Sampling Step Size Research Articles

Bayesian inversion and uncertainty analysis of transient electromagnetic data

AbstractQuantification of non‐uniqueness and uncertainty is important for transient electromagnetism (TEM). To address this issue, we develop a trans‐dimensional Bayesian inversion schema for TEM data interpretation. The trans‐dimensional posterior probability density (PPD) offers a solution to model selection and quantifies parameter uncertainty resulting from the model selection from all possible models rather than determining a single model. We use the reversible‐jump Markov chain Monte Carlo sampler to draw ensembles of models to approximate PPD. In addition to providing reasonable model selection, we address the reliability of the inversion results for uncertainty analysis. This strategy offers reasonable guidance when interpreting the inversion results. We make the following improvements in this paper. First, in terms of algorithmic acceleration, we use the nonlinear optimization inversion results as the initial model and implement the multi‐chain parallel method. Second, we develop double factors to control the sampling step size of the proposed distribution, so that the sampling models cover the high‐probability region of the parameter space as much as possible. Finally, we provide the potential scale reduction factor‐η convergence criteria to assess the convergence of the samples and ensure the rationality of the output models. The proposed methodology is first tested on synthetic data and subsequently applied to a field dataset. The TEM inversion results show that probability inversion can provide reliable references for data interpretation through uncertainty analysis.

A Semi-Implicit Parallel Leapfrog Solver With Half-Step Sampling Technique for FPGA-Based Real-Time HIL Simulation of Power Converters

Field Programmable Gate Array (FPGA) based Hardware-in-the-loop (HIL) simulation is an effective tool to verify the performance of physical controllers and shorten the development cycle of power converters. In HIL simulations, sampling accuracy is of concern and is desired to be improved by reducing the step size. However, due to the cost of computational time, the step size is hard to reduce indefinitely to meet the requirements for high switching frequency applications. To improve the sampling accuracy and simulation performance of HIL simulation, this paper proposes a semi-implicit parallel leapfrog (SPL) solver with half-step sampling technique. In this solver, the switches and the rest part of the system are implemented to be computed parallel when the switch leg model operates in continuous current mode. Besides, the solver is formulated in leapfrog format to reduce computational costs and to compute at half-step as a minimum step-size. With this format, the half-step sampling technique can be employed to increase the sampling rate by onefold, even in cases where it is challenging to reduce the simulation step size further. A dual active bridge converter case is implemented on the FPGA board with a 12.5-ns sampling step-size, retaining the simulation accuracy while switched at 400 kHz. To further verify the advantages, the results are compared with other HIL method and experimental results.

Sampling and Reconstructing Angular Domains With Uniform Arrays

The surge of massive antenna arrays in wireless networks calls for the adoption of analog/hybrid array solutions, where multiple antenna elements are driven by a common radio front end to form a beam along a specific angle in order to maximize the beamforming gain. Many heuristics have been proposed to sample the angular domain by trading off between sampling step size and overhead, where arbitrarily small angular step size is only attainable with infinite sampling overhead. We show that, for uniform linear and rectangular arrays, lossless reconstruction of the array’s angular responses at arbitrary angular precision is possible using a finite number of samples without resorting to assumptions of angular sparsity. The proposed method, sampling and reconstructing angular domain (SARA), defines how many and which angles to be sampled and the corresponding reconstruction. This general solution to scan the angular domain can therefore be applied not only to beam acquisition and channel estimation, but also to radio imaging techniques, making it a candidate for future integrated sensing and communications (ISAC). Extensive simulation results for target detection and radio imaging have demonstrated clear advantages of SARA over other considered baselines, both in terms of angular reconstruction performance and computational complexity.

