Non-uniform Sampling Data Research Articles

Non-uniformly sampled 2D NMR Spectroscopy reconstruction based on Low Rank Hankel Matrix Fast Tri-Factorization and Non-convex Factorization

Nuclear magnetic resonance (NMR) spectroscopy is widely used in chemistry and medicine to research the composition of matter and the spatial structure of proteins. However, NMR signals with larger sizes and higher dimensions are slower to acquire. Therefore, Non-Uniform Sampling (NUS) methods are used to speed up the acquisition of NMR signals, and some mathematical algorithms are used to recover the original NMR signals from the NUS data. In recent years, low-rank Hankel matrix completion is proved to recover NMR data with less error. However, it requires singular value decomposition (SVD) with high computational complexity in each iteration, which is not suitable for reconstructing signals with large sizes. In this paper, we propose a Fast Tri-Factorization (FTF) method to decompose the low-rank Hankel matrix into three small-scale matrices, and it convert the original problem into a matrix nuclear norm minimization problem on the small-scale matrix to mitigate high computation cost of multiple SVDs. Furthermore, the factor matrix size remains constant for different size of the Hankel matrices. We further replace the low-rank constraint with Non-convex Factorization (NF) to avoid the time-consuming SVD in each iteration. Numerical experiments show that the proposed method can significantly speed up the NMR reconstruction compared with several existing algorithms while ensuring the reconstruction accuracy.

Dynamic forecasting of severe acute graft-versus-host disease after transplantation

Forecasting of severe acute graft-versus-host disease (aGVHD) after transplantation is a challenging ‘large p, small n’ problem that suffers from nonuniform data sampling. We propose a dynamic probabilistic algorithm, daGOAT, that accommodates sampling heterogeneity, integrates multidimensional clinical data and continuously updates the daily risk score for severe aGVHD onset within a two-week moving window. In the studied cohorts, the cross-validated area under the receiver operator characteristic curve (AUROC) of daGOAT rose steadily after transplantation and peaked at ≥0.78 in both the adult and pediatric cohorts, outperforming the two-biomarker MAGIC score, three-biomarker Ann Arbor score, peri-transplantation features-based models and XGBoost. Simulation experiments indicated that the daGOAT algorithm is well suited for short time-series scenarios where the underlying process for event generation is smooth, multidimensional and where there are frequent and irregular data missing. daGOAT’s broader utility was demonstrated by performance testing on a remotely different task, that is, prediction of imminent human postural change based on smartphone inertial sensor time-series data.

NUScon: a community-driven platform for quantitative evaluation of nonuniform sampling in NMR.

Although the concepts of nonuniform sampling (NUS​​​​​​​) and non-Fourier spectral reconstruction in multidimensional NMR began to emerge 4 decades ago , it is only relatively recently that NUS has become more commonplace. Advantages of NUS include the ability to tailor experiments to reduce data collection time and to improve spectral quality, whether through detection of closely spaced peaks (i.e., "resolution") or peaks of weak intensity (i.e., "sensitivity"). Wider adoption of these methods is the result of improvements in computational performance, a growing abundance and flexibility of software, support from NMR spectrometer vendors, and the increased data sampling demands imposed by higher magnetic fields. However, the identification of best practices still remains a significant and unmet challenge. Unlike the discrete Fourier transform, non-Fourier methods used to reconstruct spectra from NUS data are nonlinear, depend on the complexity and nature of the signals, and lack quantitative or formal theory describing their performance. Seemingly subtle algorithmic differences may lead to significant variabilities in spectral qualities and artifacts. A community-based critical assessment of NUS challenge problems has been initiated, called the "Nonuniform Sampling Contest" (NUScon), with the objective of determining best practices for processing and analyzing NUS experiments. We address this objective by constructing challenges from NMR experiments that we inject with synthetic signals, and we process these challenges using workflows submitted by the community. In the initial rounds of NUScon our aim is to establish objective criteria for evaluating the quality of spectral reconstructions. We present here a software package for performing the quantitative analyses, and we present the results from the first two rounds of NUScon. We discuss the challenges that remain and present a roadmap for continued community-driven development with the ultimate aim of providing best practices in this rapidly evolving field. The NUScon software package and all data from evaluating the challenge problems are hosted on the NMRbox platform.

