Irregular Sampling Research Articles

Anomaly Detection Based on Convex Analysis: A Survey

As a crucial technique for identifying irregular samples or outlier patterns, anomaly detection has broad applications in many fields. Convex analysis (CA) is one of the fundamental methods used in anomaly detection, which contributes to the robust approximation of algebra and geometry, efficient computation to a unique global solution, and mathematical optimization for modeling. Despite the essential role and evergrowing research in CA-based anomaly detection algorithms, little work has realized a comprehensive survey of it. To fill this gap, we summarize the CA techniques used in anomaly detection and classify them into four categories of density estimation methods, matrix factorization methods, machine learning methods, and the others. The theoretical background, sub-categories of methods, typical applications as well as strengths and limitations for each category are introduced. This paper sheds light on a succinct and structured framework and provides researchers with new insights into both anomaly detection and CA. With the remarkable progress made in the techniques of big data and machine learning, CA-based anomaly detection holds great promise for more expeditious, accurate and intelligent detection capacities.

An extension of least-squares redatuming: Simultaneous reconstruction of overburden reflectivities and virtual data

In a controlled-source seismology scenario, scattered wavefields from deep targets, e.g., the petroleum reservoirs, are often distorted by strong heterogeneities of the overburden media, complex topography and irregular acquisition. It is key for target-oriented seismic imaging to accurately reconstruct the scattering wavefields from the deep structures. Recent studies have promoted seismic redatuming for removing the imprint of the overburden through reconstructing virtual data just above the target area. Among the model-based redatuming approaches, least-squares inversion has advantages in mitigating the artifacts due to limited recording aperture and irregular spatial sampling, and allowing for the introduction of appropriate constraints to the reconstructed data. However, conventional least-squares redatuming (LSR) suffers from the spurious events and noises associated with the wavefield interaction of the overburden reflectivities close to the datum. To overcome this problem, we establish an efficient double-parameter LSR method that simultaneously updates the overburden reflectivities and the virtual data through a constrained optimization. Synthetic and field data examples demonstrate that this extended LSR method can effectively retrieve the scattering wavefields from the deep part and improve the target-oriented prestack depth migration below the datum.

Quantifying Tumor Heterogeneity from Multiparametric Magnetic Resonance Imaging of Prostate Using Texture Analysis.

Simple SummaryProstate cancer (PCa) occurs in males at a rate of 21.8%, predominantly at the customary primary site. High cure rates are possible through early detection and therapy when the tumor is still restricted to the prostate. These tumors do not grow rapidly, allowing for periods of up to 20 years between diagnosis and death. Multiparametric MRI (mp-MRI) is used as a non-invasive approach to diagnose PCa in subjects. This imaging method uses MR imaging with at least one functional MRI sequence to detect and characterize PCa. The use of multiparametric magnetic resonance imaging has refined the diagnosis of prostate cancer in radiology. Malignancy-modified critical features in tissue composition, such as heterogeneity, are associated with adverse tumor biology. Heterogeneity can be quantified through texture analysis, an effective technique for reviewing tumor images acquired in routine clinical practice. This study focused on identifying and quantifying tumor heterogeneity from prostate mp-MRI utilizing texture analysis.(1) Background: Multiparametric MRI (mp-MRI) is used to manage patients with PCa. Tumor identification via irregular sampling or biopsy is problematic and does not allow the comprehensive detection of the phenotypic and genetic alterations in a tumor. A non-invasive technique to clinically assess tumor heterogeneity is also in demand. We aimed to identify tumor heterogeneity from multiparametric magnetic resonance images using texture analysis (TA). (2) Methods: Eighteen patients with prostate cancer underwent mp-MRI scans before prostatectomy. A single radiologist matched the histopathology report to single axial slices that best depicted tumor and non-tumor regions to generate regions of interest (ROIs). First-order statistics based on the histogram analysis, including skewness, kurtosis, and entropy, were used to quantify tumor heterogeneity. We compared non-tumor regions with significant tumors, employing the two-tailed Mann–Whitney U test. Analysis of the area under the receiver operating characteristic curve (ROC-AUC) was used to determine diagnostic accuracy. (3) Results: ADC skewness for a 6 × 6 px filter was significantly lower with an ROC-AUC of 0.82 (p = 0.001). The skewness of the ADC for a 9 × 9 px filter had the second-highest result, with an ROC-AUC of 0.66; however, this was not statistically significant (p = 0.08). Furthermore, there were no substantial distinctions between pixel filter size groups from the histogram analysis, including entropy and kurtosis. (4) Conclusions: For all filter sizes, there was poor performance in terms of entropy and kurtosis histogram analyses for cancer diagnosis. Significant prostate cancer may be distinguished using a textural feature derived from ADC skewness with a 6 × 6 px filter size.

