Non-uniform Sampling Research Articles

Three-Dimensional Non-Uniform Sampled Data Visualization from Multibeam Echosounder Systems for Underwater Imaging and Environmental Monitoring

This paper proposes a method for visualizing three-dimensional non-uniformly sampled data from multibeam echosounder systems (MBESs), aimed at addressing the requirements of monitoring complex and dynamic underwater flow fields. To tackle the challenges associated with spatially non-uniform sampling, the proposed method employs linear interpolation along the radial direction and arc length weighted interpolation in the beam direction. This approach ensures consistent resolution of three-dimensional data across the same dimension. Additionally, an opacity transfer function is generated to enhance the visualization performance of the ray casting algorithm. This function leverages data values and gradient information, including the first and second directional derivatives, to suppress the rendering of background and non-interest regions while emphasizing target areas and boundary features. The simulation and experimental results demonstrate that, compared to conventional two-dimensional beam images and three-dimensional images, the proposed algorithm provides a more intuitive and accurate representation of three-dimensional data, offering significant support for the observation and analysis of spatial flow field characteristics.

Selecting projection views based on error equidistribution for computed tomography

Background Nonuniform sampling is a useful technique to optimize the acquisition of projections with a limited budget. Existing methods for selecting important projection views have limitations, such as relying on blueprint images or excessive computing resources. Methods We aim to develop a simple nonuniform sampling method for selecting informative projection views suitable for practical CT applications. The proposed algorithm is inspired by two key observations: projection errors contain angle-specific information, and adding views around error peaks effectively reduces errors and improves reconstruction. Given a budget and an initial view set, the proposed method involves: estimating projection errors based on current set of projection views, adding more projection views based on error equidistribution to smooth out errors, and final image reconstruction based on the new set of projection views. This process can be recursive, and the initial view can be obtained uniformly or from a prior for greater efficiency. Results Comparison with popular view selection algorithms using simulated and real data demonstrates consistently superior performance in identifying optimal views and generating high-quality reconstructions. Notably, the new algorithm performs well in both PSNR and SSIM metrics while being computationally efficient, enhancing its practicality for CT optimization. Conclusions A projection view selection algorithm based on error equidistribution is proposed, offering superior reconstruction quality and efficiency over existing methods. It is ready for real CT applications to optimize dose utilization.

Homonuclear decoupled INADEQUATE NMR methods with improved sensitivity and resolution in solid-state NMR.

The two-dimensional (2D) refocused INADEQUATE NMR experiment, which correlates double-quantum (DQ) and single-quantum (SQ) coherences, is widely used to probe the chemical connectivities in solids. Nevertheless, the multiplets along the F2 dimension reduce the resolution and sensitivity of this experiment. The Composite-Refocusing (CR) technique with two excitation pulses has been proposed to suppress these multiplets in 2D INADEQUATE spectra of liquids. Recently (Kolyagin et al., J. Phys. Chem. Lett., 13 (2022) 10793), we showed that this technique can also be applied to suppress doublets in 2D 29Si INADEQUATE spectra of 29Si-enriched zeolites, which resulted in improved sensitivity and resolution. We investigate here how this INADEQUATE-CR scheme can also be applied for two other spin-1/2 isotopes: 13C and 31P. We also demonstrate the possibility to accelerate the acquisition of these 2D INADEQUATE-CR spectra with a very simple bi-exponential non-uniform sampling (NUS). For instance, in the case of 31P nuclei in SnP2O7, the use of the INADEQUATE-CR method with NUS yields a 7.5-fold reduction in experimental time with a simultaneous 1.4-1.5 gain in resolution with respect to a conventional INADEQUATE acquisition. Furthermore, we analyze the origins of the possible artifacts in these 2D spectra, including mismatching between J-coupling constants and refocusing delays, differences in relaxation times, coupling with a proton bath, and spin systems containing multiple identical nuclei. Based on this analysis, we introduce a new z-filtered INADEQUATE-CR version, which produces artifact-free 2D spectra, even in the presence of several distinct J-couplings and relaxation times or for multi-spin systems, and notably samples with high proton density.