DAS: Efficient Street View Image Sampling for Urban Prediction

Street view data is one of the most common data sources for urban prediction tasks, such as estimating socioeconomic status, sensing physical urban changes, and identifying urban villages. Typical research in this field consists of two steps: acquiring a dataset with a street view image sampling algorithm and designing a prediction algorithm for urban prediction tasks. However, most of the previous research focuses on the prediction algorithms, leaving the sampling algorithms underexplored. To fill this gap, we set out to investigate how different street view image sampling algorithms affect the performance of the follow-up tasks and develop an effective street view image sampling algorithm for urban prediction. Through a comprehensive analysis of the performance of different sampling algorithms in three of the most common urban prediction tasks, including commercial activeness prediction, urban liveliness prediction, and urban population prediction, we provide solid empirical evidence that the sampling algorithm significantly affects the performance of the prediction model. Specifically, the performance differences of different sampling algorithms can reach over 25%. Further, we revealed that the sampling step size and the sampling quality are two important factors that affect the performance of a sampling algorithm, while the sampling angle has little influence. Inspired by our analysis results, we propose an effective street view image sampling algorithm, DAS, which contains a denoising module and an adaptive sampling module. It can dynamically adjust the sampling step size to adapt to the optimal size for each region and get rid of the impact of noise images in the meantime. Experiments on three large-scale datasets demonstrate its superior performance over multiple state-of-the-art baselines, and further ablation study shows the effectiveness of each module. Finally, through a thorough discussion of our findings and experimental results, we provide insights into the street view image sampling algorithm design, and we call for more researches in this blank area.

An Improved Shape from Focus Method for Measurement of Three-Dimensional Features of Fuel Nozzles

The precise three-dimensional measurement of fuel nozzles is of great significance to assess the manufacturing accuracy and improve the spray and atomization performance. This paper proposes an improved fast shape from focus (SFF) method for three-dimensional measurement of key features of fuel nozzles. In order to ensure the measurement accuracy and efficiency of the SFF, the dispersion of the measured points from a standard flat plane was used to select the optimal combination of the focus measure operator, window size and sampling step size. In addition, an approximate method for the focus measure interval is proposed to improve the measurement efficiency, which uses the peak region of the central pixel to replace the peak region of other pixels. The results show that the proposed method decreased the average computation time of the focus measure by 79.19% for the cone section and by 38.30% for the swirl slot. Compared with a reference laser scanning microscope, the measurement error in length is within 10 μm and the error in angle is within a maximum 0.15°.

Jitter noise modeling and its removal using recursive least squares in shape from focus systems

Three-dimensional shape recovery from the set of 2D images has many applications in computer vision and related fields. Passive techniques of 3D shape recovery utilize a single view point and one of these techniques is Shape from Focus or SFF. In SFF systems, a stack of images is taken with a single camera by manipulating its focus settings. During the image acquisition, the inter-frame distance or the sampling step size is predetermined and assumed constant. However, in a practical situation, this step size cannot remain constant due to mechanical vibrations of the translational stage, causing jitter. This jitter produces Jitter noise in the resulting focus curves. Jitter noise is invisible in every image, because all images in the stack are exposed to the same error in focus; thus, limiting the use of traditional noise removal techniques. This manuscript formulates a model of Jitter noise based on Quadratic function and the Taylor series. The proposed method, then, solves the jittering problem for SFF systems through recursive least squares (RLS) filtering. Different noise levels were considered during experiments performed on both real as well as simulated objects. A new metric measure is also proposed, referred to as depth distortion (DD), which calculates the number of pixels contributing to the RMSE in percentage. The proposed measure is used along with the RMSE and correlation, to compute and test the reconstructed shape quality. The results confirm the effectiveness of the proposed scheme.

Sampled-data-based consensus of multi-agent systems with multiplicative noise and time-delays

The sampled-data-based consensus control problem of multi-agent systems (MASs) with multiplicative noise and time-delays is studied in this paper. The MASs are given in a continuous-time setting while information exchange occurs only at the sampling instants. Therefore, the traditional methods for continuous-time or discrete-time models are not applicable. To resolve the problem, a discretization-reconnection method is developed to investigate the consensus control of first-order and second-order MASs, respectively. Some sufficient conditions, explicitly related to the control gains and the sampling step size, are established for both mean-square (m.s.) and almost sure (a.s.) consensus. Under these conditions, consensus can be achieved by designing appropriate control gains and the sampling step size for MASs with given noise intensity and time-delays. Numerical simulations verify the effectiveness of the theoretical results.

