRM is a novel physical characteristic parameter called the scattering-phase-mutation feature (SPMF), which reveals the most essential difference between the residual endpoints of a disappeared SLE and points. Numerical simulations and real-data experiments demonstrate the robustness and effectiveness of the proposed method.

Multistatic inverse synthetic aperture radar imaging based on parametric block-sparse reconstruction

By combining the data of different spatially distributed sensors, multistatic inverse synthetic aperture radar (ISAR) can provide more stable imaging results compared with monostatic ISAR. In most previous studies of multistatic ISAR imaging, the scatterers on the target are modeled as isotropic points and a conventional monostatic ISAR imaging method is directly applied after rearranging the data of multiple sensors, which will result in the degradation of image quality, especially when the measurements are limited. In practice, the complex amplitude of the scatterer is usually strongly angle dependent; therefore, the echo of different sensors cannot be assumed to be coherent. We consider the fluctuation of the radar cross section and propose a method based on compressed sensing (CS) for multistatic ISAR imaging. By utilizing the block orthogonal matching pursuit (BOMP) method to reconstruct the target image, the requirement of coherence between different sensors can be eliminated. Moreover, in order to apply the CS method, a two-step target motion estimation approach is also presented. A coarse motion estimation method is first applied by tracking the target trajectory with the distance-sum measurement. Then, associating the gradient-based optimization algorithm with BOMP, a parametric block-sparse reconstruction method is developed to jointly correct the residual position error and recover the target image with incoherent echo. Simulation results show the effectiveness of the proposed method.

Parametric Reconstruction Method for the Long Time-Series Return-Stroke Current of Triggered Lightning Based on the Particle Swarm Optimization Algorithm

The lightning research group of the Chinese Academy of Meteorological Sciences has carried out observations and experiments with artificially triggered lightning for more than ten years, and it accumulated thousands of examples of channel base current data on the return stroke of artificially triggered lightning prior to 2020. Based on the current data, this paper explores ways of improving the constructed function of a long time-series (400 μs) return stroke and the parametric reconstruction of the current waveform. The long time-series current can be divided into three components: the breakdown pulse current, corona current and quasi-uniform current. The corona current and quasi-uniform current are constructed by a Heidler function, while the breakdown pulse current is determined by the waveform characteristics of the current peak, which can be divided into the Heidler type and high-order exponential type. According to the three-component model of the return-stroke current, a two-step parametric reconstruction method for the long time-series lightning return-stroke current based on the particle swarm optimization (PSO) algorithm is proposed. In this paper, the results of the parameterized reconstruction of 14 return strokes are given, and the results of the multidimensional error analysis of 13 long time-series return strokes are given to illustrate the accuracy of the improved parameterized model of the return-stroke current and the effectiveness of the two-step reconstruction method based on the PSO algorithm.

Total-Body Dynamic Reconstruction and Parametric Imaging on the uEXPLORER.

The world's first 194-cm-long total-body PET/CT scanner (uEXPLORER) has been built by the EXPLORER Consortium to offer a transformative platform for human molecular imaging in clinical research and health care. Its total-body coverage and ultra-high sensitivity provide opportunities for more accurate tracer kinetic analysis in studies of physiology, biochemistry, and pharmacology. The objective of this study was to demonstrate the capability of total-body parametric imaging and to quantify the improvement in image quality and kinetic parameter estimation by direct and kernel reconstruction of the uEXPLORER data. Methods: We developed quantitative parametric image reconstruction methods for kinetic analysis and used them to analyze the first human dynamic total-body PET study. A healthy female subject was recruited, and a 1-h dynamic scan was acquired during and after an intravenous injection of 256 MBq of 18F-FDG. Dynamic data were reconstructed using a 3-dimensional time-of-flight list-mode ordered-subsets expectation maximization (OSEM) algorithm and a kernel-based algorithm with all quantitative corrections implemented in the forward model. The Patlak graphical model was used to analyze the 18F-FDG kinetics in the whole body. The input function was extracted from a region over the descending aorta. For comparison, indirect Patlak analysis from reconstructed frames and direct reconstruction of parametric images from the list-mode data were obtained for the last 30 min of data. Results: Images reconstructed by OSEM showed good quality with low noise, even for the 1-s frames. The image quality was further improved using the kernel method. Total-body Patlak parametric images were obtained using either indirect estimation or direct reconstruction. The direct reconstruction method improved the parametric image quality, having a better contrast-versus-noise tradeoff than the indirect method, with a 2- to 3-fold variance reduction. The kernel-based indirect Patlak method offered image quality similar to the direct Patlak method, with less computation time and faster convergence. Conclusion: This study demonstrated the capability of total-body parametric imaging using the uEXPLORER. Furthermore, the results showed the benefits of kernel-regularized reconstruction and direct parametric reconstruction. Both can achieve superior image quality for tracer kinetic studies compared with the conventional indirect OSEM for total-body imaging.