Concentration properties of fractional posterior in 1-bit matrix completion

The problem of estimating a matrix based on a set of observed entries is commonly referred to as the matrix completion problem. In this work, we specifically address the scenario of binary observations, often termed as 1-bit matrix completion. While numerous studies have explored Bayesian and frequentist methods for real-value matrix completion, there has been a lack of theoretical exploration regarding Bayesian approaches in 1-bit matrix completion. We tackle this gap by considering a general, non-uniform sampling scheme and providing theoretical assurances on the efficacy of the fractional posterior. Our contributions include obtaining concentration results for the fractional posterior and demonstrating its effectiveness in recovering the underlying parameter matrix. We accomplish this using two distinct types of prior distributions: low-rank factorization priors and a spectral scaled Student prior, with the latter requiring fewer assumptions. Importantly, our results exhibit an adaptive nature by not mandating prior knowledge of the rank of the parameter matrix. Our findings are comparable to those found in the frequentist literature, yet demand fewer restrictive assumptions.

Exponential Approximation of Band-Limited Functions from Nonuniform Sampling by Regularization Methods

Exponential Approximation of Band-Limited Functions from Nonuniform Sampling by Regularization Methods

An Extended Omega-K Algorithm for Automotive SAR with Curved Path

Automotive millimeter-wave (MMW) synthetic aperture radar (SAR) systems can achieve high-resolution images of detection areas, providing environmental perceptions that facilitate intelligent driving. However, curved path is inevitable in complex urban road environments. Non-uniform spatial sampling, brought about by curved path, leads to cross-coupling and spatial variation deteriorates greatly, significantly impacting the imaging results. To deal with these issues, we developed an Extended Omega-K Algorithm (EOKA) for an automotive SAR with a curved path. First, an equivalent range model was constructed based on the relationship between the range history and Doppler frequency. Then, using azimuth time mapping, the echo data was reconstructed with a form similar to that of a uniform linear case. As a result, an analytical two-dimensional (2D) spectrum was easily derived without using of the method of series reversion (MSR) that could be exploited for EOKA. The results from the parking lot, open road, and obstacle experimental scenes demonstrate the performance and feasibility of an MMW SAR for environmental perception.

Distribution Fitting for Combating Mode Collapse in Generative Adversarial Networks.

Mode collapse is a significant unsolved issue of generative adversarial networks (GANs). In this work, we examine the causes of mode collapse from a novel perspective. Due to the nonuniform sampling in the training process, some subdistributions may be missed when sampling data. As a result, even when the generated distribution differs from the real one, the GAN objective can still achieve the minimum. To address the issue, we propose a global distribution fitting (GDF) method with a penalty term to confine the generated data distribution. When the generated distribution differs from the real one, GDF will make the objective harder to reach the minimal value, while the original global minimum is not changed. To deal with the circumstance when the overall real data is unreachable, we also propose a local distribution fitting (LDF) method. Experiments on several benchmarks demonstrate the effectiveness and competitive performance of GDF and LDF.

The Development of a High-Throughput Homonuclear Decoupling HSQC NMR Platform for the Determination of 10 Sex Hormones in Animal-Source Food and Medicines

Owing to their endocrine disruption effect, the hormone levels in animal-source food and medicines need to be efficiently and accurately quantified by a reliable analytical method. In the current study, by using a homonuclear decoupling and heteronuclear single quantum correlation (HSQC) experiment, coupled with non-uniform sampling (NUS) that was used to shorten the experimental time, we developed a method to quantify 10 hormone residues in animal-source products. This method was validated following the guidelines of USP–NF 2022. The application of the homonuclear decoupling (HD) technique to conventional HSQC yielded 2D spectra that exhibited excellent signal separation and specificity. For all the tested hormones, good linearity with correlation coefficients of more than 0.99 was observed in the linear range of 0.2–6 mg/0.6 mL. Satisfactory precision and recoveries of spiked animal samples were also obtained. Finally, the method was applied in residue determination of 10 hormones in real animal-source samples at the ug/g level.