An Optimized Triggering Algorithm for Event-Triggered Control of Networked Control Systems

This paper presents an optimized algorithm for event-triggered control (ETC) of networked control systems (NCS). Initially, the traditional backstepping controller is designed for a generalized nonlinear plant in strict-feedback form that is subsequently extended to the ETC. In the NCS, the controller and the plant communicate with each other using a communication network. In order to minimize the bandwidth required, the number of samples to be sent over the communication channel should be reduced. This can be achieved using the non-uniform sampling of data. However, the implementation of non-uniform sampling without a proper event triggering rule might lead the closed-loop system towards instability. Therefore, an optimized event triggering algorithm has been designed such that the system states are always forced to remain in stable trajectory. Additionally, the effect of ETC on the stability of backstepping control has been analyzed using the Lyapunov stability theory. Two case studies on an inverted pendulum system and single-link robot system have been carried out to demonstrate the effectiveness of the proposed ETC in terms of system states, control effort and inter-event execution time.

Elastic full waveform inversion on unstructured meshes by the finite element method

In this paper, we develop a new numerical method for elastic full waveform inversion (FWI) on unstructured triangular meshes. With the triangular meshes, the elastic wave system is solved by the finite element method in the frequency domain and so irregular topography and nonuniform data sampling in space are allowed. The inversion is an optimization iterative process to minimize the residual between the synthetic data and observed data. It is implemented iteratively based on the nonlinear conjugate gradient method from low frequency to high frequency successively. Furthermore, the inverse result at current frequency is used as the initial model for the next frequency inversion, which avoids local minima of objective function effectively. The inverted parameters in the method are approximated by a piecewise linear polynomial rather than point values like the finite difference method, which improves the inversion accuracy. To improve accuracy further in the noise case, the iterative Tikhonov regularization is incorporated into FWI effectively. Unlike the commonly used regularization methods in FWI on rectangular meshes, the developed iterative Tikhonov regularization can be computed efficiently on the unstructured triangular meshes. Numerical computations for models with irregular topography and complex structures are completed. The results show that our method can adapt complex topography effectively while it yields very high accurate inversion results even in the case of certain noise.

Modified slanted-edge method to measure the modulation transfer function of camera

The slanted-edge method specified in ISO Standard 12223, which experiences large errors in the camera modulation transfer function(MTF) due to tilt angle error in the knife-edge resulting in non-uniform sampling of the edge spread function. In order to resolve this problem, a modified slanted-edge method for camera MTF measurement is proposed. By applying a simple direct calculation of the Fourier transform of the derivative for the non-uniform sampling data, the camera super-sampled MTF results are obtained. Theoretical simulations for images with and without noise under different tilt angle errors are run using the proposed method. It is demonstrated that the MTF results are insensitive to tilt angle errors. To verify the accuracy of the proposed method, an experimental setup for camera MTF measurement is established. Measurement results show that the proposed method is superior to traditional methods, and improves the universality of the slanted knife-edge method for camera MTF measurement.

Nonequispaced grid sampling in photoacoustics with a nonuniform fast Fourier transform.

To obtain the initial pressure from the collected data on a planar sensor arrangement in photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to cope with the evaluation of the data's Fourier transform on a non-equispaced mesh. In this paper, we use the non-uniform fast Fourier transform to handle this issue and show its feasibility in 3D experiments with real and synthetic data. This is done in comparison to the standard approach that uses linear, polynomial or nearest neighbor interpolation. Moreover, we investigate the effect and the utility of flexible sensor location to make optimal use of a limited number of sensor points. The computational realization is accomplished by the use of a multi-dimensional non-uniform fast Fourier algorithm, where non-uniform data sampling is performed both in frequency and spatial domain. Examples with synthetic and real data show that both approaches improve image quality.

Modeling the plasmasphere to topside ionosphere scale height ratio

A new model of plasmasphere to topside ionosphere scale heights ratio is developed, based on topside electron density ( N e ) profiles deduced from the International Satellites for Ionospheric Studies (ISIS)-1 satellite measurements. The model is able to improve operational algorithms for space weather predictions. The topside ionospheric and plasmaspheric scale heights are determined by the lowest and largest gradients of measured profiles, respectively, converted in d h /dlnNe units. The new model depends on four parameters: the month of the year ( M ), the local time (LT), the geomagnetic latitude (glat), and the ln(O + ) density ( z O) at the O + -H + ion transition height. It is designed to replace the old one-dimensional model of the ratio in the TaD (TSM-assisted Digisonde) profiler. The parameters M , LT, and glat are approximated by trigonometric basis functions, while z O is described by a polynomial. A series of models were produced with different number of coefficients (number of terms) of the basis functions. Comparison between models revealed that those with larger number of coefficients can produce unrealistic extremes of the model curves due to the non-uniform sampling of data along the axes. Further considered is the simplest model approximating M , LT, and glat by simple 24 sinusoidal functions and linearly depending on z O. The model description and its 54 coefficients are given in and can be used by other users for reconstruction of plasmasphere density profiles. The main variation of the ratio along geomagnetic latitude at fixed values of the other model parameters is illustrated in a series of plots.