Atomic Force Microscopy (AFM) on Biopolymers and Hydrogels for Biotechnological Applications-Possibilities and Limits.

Atomic force microscopy (AFM) is one of the microscopic techniques with the highest lateral resolution. It can usually be applied in air or even in liquids, enabling the investigation of a broader range of samples than scanning electron microscopy (SEM), which is mostly performed in vacuum. Since it works by following the sample surface based on the force between the scanning tip and the sample, interactions have to be taken into account, making the AFM of irregular samples complicated, but on the other hand it allows measurements of more physical parameters than pure topography. This is especially important for biopolymers and hydrogels used in tissue engineering and other biotechnological applications, where elastic properties, surface charges and other parameters influence mammalian cell adhesion and growth as well as many other effects. This review gives an overview of AFM modes relevant for the investigations of biopolymers and hydrogels and shows several examples of recent applications, focusing on the polysaccharides chitosan, alginate, carrageenan and different hydrogels, but depicting also a broader spectrum of materials on which different AFM measurements are reported in the literature.

Dynamic historical information incorporated attention deep learning model for industrial soft sensor modeling

Due to the limitations of sampling conditions and sampling techniques in many real industrial processes, the process data under different sampling conditions subject to different sampling frequencies, which leads to irregular interval sampling characteristics of the entire process data. The dynamic historical data information reflecting the production status under irregular sampling frequency has an important influence on the performance of data feature extraction. However, the existing soft sensor modeling methods based on deep learning do not consider introducing dynamic historical information into the feature extraction process. To combat this issue, a novel attention-based dynamic stacked autoencoder networks (AD-SAE) for soft sensor modeling is proposed in this paper. First, the sliding window technology and attention mechanism based on position coding are introduced to select dynamic historical samples and calculate the contribution of different historical samples to the current sample, respectively. Then, AD-SAE combines obtained historical sample information and current sample information as the input of the network for deep feature extraction and industrial soft sensor modeling. The experimental results on the actual hydrocracking process data set show that the proposed method has better performance than traditional methods.

An empirical dynamic modeling framework for missing or irregular samples

Empirical dynamic modeling (EDM) is a powerful method for forecasting and analyzing nonlinear dynamics. However, typical applications of EDM assume that samples are evenly spaced over time. This presents problems in ecology, in which data are often missing or sampled irregularly. Standard methods for handling irregularity in EDM suffer under conditions that are common in ecology, such as short time series and large dynamic fluctuations, so there is a need to adapt the framework to cope with these challenges more effectively. Here we consider a variable step-size extension of EDM, which incorporates the temporal spacing between samples into EDM delay-coordinate vectors and circumvents the challenges faced by other approaches. We evaluated the forecast accuracy of the variable step-size method along with that of two other methods: (1) exclusion of delay-coordinate vectors with missing data and (2) linear interpolation along with ordinary EDM. We tested these methods using simulated data from three chaotic ecological models with various amounts and patterns of missing data. We also evaluated them using two empirical datasets: laboratory rotifer dynamics and aphid dynamics from the field. Results showed that while exclusion and linear interpolation can produce accurate forecasts in some scenarios, the variable step-size method consistently gives accurate forecasts in a wide range of scenarios. Our analysis demonstrates that variable step-size EDM is an effective method for coping with missing or irregular samples and expands the number of datasets to which EDM can be applied. Furthermore, EDM can be extended to estimate Lyapunov exponents from irregularly sampled time series and approximate continuous dynamics from discrete-time data.

Detecting the periodicity of highly irregularly sampled light curves with Gaussian processes: the case of SDSS J025214.67−002813.7

ABSTRACT Based on a 20-yr-long multiband observation of its light curve, it was conjectured that the quasar SDSS J025214.67−002813.7 has a periodicity of ∼4.4 yr. These observations were acquired at a highly irregular sampling rate and feature long intervals of missing data. In this setting, the inference over the light curve’s spectral content requires, in addition to classic Fourier methods, a proper model of the probability distribution of the missing observations. In this article, we address the detection of the periodicity of a light curve from partial and irregularly sampled observations using Gaussian processes, a Bayesian non-parametric model for time series. This methodology allows us to evaluate the veracity of the claimed periodicity of the above-mentioned quasar and also to estimate its power spectral density. Our main contribution is the confirmation that considering periodic component definitely improves the modelling of the data, although being the source originally selected by a large sample of objects, the possibility that this is a chance result cannot be ruled out.