Three-dimensional quasi-complete information numerical simulation of gravity anomalies and parallel computing on CPU-GPU

Abstract In order to improve the efficiency and accuracy of numerical simulation of gravity anomalies in large-scale complex models, this paper proposes a method for three-dimensional numerical simulation of gravity anomalies under arbitrary terrain, and implements its CPU-GPU parallel acceleration scheme. By performing a two-dimensional Fourier transform along the horizontal direction, three-dimensional partial differential satisfied by gravitational potential are transformed into one-dimensional ordinary differential equations in different wavenumbers, reducing computational and storage requirements. Moreover, the ordinary differential equations in different wavenumbers are independent of each other and have good parallelism. By retaining the vertical direction as the spatial domain and introducing traveling wave decomposition, the effects caused by upper and lower boundaries are eliminated. The vertical grid is arbitrary. A two-dimensional quasi-complete information Fourier transform is utilized to enhance both the accuracy and efficiency of the Fourier transform process, allowing both uniform and non-uniform flexible sampling. Based on the high parallelism, one-dimensional ordinary differential equations are solved in parallel using CPU, and quasi-complete information Fourier transform are computed in parallel using GPU. An abnormal sphere is designed to analyze the wavenumber spectral distribution characteristics of the anomalous potential and summarize the wavenumber sampling rules. The logarithmic uniform sampling in the wavenumber domain has high accuracy. Compared with Gauss-FFT, the quasi-complete information Fourier transform selects fewer wavenumbers and exhibits higher accuracy. The computational efficiency is greatly enhanced through the use of single-precision CPU-GPU parallel scheme, and a model with tens of millions of nodes only takes a few seconds. Two terrain models are designed to verify the algorithm’s adaptability to arbitrary complex terrains. This is significant for achieving fine inversion imaging and interpretation of gravity anomalies under large-scale complex conditions.

Uncertainty-Adjusted Recommendation via Matrix Factorization With Weighted Losses.

In a recommender systems (RSs) dataset, observed ratings are subject to unequal amounts of noise. Some users might be consistently more conscientious in choosing the ratings they provide for the content they consume. Some items may be very divisive and elicit highly noisy reviews. In this article, we perform a nuclear-norm-based matrix factorization method which relies on side information in the form of an estimate of the uncertainty of each rating. A rating with a higher uncertainty is considered more likely to be erroneous or subject to large amounts of noise, and therefore more likely to mislead the model. Our uncertainty estimate is used as a weighting factor in the loss we optimize. To maintain the favorable scaling and theoretical guarantees coming with nuclear norm regularization even in this weighted context, we introduce an adjusted version of the trace norm regularizer which takes the weights into account. This regularization strategy is inspired from the weighted trace norm which was introduced to tackle nonuniform sampling regimes in matrix completion. Our method exhibits state-of-the-art performance on both synthetic and real life datasets in terms of various performance measures, confirming that we have successfully used the auxiliary information extracted.

A Simple and Effective Planar Near-Field Measurement Method With Sparse Nonuniform Sampling

A Simple and Effective Planar Near-Field Measurement Method With Sparse Nonuniform Sampling

Synthetic aperture image enhancement with near-coinciding Nonuniform sampling case

Multireceiver synthetic aperture sonar (SAS) uses multiple receivers to collect echoed signals, leading to nonuniform sampling in the azimuth dimension if the moving distance between adjacent pings is not half the receiver array length. The filter bank reconstruction (FBR) method, based on matrix inversion, is commonly used to address this by reconstructing uniform data from nonuniform signals. However, in practice, near-coinciding sampling can occur due to inaccuracies in the towed velocity of the SAS system, influenced by ocean conditions. The signal correlation of these near-coinciding receivers is very strong, and thus the steering vectors corresponding to these receivers are not completely independent. This further leads to an ill-conditioned system transfer function matrix made up of the receiver steering vectors, and results in inaccurate calculations of inverse matrix. Consequently, the FBR method suffers from significant signal-to-noise ratio loss or fails to reconstruct uniform signals accurately. This degradation in signal quality directly impacts the accuracy of target reconstruction, leading to errors in identifying and locating targets. This paper quantitatively defines nonuniform sampling with near-coinciding samples and discusses performance loss in various cases. To enhance imaging performance, we propose a method for reconstructing uniform signals. Simulation results demonstrate that the proposed method outperforms the conventional FBR method, providing better target reconstruction and higher efficiency.