A novel trans-dimensional Bayesian inversion strategy for airborne time-domain electromagnetic data

The trans-dimensional Bayesian inversion method based on statistical theory regards the inversion parameters as random variable, it not only provides a reasonable inverse model based on the probability, but also offers the probability distribution and the uncertainty information of the inverse model parameters. However, for the conventional trans-dimensional Bayesian inversion, the model sampling efficiency and inversion convergence rate are influenced by several factors, and it requires sampling over a big model space, those limit the application of the trans-dimensional Bayesian inversion for airborne time-domain electromagnetic data. In this paper, we present a novel trans-dimensional Bayesian inversion strategy for airborne time-domain electromagnetic data, which uses a combining sampling update method to implement the model sampling. This method uses the block-wise updating method to run only one Markov chain with the initial state constructed by conductivity-depth imaging during the burn-in period, and adopts the component-wise updating method with an adaptive sampling step size to perform multiple Markov chains in parallel after the burn-in period ends. The effectiveness of the novel Bayesian inversion strategy was validated by both synthetic data and survey data. The experimental results showed that this inversion strategy can not only obtain better inversion results, but also shorten the burn-in period and reduce the total sampling times of the Markov chain.

An adaptive reversible jump MCMC inversion algorithm for airborne time-domain electromagnetic data

The reversible jump Markov Chain Monte Carlo algorithm is a trans-dimensional Bayesian inversion method, which can not only obtain the best inversion solution, but also provide the uncertainty information of inversion parameters, so as to effectively evaluate the reliability of inversion results. However, in trans-dimensional Bayesian inversion, the step size of model sampling has a great influence on the efficiency and precision of inversion. To solve the selection problem of sampling step size, this paper presents an adaptive reversible jump MCMC inversion algorithm for airborne time-domain electromagnetic data. In this method, the sampling step length is automatically adjusted in the sampling process through the data fitting error of each sampling model, so as to avoid the influence of unreasonable sampling step size and improve the acceptance rate of model sampling. The validity of the proposed method is verified by inversion test on the synthetic data and compared with the regularized inversion results. The inversion results demonstrate that the adaptive reversible jump MCMC inversion algorithm can improve the acceptance rate of model sampling and the accuracy of inversion results.

Sampling-Noise Modeling & Removal in Shape From Focus Systems Through Kalman Filter

Shape from Focus (SFF) is one of the passive techniques to recover the shape of an object under consideration. It utilizes the focus cue present in the stack of images, obtained by a single camera. In SFF when the images are acquired, the inter-frame distance, also known as the sampling step size, is assumed to be constant. However, in practice, due to mechanical constraints, sampling step size cannot remain constant. The inconsistency in the sampling step size causes the problem of jitter, and produces Jitter noise in focus curves. This Jitter noise is not visible in images, because each pixel in an image (of the stack) will be subjected to the same error in focus. Thus, traditional image denoising techniques will not work. This paper formulates a model of the Jitter noise, followed by the design of system and measurement models for Kalman filter. Then, the jittering problem for SFF systems is solved using the proposed filtering technique. Experiments are performed on simulated and real objects. Ten noise levels are considered for simulated, and four for real objects. RMSE and Correlation are used to measure the reconstructed shape. The results show the effectiveness of the proposed scheme.

Adaptive volumetric light and atmospheric scattering.

An adaptive sampling-based atmospheric scattering and volumetric light framework for flight simulator (FS) is proposed to enhance the immersion and realism in real-time. The framework comprises epipolar sampling (ES), visible factor culling (VFC), interactive participating media density estimating (IPMDE). The main process of proposed architecture is as follows: the scene is divided into two levels according to the distance from the camera. In the high-level pipeline, the layer close to the camera, more samples, and smaller sampling step size is used to improve image quality. Further, the IPMDE method is designed to enhance realism by achieving interactivity with the participating media and multiple light sources. Further optimization is performed by the lookup table and 3D volumetric textures, by which we can compute the density of participating media and the scattering coefficient in parallel. In the low-level pipeline, when the samples are far away from the camera, its influence on the final output is also reduced, which results in fewer samples and a bigger sampling step size. The improved ES method further reduces the number of samples involved in ray marching using the features of epipolar geometry. It then generates global light effects and shadows of distant terrain. The VFC method uses an acceleration structure to quickly find the lit segments which eliminate samples blocked by obstacles. The experimental results demonstrate our architecture achieves a better sense of reality in real-time and is very suitable for FS.