Overhead Transmission Line Parameter Reconstruction for UAV Inspection Based on Tunneling Magnetoresistive Sensors and Inverse Models

Overhead transmission lines have played an important role in power transmission and distribution, and real-time monitoring of the line status is essential to maintain the stability and reliability of the power system. As the unmanned aerial vehicle (UAV) has gradually become the novel and effective tool for inspection of transmission lines, the acquisition of dynamic line parameters is also important to keep the UAV's track and safety. In this paper, a novel parameter reconstruction method for overhead transmission lines was proposed. A framework of approximated transmission line inverse problem was constructed, which transformed the problem into a nonlinear optimization problem. Based on the proposed comprehensive algorithm that combined metaheuristic algorithm and interior point method, the position and current parameters of the lines were reconstructed from the magnetic field data. Theoretical simulation indicated that the algorithm avoided the results being stuck in the local optima effectively. In terms of the experimental implementation, a dual-axial tunneling magnetoresistive magnetic field measurement device was prepared. The measurement and calculation results proved the robustness and accuracy of the comprehensive reconstruction algorithm together with the magnetic field measurement device, leading to a more promising approach for real-time transmission line monitoring and UAV trajectory controlling.

Direct parametric reconstruction in dynamic PET myocardial perfusion imaging: in vivo studies

Dynamic PET myocardial perfusion imaging (MPI) used in conjunction with tracer kinetic modeling enables the quantification of absolute myocardial blood flow (MBF). However, MBF maps computed using the traditional indirect method (i.e. post-reconstruction voxel-wise fitting of kinetic model to PET time-activity-curves-TACs) suffer from poor signal-to-noise ratio (SNR). Direct reconstruction of kinetic parameters from raw PET projection data has been shown to offer parametric images with higher SNR compared to the indirect method. The aim of this study was to extend and evaluate the performance of a direct parametric reconstruction method using in vivo dynamic PET MPI data for the purpose of quantifying MBF. Dynamic PET MPI studies were performed on two healthy pigs using a Siemens Biograph mMR scanner. List-mode PET data for each animal were acquired following a bolus injection of ~7–8 mCi of 18F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Additionally, eight independent noise realizations of both scans—each containing 1/8th of the total number of events—were generated from the original list-mode data. Dynamic sinograms were then used to compute parametric maps using the conventional indirect method and the proposed direct method. For both methods, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of 18F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using two fully-3D reconstruction techniques: the standard ordered subset expectation maximization (OSEM) reconstruction algorithm on one side, and the one-step late maximum a posteriori (OSL-MAP) algorithm on the other side, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel- and segment-wise estimates of , the tracer transport rate (ml · min−1 · ml−1), to those obtained using the indirect method applied to both OSEM and OSL-MAP dynamic reconstructions. The proposed direct reconstruction method produced maps with visibly lower noise than the indirect method based on OSEM and OSL-MAP reconstructions. At normal count levels, the direct method was shown to outperform the indirect method based on OSL-MAP in the sense that at matched level of bias, reduced regional noise levels were obtained. At lower count levels, the direct method produced estimates with significantly lower standard deviation across noise realizations than the indirect method based on OSL-MAP at matched bias level. In all cases, the direct method yielded lower noise and standard deviation than the indirect method based on OSEM. Overall, the proposed direct reconstruction offered a better bias-variance tradeoff than the indirect method applied to either OSEM and OSL-MAP. Direct parametric reconstruction as applied to in vivo dynamic PET MPI data is therefore a promising method for producing MBF maps with lower variance.