Noise aware parameter estimation in bioprocesses: Using neural network surrogate models with nonuniform data sampling

AbstractThis article demonstrates a parameter estimation technique for bioprocesses that utilizes measurement noise in experimental data to determine credible intervals on parameter estimates, with this information of potential use in prediction, robust control, and optimization. To determine these estimates, the work implements Bayesian inference using nested sampling, presenting an approach to develop neural network‐ (NN) based surrogate models. To address challenges associated with nonuniform sampling of experimental measurements, an NN structure is proposed. The resultant surrogate model is utilized within a Nested Sampling Algorithm that samples possible parameter values from the parameter space and uses the NN to calculate model output for use in the likelihood function based on the joint probability distribution of the noise of output variables. This method is illustrated against simulated data, then with experimental data from a Sartorius fed‐batch bioprocess. Results demonstrate the feasibility of the proposed technique to enable rapid parameter estimation for bioprocesses.

Error analysis based on a tunable wave plate polarization interferometric imaging spectrometer

Interference imaging spectroscopy combines modern imaging technology with spectral technology, holding significant importance for object imaging and spectral detection. This article introduces the principle of an adjustable wave plate polarization interferometric imaging spectrometer. The example design specifications are set for an observation wavelength range of 450–780 nm and a maximum resolution of 2 nm at 450 nm, with a 0.5 in detector as the base for calculating the specific dimensions of the Soleil–Babinet compensator. An investigation was conducted on the issues of nonuniform sampling, as well as three types of mechanical errors: flatness, wedge angle tolerance, and optical axis orientation accuracy. Emphasis was placed on discussing the impact of these errors on the instrument’s optical path difference and spectral reconstruction accuracy. This research provides theoretical guidance for the design and engineering of this miniaturized imaging spectrometer.

UltraStat: Ultrafast Spectroscopy beyond the Fourier Limit Using Bayesian Inference.

The discrete Fourier transform (dFT) plays a central role in many ultrafast experiments, allowing the recovery of spectroscopic observables from time-domain measurements. In resonant experiments when population relaxation and coherence components of the signal coexist, the dFT is usually preceded by multiexponential fitting to remove the large population term. However, this procedure results in errors in both the recovered decay rates and the line shapes of the coherence spectral components. While other methods such as linear prediction singular value decomposition fit both terms simultaneously, they are limited to specific models that may not represent the true signal. These methods do not allow for systematic noise analysis or error estimation and require a priori knowledge of the signal rank. Here, we describe a general approach to parameter estimation in ultrafast spectroscopy─UltraStat─grounded in Bayesian analysis without the limitations set by Fourier theory. Using simulated, but realistic data, we demonstrate in a statistical sense how UltraStat provides accurate parameter estimation in the presence of many experimental constraints: noise, signal truncation, limited photon budget, and nonuniform sampling. UltraStat provides superior resolution compared to the dFT, up to an order of magnitude in cases where the line shapes are well-approximated. In these cases, we establish that primarily noise, not sampling, limits spectral resolution. Moreover, we show that subsampling may reduce the number of acquired points by 90% compared to the Nyquist-Shannon criteria. UltraStat greatly improves parameter estimation by providing statistically bound spectral and dynamics analysis, pushing the limits of ultrafast science.

Staged suppression of main-lobe compound jamming using airborne distributed arrays

For the compound jamming scenario where noise suppression jamming and interrupted sampling repeater jamming simultaneously exist, we propose a method of staged suppression of them using distributed arrays. The basic principle is using the generalized inner product for the selection of non-uniform samples. By using the generalized inner product quadratically for the staged selection of the samples, we can obtain the statistical feature estimates of the noise suppression jamming and the interrupted sampling repeater jamming, respectively, and then complete the robust suppression of the compounded jamming using the distributed array spatial domain adaptive processing. With typical configuration of parameters, we validate and analyze the effectiveness and performance of the proposed method through numerical simulation experiments.

Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials

AbstractWe introduce two families of generators (functions) $${\mathcal {G}}$$ G that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved on the density of separated sets that provide non-uniform sampling for the shift-invariant and quasi shift-invariant spaces generated by elements of these families. As an application, new sharp results are obtained on the density of semi-regular lattices for the Gabor frames generated by elements from these families.

Förster Resonance Energy Transfer and Enhanced Emission in Cs4PbBr6 Nanocrystals Encapsulated in Silicon Nano-Sheets for Perovskite Light Emitting Diode Applications.