The ANSDM Converters Dynamic Range Design Process

The results of analytic and simulating works proved that for nonstationary sources, the delta converters with adaptive sampling expose higher coding efficiency than the former proposals, based on uniform sampling methods. The knowledge of the sampling interval range and the algorithm of the Nonuniform Sampling Delta Modulation and Adaptive Nonuniform Sampling Delta Modulation allows finding the necessary number of the sampling intervals and their values that maximizes SNR. The total dynamic range of the ANSDM modulator is the product of the dynamic range both from sampling interval and step size adaptation. Due to the high complexity of the calculations, the ANSDMsoft program was developed to support computing. All computational works were carried out using the Maple environment. Maple allows to solve complex mathematical functions and display their results in a simple way. Most importantly, it supports the LambertW function, used in the computing of NSDM or ANSDM modulators parameters. Graphic illustrations of the NSDM and ANSDM modulator dynamic range as a function of the minimum and maximum sampling frequency are presented.

NURBS Interpolator with Adaptive Smooth Feedrate Scheduling and Minimal Feedrate Fluctuation

For an effective NURBS interpolator, generating the smooth feedrate profile and minimizing the feedrate fluctuation are two main tasks, which have a great influence on the machining quality. In this paper, a NURBS interpolator is proposed to solve the problem with offline-online two stages, which contain curving splitting, feedrate scheduling, and real-time interpolation modules. At first, in offline module, the limited feedrate of the curve is calculated with consideration of geometric characteristics and dynamic constraints, and the curve is split into several segments according to the key regions. Thus the necessary information is stored. Then the feedrate scheduling algorithm is applied with constant feedrate scheduling method at each segment, where tangential acceleration and jerk are taken into consideration to generate an adaptive smooth S-type feedrate profile. Moreover, in real-time interpolation module, an average feedrate calculation method is proposed to determine the sampling step size. And to minimize the feedrate fluctuation, a double interpolation algorithm based on the cosine theorem is presented, which use the second-order Taylor’s expansion method two times in one interpolation period. Finally, simulations and experiments are conducted to verify the performance of the proposed interpolator.

Data driven time scale in Gaussian quasi-likelihood inference

We study parametric estimation of ergodic diffusions observed at high frequency. Different from the previous studies, we suppose that sampling stepsize is unknown, thereby making the conventional Gaussian quasi-likelihood not directly applicable. In this situation, we construct estimators of both model parameters and sampling stepsize in a fully explicit way, and prove that they are jointly asymptotically normally distributed. High order uniform integrability of the obtained estimator is also derived. Further, we propose the Schwarz (BIC) type statistics for model selection and show its model-selection consistency. We conducted some numerical experiments and found that the observed finite-sample performance well supports our theoretical findings.

A polynomial equation-based interpolation method of NURBS tool path with minimal feed fluctuation for high-quality machining

Due to the approximation errors of interpolation methods in non-uniform rational b-spline (NURBS) interpolation, feed fluctuation is inevitable, which has great effects on the machining quality and should be minimized. Based on the idea of zero feed fluctuation, a polynomial equation-based interpolation method of NURBS tool path is proposed in this paper. Firstly, a polynomial equation with respect to the curve parameter increment is formulized according to the sampling step size, which is determined by the scheduled feedrate, acceleration, and jerk. Then, Newton’s method is utilized to solve the high-degree polynomial equation with taking both convergence rate and computational load. In order to improve the computing efficiency in real-time interpolation, a fast-evaluation and derivation algorithm is proposed, which uses the Taylor series expansion to accelerate the calculation of any order derivatives of NURBS. Simulations are conducted among the proposed method and the chord-tracking algorithm (CTA) method, and the results of each method are compared on the basis of computing time and feed fluctuation, which shows that the proposed method is better than the CTA method. Experiment is also conducted to verify the feasibility and applicability of the proposed method in practical application.