Reconstruction of polarization parameters in channel modulated polarization imaging system

Based on the reconstruction of the polarization parameters in a channel modulating polarization imaging system, the polarization features of the target could be extracted effectively. Considering that the reconstruction of polarization parameters can provide important reference for target recognition, material analysis, remote sensing and bio-medical treatment, the research on accurate reconstruction of polarization parameters is now urgently required. In order to improve the accuracy of polarization parameter reconstruction, we first study the influence of sample frequency of interference fringes on the imaging process. For the same carrier frequency, conjugate spectra are separated and also the spectra are not aliasing for two adjacent spectral lines. It is concluded that to prevent the image spectrum from aliasing, the sample frequency should be at least 4 times the maximum fringe frequency of the polarization interference image. Then we study Stokes parameter reconstruction method when the spectral line positions of interference image are changed by assembling error. Since different Stokes parameters are amplitude modulated at different frequencies, we apply segment filters to split the frequency domain into different regions, and seek for the largest spectrum in corresponding regions. The largest spectrum in different regions can be used to determine the spectral line position of polarization carrier frequency, and the two-dimensional images of the target are rebuilt in sequence by the frequency shifting, spectral filtering, and Fourier inversion transforming. According to the above method, we could obtain an exact polarization rebuilding image when the line position of polarization carrier frequency is modified. Finally, we use the computer simulation and experiment to verify the feasibility and effectiveness of such a rebuilding method. The results demonstrate that the reconstruction of polarization parameters in channel modulating polarization imaging by this rebuilding method is better than by the traditional theoretical rebuilding method. In detail, the mean square error between the reconstruction and original input image could be suppressed to 0.001 while the peak-signal-to-noise ratio is improved and the structural similarity index measurement could be more than 0.9 by utilizing the new rebuilding method. It turns out that the reconstruction method with great superiority can provide a promising reference for further research of channel modulating polarization imaging system.

Freeway traffic incident reconstruction – A bi-parameter approach

The paper suggests a novel alternative to generalized traffic incident descriptions within the macroscopic traffic model framework. The contribution of the paper is twofold. First, by extending already existing second order macroscopic conservation laws to characterize off-nominal traffic conditions, we define two main incident parameters such as direct and indirect ones. Physical interpretations of this incident parametrization is provided. These incident indicators are relative in view of the nominal traffic flow model parameters and carries physically meaningful macroscopic content. Second, the paper proposes to use a constrained and nonlinear, joint traffic state- and incident parameter reconstruction method and validates the suggested modeling idea via real traffic measurements fitting. Evaluation of the numerical results demonstrate the effectiveness of the methodology.

Direct Parametric Image Reconstruction in Reduced Parameter Space for Rapid Multi-Tracer PET Imaging.

The separation of multiple PET tracers within an overlapping scan based on intrinsic differences of tracer pharmacokinetics is challenging, due to limited signal-to-noise ratio (SNR) of PET measurements and high complexity of fitting models. In this study, we developed a direct parametric image reconstruction (DPIR) method for estimating kinetic parameters and recovering single tracer information from rapid multi-tracer PET measurements. This is achieved by integrating a multi-tracer model in a reduced parameter space (RPS) into dynamic image reconstruction. This new RPS model is reformulated from an existing multi-tracer model and contains fewer parameters for kinetic fitting. Ordered-subsets expectation-maximization (OSEM) was employed to approximate log-likelihood function with respect to kinetic parameters. To incorporate the multi-tracer model, an iterative weighted nonlinear least square (WNLS) method was employed. The proposed multi-tracer DPIR (MT-DPIR) algorithm was evaluated on dual-tracer PET simulations ([18F]FDG and [11C]MET) as well as on preclinical PET measurements ([18F]FLT and [18F]FDG). The performance of the proposed algorithm was compared to the indirect parameter estimation method with the original dual-tracer model. The respective contributions of the RPS technique and the DPIR method to the performance of the new algorithm were analyzed in detail. For the preclinical evaluation, the tracer separation results were compared with single [18F]FDG scans of the same subjects measured two days before the dual-tracer scan. The results of the simulation and preclinical studies demonstrate that the proposed MT-DPIR method can improve the separation of multiple tracers for PET image quantification and kinetic parameter estimations.

Parametric 3D reconstruction of the distribution density of point objects

The parametric reconstruction method has been developed for solving the problems concerning computer simulation of the 3D distributions of discrete objects, which are commonly specified by the parallel cross sections in the initial point cloud. The role of simulation and the model itself is examined as applied to the visualization of 3D distributions of objects and the analysis of microscopy data. The conceptual prerequisites and particularities of the technical implementation of the proposed method are compared with the lofting technique, which is widespread in modern 3D simulation systems. The peculiarities of method application are demonstrated by the example of reconstruction based on a series of model data.