Encapsulating Cs4PbBr6 quantum dots in silicon nano-sheets not only stabilizes the halide perovskite, but also takes advantage of the nano-sheet for a compatible integration with the traditional silicon semiconductor. Here, we report the preparation of un-passivated Cs4PbBr6 ellipsoidal nanocrystals and pseudo-spherical quantum dots in silicon nano-sheets and their enhanced photoluminescence (PL). For a sample with low concentrations of quantum dots in silicon nano-sheets, the emission from Cs4PbBr6 pseudo-spherical quantum dots is quenched and is dominated with Pb2+ ion/silicene emission, which is very stable during the whole measurement period. For a high concentration of Cs4PbBr6 ellipsoidal nanocrystals in silicon nano-sheets, we have observed Förster resonance energy transfer with up to 87% efficiency through the oscillation of two PL peaks when UV excitation switches between on and off, using recorded video and PL lifetime measurements. In an area of a non-uniform sample containing both ellipsoidal nanocrystals and pseudo-spherical quantum dots, where Pb2+ ion/silicene emissions, broadband emissions from quantum dots, and bandgap edge emissions (515 nm) appear, the 515 nm peak intensity increases five times over 30 min of UV excitation, probably due to a photon recycling effect. This irradiated sample has been stable for one year of ambient storage. Cs4PbBr6 quantum dots encapsulated in silicon nano-sheets can lead to applications of halide perovskite light emitting diodes (PeLEDs) and integration with traditional semiconductor materials.

Comparative Evaluation of Neural Network Models for Optimizing ECG Signal in Non-Uniform Sampling Domain

Electrocardiographic signals (ECG) are ubiquitous, which justifies the research of their optimal storage and transmission. However, proposals for non-uniform signal sampling must take into account the priority of diagnostic data accuracy and record integrity, as well as robustness to noise and interference. In this study, two novel methods are introduced, each utilizing a distinct neural network architecture for optimizing non-uniform sampling of ECG signal. A transformer model refines each time point selection through an iterative process using gradient descent optimization, with the goal of minimizing the mean squared error between the original and resampled signals. It adaptively modifies time points, which improves the alignment between both signals. In contrast, the Temporal Convolutional Network model trains on the original signal, and gradient descent optimization is utilized to improve the selection of time points. Evaluation of both strategies’ efficacy is performed by calculating signal distances at lower and higher sampling rates. First, a collection of synthetic data points that resembled the P-QRS-T wave was used to train the model. Then, the ECG-ID database for real data analysis was used. Filtering to remove baseline wander followed by evaluation and testing were carried out in the real patient data. The results, in particular MSE = 0.0005, RMSE = 0.0216, and Pearson’s CC = 0.9904 for 120 sps in the case of the transformer patient data model, provide viable paths for maintaining the precision and dependability of ECG-based diagnostic systems at much lower sampling rate. Outcomes indicate that both techniques are effective at improving the fidelity between the original and modified ECG signals.

NsDCC: dual-level contrastive clustering with nonuniform sampling for scRNA-seq data analysis.

Dimensionality reduction and clustering are crucial tasks in single-cell RNA sequencing (scRNA-seq) data analysis, treated independently in the current process, hindering their mutual benefits. The latest methods jointly optimize these tasks through deep clustering. However, contrastive learning, with powerful representation capability, can bridge the gap that common deep clustering methods face, which requires pre-defined cluster centers. Therefore, a dual-level contrastive clustering method with nonuniform sampling (nsDCC) is proposed for scRNA-seq data analysis. Dual-level contrastive clustering, which combines instance-level contrast and cluster-level contrast, jointly optimizes dimensionality reduction and clustering. Multi-positive contrastive learning and unit matrix constraint are introduced in instance- and cluster-level contrast, respectively. Furthermore, the attention mechanism is introduced to capture inter-cellular information, which is beneficial for clustering. The nsDCC focuses on important samples at category boundaries and in minority categories by the proposed nearest boundary sparsest density weight assignment algorithm, making it capable of capturing comprehensive characteristics against imbalanced datasets. Experimental results show that nsDCC outperforms the six other state-of-the-art methods on both real and simulated scRNA-seq data, validating its performance on dimensionality reduction and clustering of scRNA-seq data, especially for imbalanced data. Simulation experiments demonstrate that nsDCC is insensitive to "dropout events" in scRNA-seq. Finally, cluster differential expressed gene analysis confirms the meaningfulness of results from nsDCC. In summary, nsDCC is a new way of analyzing and understanding scRNA-seq data.