A neural network-based 2D/3D image registration quality evaluator for pediatric patient setup in external beam radiotherapy.

Our purpose was to develop a neural network‐based registration quality evaluator (RQE) that can improve the 2D/3D image registration robustness for pediatric patient setup in external beam radiotherapy. Orthogonal daily setup X‐ray images of six pediatric patients with brain tumors receiving proton therapy treatments were retrospectively registered with their treatment planning computed tomography (CT) images. A neural network‐based pattern classifier was used to determine whether a registration solution was successful based on geometric features of the similarity measure values near the point‐of‐solution. Supervised training and test datasets were generated by rigidly registering a pair of orthogonal daily setup X‐ray images to the treatment planning CT. The best solution for each registration task was selected from 50 optimizing attempts that differed only by the randomly generated initial transformation parameters. The distance from each individual solution to the best solution in the normalized parametrical space was compared to a user‐defined error tolerance to determine whether that solution was acceptable. A supervised training was then used to train the RQE. Performance of the RQE was evaluated using test dataset consisting of registration results that were not used in training. The RQE was integrated with our in‐house 2D/3D registration system and its performance was evaluated using the same patient dataset. With an optimized sampling step size (i.e., 5 mm) in the feature space, the RQE has the sensitivity and the specificity in the ranges of 0.865–0.964 and 0.797–0.990, respectively, when used to detect registration error with mean voxel displacement (MVD) greater than 1 mm. The trial‐to‐acceptance ratio of the integrated 2D/3D registration system, for all patients, is equal to 1.48. The final acceptance ratio is 92.4%. The proposed RQE can potentially be used in a 2D/3D rigid image registration system to improve the overall robustness by rejecting unsuccessful registration solutions. The RQE is not patient‐specific, so a single RQE can be constructed and used for a particular application (e.g., the registration for images acquired on the same anatomical site). Implementation of the RQE in a 2D/3D registration system is clinically feasible.PACS numbers: 87.57.nj, 87.85.dq, 87.55.Qr

Convergence of Wachspress coordinates: from polygons to curved domains

Given a smooth, strictly convex planar domain, we investigate point-wise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain. Based on a relation between the discrete Wachspress case and the limit smooth case given by the Wachspress kernel defined by Warren et al., we show that the corresponding sequences of Wachspress interpolants and mappings converge as 𝓞(h 2) for a sampling step size h of the boundary curve of the domain as h → 0. Several examples are shown to numerically validate the results and to visualise the behaviour of discrete interpolants and mappings as they converge to their smooth counterparts. Empirically, the same convergence order is observed also for mean value coordinates. Moreover, our numerical tests suggest that the convergence of interpolants and mappings is uniform both in the Wachspress and mean value cases.

SU-E-QI-02: A Quantitative Method for 3D Morphology Analysis of Cancer Cells

Purpose: Morphological identification is a widespread procedure for assessment of cells by visual inspection of the morphological characteristics or the fluorescence images. It is lengthy and can only provide quantitative results. A quick and qualitative method is highly desired. In this abstract, a stereology based quick method for morphology measurement is reported. Methods: The 3D images of 110 breast cancer cells(MCF7) and 96 melanoma cells(B16) acquired with fixed z-step size of 0.5?m using a confocal-laser-scanning-microscope(CLSM)(Zeiss-LSM510) were used. The stereological measurement method includes three steps: 1. randomly select a starting slice from the 3D image stack of a cell and go through the whole image stack with a uniform sampling step-size, 2. an in-house software generated square-grid containing the array of test points with known separation is superimposed on a picked slice, and points located at edge of the nucleus/cell membrane are counted in x and y directions respectively, 3. calculate cell morphology parameters based on the known slice spacing, test point separation and measured numbers of points. The step-size used in the experiments was determined by keeping the coefficient-of- error(CE) less than 5%. The circumference, areas and volumes of the cells and nuclei were measured. The averaged volume of nuclei(Vn), volume density of nuclei(Vvn), surface area density of nuclei(Svn), ratio of surface area and volume of nuclei(Rsvn), and ratio of nuclei and plasma(Rnp) were calculated. The maximum, minimum and median diameters of the cells were calculated from the binarized image of the cells. To validate the new method, the data were compared with the data reported in literatures. Results: The morphology parameters measured with the new method are consistent and repeatable (maximum standard deviation SD<2.3μm,p<0.03), and close to the values reported in literatures(p>0.1). Conclusion: The stereological method is a quick and easy-to-use tool for quantitative analysis of cancer cell morphology.