Fast determination method of cerebral metabolic rate images of glucose using dynamic PET data.

Measurement of the rate constant parameters of the tracer 18F-FDG, used with positron emission tomography (PET) to determine the cerebral metabolic rate of glucose (CMRGlc), can provide a clear understanding of the physiological processes in the human brain. At present, the methods that are widely used to obtain CMRGlc, such as nonlinear least squares (NLS), first require the reconstruction of a time sequence of images. The reconstruction of these images requires a large amount of computation, especially in 3D Depth-of Interaction PET (DOI-PET), and the nonlinear based methods also require a large amount of computation. In this paper, we propose a fast parametric image reconstruction method for 18F-FDG dynamic PET studies. In our method a deconvolving process is first employed on the time sequential projection data to remove the effect of the measured plasma time activity. The deconvolved terms are integrated over three different time intervals and the parameters for determining CMRGlc can be obtained analytically. Our method requires only three reconstructing processes and reduces the computational demand to estimate CMRGlc. The algorithm performance is evaluated using a digital phantom and a clinical data set and the results show that the proposed method produces images with the same or better quality as the images from the NLS method, with much less computation compared to the NLS method.

Reconstruction of the interaction term between dark matter and dark energy using SNe Ia

We apply a parametric reconstruction method to a homogeneous, isotropic and spatially flat Friedmann-Robertson-Walker (FRW) cosmological model filled of a fluid of dark energy (DE) with constant equation of state (EOS) parameter interacting with dark matter (DM)\\@. The reconstruction method is based on expansions of the general interaction term and the relevant cosmological variables in terms of Chebyshev polynomials which form a complete set orthonormal functions. This interaction term describes an exchange of energy flow between the DE and DM within dark sector. To show how the method works we do the reconstruction of the interaction function expanding it in terms of only the first six Chebyshev polynomials and obtain the best estimation for the coefficients of the expansion assuming three models: (a) a DE equation of the state parameter w = −1 (an interacting cosmological Λ), (b) a DE equation of the state parameter w = constant with a dark matter density parameter fixed, (c) a DE equation of the state parameter w = constant with a free constant dark matter density parameter to be estimated, and using the Union2 SNe Ia data set from ``The Supernova Cosmology Project'' (SCP) composed by 557 type Ia supernovae. In both cases, the preliminary reconstruction shows that in the best scenario there exist the possibility of a crossing of the noninteracting line Q = 0 in the recent past within the 1σ and 2σ errors from positive values at early times to negative values at late times. This means that, in this reconstruction, there is an energy transfer from DE to DM at early times and an energy transfer from DM to DE at late times. We conclude that this fact is an indication of the possible existence of a crossing behavior in a general interaction coupling between dark components.

Exponential Sampling: A Gibbs Phenomena Removal Model for Finite Rate of Innovation Sampling Framework

We propose an exponential approximating function as a sampling kernel with finite rate of innovation. The performance of reconstruct non-bandlimited signals from its low frequency components would inevitably induce Gibbs phenomenon. This paper establishes the theoretical model on relationship between sampling kernel filter and parametric reconstruction method of non-bandlimited signals, and designs a new window function exponential sampling kernel filter to removal Gibbs Influence. Simulation results show that, compared to Sinc sampling kernel filter, the reconstruction ability of exponential filter based finite rate sampling system is improved under the white Gaussian noise environment.

Methods to infer transmission risk factors in complex outbreak data

Data collected during outbreaks are essential to better understand infectious disease transmission and design effective control strategies. But analysis of such data is challenging owing to the dependency between observations that is typically observed in an outbreak and to missing data. In this paper, we discuss strategies to tackle some of the ongoing challenges in the analysis of outbreak data. We present a relatively generic statistical model for the estimation of transmission risk factors, and discuss algorithms to estimate its parameters for different levels of missing data. We look at the problem of computational times for relatively large datasets and show how they can be reduced by appropriate use of discretization, sufficient statistics and some simple assumptions on the natural history of the disease. We also discuss approaches to integrate parametric model fitting and tree reconstruction methods in coherent statistical analyses. The methods are tested on both real and simulated datasets of large outbreaks in structured populations.