Study on rapid measurement technic of dry rubber content in latex cup lump by electrical properties

Dry rubber content meter is substantial tool for Impartial trade on rubber cup lump. Department of Agriculture researchers proposed rapid measurement technic of dry rubber content in latex cup lumps by their electrical properties. Two probe types needle and roller were designed, in the first phase, constructed, installed and tested. Needle type probe of 25 mm. in length and 5 mm. apart was selected in measuring electrical properties of cup lump samples as its penetration depth is half of the thickness. Two cylindrical rollers probe of 220 mm. in length and 101.6 mm. (4 inches) in diameter powered by 2 HP gear motor were designed, constructed, installed and tested. Rubber cup lump samples were each statistical divided into 9 regularly measuring parts in needle type probe. Rubber cup lump samples in rollers type probe were typically enforced to pass through 1-inch gap between two rollers. Irregular size sample of more than 76.2 mm. (3 inches) thickness of rubber cup were sliced before measuring into 2 equal thickness pieces. Electrical properties of samples were acquired by standard electrical measuring instruments and percentage of dry rubber content were determined by standard oven method for all sample segments. As the results of this study, rubber content percentage of cup lump was correlated with electrical capacitance than resistance. Electrical capacity value of the latex cup lump from needle-type and two roller-type probes were inversely correlated with the percentage of dry rubber content within the range of 0 – 75 nF and 0 – 380 nF and coefficient of determinations were 0.90 and 0.97, respectively. These initiate features will be utilized in designing of percentage of dry rubber content prototype meter by electrical property values in the future. Percentage of dry rubber content from DRC method of lump from fresh latex and conventional cup lump by oven method was significantly correlate. Electrical properties of latex cup lump produced in the laboratory and farmers are also significantly consistent.

Wavefield reconstruction and wave equation inversion for seismic surface waves

SUMMARY Surface waves are a particular type of seismic wave that propagate around the surface of the Earth, but which oscillate over depth ranges beneath the surface that depend on their frequency of oscillation. This causes them to travel with a speed that depends on their frequency, a property called dispersion. Estimating surface wave dispersion is of interest for many geophysical applications using both active and passive seismic sources, not least because the speed–frequency relationship can be used to infer the subsurface velocity structure at depth beneath the surface. We present an inversion scheme that exploits spatial and temporal relationships in the scalar Helmholtz (wave) equation to estimate dispersion relations of the elastic surface wave data in both active and passive surveys, while also reconstructing the wavefield continuously in space (i.e. between the receivers at which the wavefield was recorded). We verify the retrieved dispersive phase velocity by comparing the results to dispersion analysis in the frequency-slowness domain, and to the local calculation of dispersion using modal analysis. Synthetic elastic examples demonstrate the method under a variety of recording scenarios. The results show that despite the scalar approximation made to represent these intrinsically elastic waves, the proposed method reconstructs both the wavefield and the phase dispersion structure even in the case of strong aliasing and irregular sampling.

Irregular stable sampling and interpolation in functional normed spaces

We define the concepts of stable sampling set and stable interpolation set, uniqueness set and complete interpolation set for a normed space of functions. In addition we will show some relationships between these concepts. The main relationships arise when one wants to reduce an stable sampling set or to extend an stable interpolation set. We will prove that for Banach spaces verifying certain conditions, the complete interpolation sets are precisely the minimal stable sampling sets and are also the maximal stable interpolation sets. Finally we illustrate these results applying them to Paley-Wiener spaces, where we use a result by B. Matei, Yves Meyer and J. Ortega-Cerd´a based on the celebrated Fefferman theorem.
 
 

Efficient 3-D Near-Field MIMO-SAR Imaging for Irregular Scanning Geometries

In this article, we introduce a novel algorithm for efficient near-field synthetic aperture radar (SAR) imaging for irregular scanning geometries. With the emergence of fifth-generation (5G) millimeter-wave (mmWave) devices, near-field SAR imaging is no longer confined to laboratory environments. Recent advances in positioning technology have attracted significant interest for a diverse set of new applications in mmWave imaging. However, many use cases, such as automotive-mounted SAR imaging, unmanned aerial vehicle (UAV) imaging, and freehand imaging with smartphones, are constrained to irregular scanning geometries. Whereas traditional near-field SAR imaging systems and quick personnel security (QPS) scanners employ highly precise motion controllers to create ideal synthetic arrays, emerging applications, mentioned previously, inherently cannot achieve such ideal positioning. In addition, many Internet of Things (IoT) and 5G applications impose strict size and computational complexity limitations that must be considered for edge mmWave imaging technology. In this study, we propose a novel algorithm to leverage the advantages of non-cooperative SAR scanning patterns, small form-factor multiple-input multiple-output (MIMO) radars, and efficient monostatic planar image reconstruction algorithms. We propose a framework to mathematically decompose arbitrary and irregular sampling geometries and a joint solution to mitigate multistatic array imaging artifacts. The proposed algorithm is validated through simulations and an empirical study of arbitrary scanning scenarios. Our algorithm achieves high-resolution and high-efficiency near-field MIMO-SAR imaging, and is an elegant solution to computationally constrained irregularly sampled imaging problems.