Noise Power Spectrum in PROPELLER MR Imaging.

The noise power spectrum (NPS), an index for noise evaluation, represents the frequency characteristics of image noise. We measured the NPS in PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) magnetic resonance (MR) imaging, a nonuniform data sampling technique, as an initial study for practical MR image evaluation using the NPS. The 2-dimensional (2D) NPS reflected the k-space sampling density and showed agreement with the shape of the k-space trajectory as expected theoretically. Additionally, the 2D NPS allowed visualization of a part of the image reconstruction process, such as filtering and motion correction.

Integrated control circuit for adaptive sampling

A fully integrated controller for non-uniform data sampling suitable for the pre-processing of signals in a power- and size-restricted sensor front-end is presented. The sample rate is dynamically varied based on signal activity determined by the 2nd derivative of the input voltage. The derivative is realized with high-pass filters having 647 Hz cut-off frequency. A digital circuit generates the time-stamps and the trigger for an external analog-to-digital converter. Measured results of a 0.35 μm CMOS implementation show a sample rate variation of 7:1 and a system power advantage compared to conventional front-ends. The circuit dissipates 48 μW from ±1.5 V supplies and consumes an active area of 0.068 mm2.

Sensitivity analysis of solutions of the harmonic inversion problem: Are all data points created equal?

We consider the harmonic inversion problem, and the associated spectral estimation problem, both of which are key numerical problems in NMR data analysis. Under certain conditions (in particular, in exact arithmetic) these problems have unique solutions. Therefore, these solutions must not depend on the inversion algorithm, as long as it is exact in principle. In this paper, we are not concerned with the algorithmic aspects of harmonic inversion, but rather with the sensitivity of the solutions of the problem to perturbations of the time-domain data. A sensitivity analysis was performed and the counterintuitive results call into question the common assumption made in “super-resolution” methods using non-uniform data sampling, namely, that the data should be sampled more often where the time signal has the largest signal-to-noise ratio. The numerical analysis herein demonstrates that the spectral parameters (such as the peak positions and amplitudes) resulting from the solution of the harmonic inversion problem are least susceptible to the perturbations in the values of data points at the edges of the time interval and most susceptible to the perturbations in the values at intermediate times.

Characterization of the timing noise of the Crab pulsar

We present a power spectral analysis of the timing noise of the Crab pulsar, mainly using radio measurements from Jodrell Bank taken over the period 1982–89, an interval bounded by sparse data sampling and a large glitch. The power spectral analysis is complicated by non-uniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power ‘leakage’. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of non-integer spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation on to a uniform time-series is possible. A windowed power spectrum is computed, revealing a periodic or nearly periodic component with a period of 568 ± 10 d and a 1/f3 power-law noise component in pulse phase with a noise strength Sφ= (1.24 ± 0.067) × 10−16 cycle2 s−2 over the analysis frequency range f= 0.003–0.1 cycle d−1. This result deviates from past analyses which characterized the pulse phase timing residuals as either 1/f4 power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of non-uniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f, implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a mass function f(M) = (6.8 ± 2.4) × 10−16 M⊙ and a companion mass, Mc≥ 3.2 M⊕, assuming a Crab pulsar mass of 1.4 M⊙.

欠損データ推定に基づく不等間隔サンプリングデータに対するシステム同定法

欠損データ推定に基づく不等間隔サンプリングデータに対するシステム同定法

Optimal nonuniform sampling interval and test-input design for identification of physiological systems from very limited data

Optimal design of test-inputs and sampling intervals in experiments for linear system identification is treated as a nonlinear integer optimization problem. The criterion is a function of the Fisher information matrix, the inverse of which gives a lower bound for the covariance matrix of the parameter estimates. Emphasis is placed on optimum design of nonuniform data sampling intervals when experimental constraints allow only a limited number of discrete-time measurements of the output. A solution algorithm based on a steepest descent strategy is developed and applied to the design of a biologic experiment for estimating the parameters of a model of the dynamics of thyroid hormone metabolism. The effects on parameter accuracy of different model representations are demonstrated numerically, a canonical representation yielding far poorer accuracies than the original process model for nonoptimal sampling schedules, but comparable accuracies when these schedules are optimized. Several objective functions for optimization are compared. The overall results indicate that sampling schedule optimization is a very fruitful approach to maximizing expected parameter estimation accuracies when the sample size is small.