Bilateral prediction and intersection calculation autofocus method for automated microscopy

In this paper, a bilateral prediction and intersection calculation autofocus method for automated microscopy, which obtains the in-focus position by calculating the intersection of the predicted left and right focus measure curves located respectively in the left and right sides of the peak position of the focus measure curve, is proposed and performed. According to the autofocus method, the area including the peak position of the focus measure curve and its left and right neighbourhoods should be determined firstly, and the left and right neighbourhoods are considered as the left and right sampling areas. The left and right focus measure curves are predicted by appropriate predicting models according to the two sample sequences, which comprise the focus values by evaluating the sampled images in the left sampling area and right sampling area, respectively and their corresponding sampling positions. The intersection of the predicted left and right focus measure curves is calculated and can be considered as the in-focus position. The autofocus can be realized by moving the focus plane of the microscope to the intersection of the predicted left and right focus measure curves. The proposed bilateral prediction and intersection calculation autofocus method is experimentally verified in an automated light microscopy for implementing microassembly and micromanipulation. The theoretical analyses have shown that the proposed bilateral prediction and intersection calculation autofocus method can not only effectively avoid the principle error caused by assuming the symmetrical focus measure curve in the autofocus methods based on curve fitting, but also eliminate the possible waver search near the peak position in the modified fast climbing servo method. The experimental results have shown that the proposed bilateral prediction and intersection calculation autofocus method possesses the merits as follows: (1) the focusing accuracy is high and slightly affected by the sampling step size and (2) the focusing speed is higher than those of the 7-point hill-climbing search method and the quadratic curve fitting method with a determinate focusing accuracy.

WE-E-213CD-10: A Robust 2D/3D Image Registration System for Pediatric Patient Setup in External Beam Radiotherapy.

To develop a neural network based registration quality evaluator (RQE) that can improve the 2D/3D image registration robustness for pediatric patient setup in external beam radiotherapy. X-ray setup images of six pediatric patients with brain tumors received proton therapies were retrospectively registered with their treatment planning computed tomography (CT) images. A neural network based pattern classifier was used as an RQE to classify 2D/3D rigid registration solutions as successful or unsuccessful based on features of the similarity value surfaces near the point-of-solution. The supervised training and test datasets were generated by rigidly registering a pair of orthogonal daily setup x-ray images to the treatment planning CTs. The best solution for each registration task was selected from 50 optimizing attempts that differed only by the initial transformation parameters. The distance from each individual solution to the best solution in the normalized parametrical space was compared to a user- defined error threshold to determine whether that solution was successful. The supervised training was then used to train the RQE. The performance of the RQE was evaluated using the test dataset that consisted of registration results that were not used in training. With the optimized sampling step size, i.e., 5 mm, in the feature space, the RQE has the sensitivity and the specificity in the ranges of 0.865-0.964 and 0.797-0.990, respectively, when it was used to detect the registration error with the mean voxel displacement (MVD) greater than 1 mm. The proposed RQE can potentially be used in a 2D/3D rigid image registration system to improve its robustness by rejecting unsuccessful registration solutions. The RQE is non-patient specific and needs only to be trained once for each treatment site. The implementation the RQE in a 2D/3D registration system results only 10% to 20% increase of the overall computation time. The authors have no conflict of interest to disclose.