Artifact Mitigation for High-Resolution Near-Field SAR Images by Means of Conditional Generative Adversarial Networks

This work presents an approach to enhance the quality of high-resolution images obtained by means of systems relying on synthetic aperture radar (SAR). For this purpose, a deep learning method called conditional generative adversarial networks (cGAN) is applied to the imager outcome when it is prone to suffer artifacts. This is specially the case of novel systems pushing the limits of SAR (e.g., irregular sampling, multilayered media, etc.) resulting in very chaotic clutter and image artifacts that cannot be easily removed with conventional approaches. The cGAN can be trained to detect high-level characteristic features in the image (e.g., parts of a scissor blade) so another output based on these detected features can be tailored. In other words, it can translate features contaminated by artifacts into clean features, effectively improving the quality of SAR images. Unlike other deep learning approaches, the training of the involved neural networks tends to be stable thanks to the structure based on two competing subsystems. The proposed approach is illustrated using simulated and measurement data in the context of two advanced near-field SAR systems considering: i) cylindrical multi-layered media, and ii) freehand acquisitions. Results show that cGANs clearly outperform conventional approaches removing most of the artifacts, enabling to produce a clean output image.

A Practical Root Cause Diagnosis Framework for Quality-Related Faults in Manufacturing Processes With Irregular Sampling Measurements

In actual manufacturing processes, because of the difference of sampling intervals of different process and quality variables, most of the collected data have characteristics of multiple sampling rates. How to fully use those irregular sampling data to realize nonlinear dynamic causality modeling for root cause location and propagation path identification of quality-related faults remains an open question. For this end, a practical root cause diagnosis framework is developed for manufacturing processes with irregular sampling measurements, in which a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest mutual information (MI)-based optimal variable division method is proposed to obtain quality-related and quality-unrelated variables. Then, a sampling interval attention network is designed for adaptively adjusting the dynamic temporal relationships among consecutive samples. Subsequently, a gated recurrent neural network (RNN) for improved design of conditional Granger causality (GC) analysis models is designed for diagnosing root causes and identifying propagation pathways of quality-related faults. Finally, the hot rolling process (HRP) is taken as an example for verification, and the accuracy rate of root cause diagnosis reaches 90.91% and 92.31%, which indicates its practicability and feasibility.

Maneuvering Target Coherent Integration and Detection in PRI-Staggered Radar Systems

As for a new-style radar, the random pulse repetition interval (PRI) pulse waveform may be transmitted, and then the target Doppler parameter estimation precision and detection ability by using the conventional techniques may be invalid due to the irregular signal sampling. To solve these problems, this letter proposes a simple, yet effective and quasi-optimal coherent integration method with random pulse resampling. The proposed method first reconstructs the nonuniformly sampled signal into a uniform grid in the range frequency domain based on the modified sinc interpolation theory. Then, a matched filtering function related to the target chirp parameter is constructed in order to eliminate the residual coupling between range and azimuth. Finally, a moving target can be well imaged after performing the target motion compensation.

Testing for Endogeneity of Irregular Sampling Schemes

Testing for Endogeneity of Irregular Sampling Schemes

Testing for Endogeneity of Irregular Sampling Schemes

Testing for Endogeneity of Irregular Sampling Schemes

Sampling Analysis and Processing Approach for Distributed SAR Constellations With Along-Track Baselines

In the constant strive for improving the capacity of next-generation spaceborne SARs while containing the increase in system complexity, distributed along-track constellations operated below Nyquist appear as one of the most promising solutions for delivering metric resolution imagery over swaths of hundreds of kilometers. In the operation of multistatic SAR constellations, however, sampling singularities typically result in dramatic noise scaling and the impossibility to recover the entire Doppler bandwidth unambiguously. We investigate in this article the likelihood of these singularities in the case of along-track distributed constellations and justify the use of irregular sampling schemes to reduce the percentage of invalid samples of an acquisition. This article also presents a bistatic polychromatic reconstruction algorithm, which is used for the evaluation of the performance of along-track distributed constellations. With all these elements, the performance of along-track multistatic systems is assessed by means of a Monte Carlo analysis and conclusions on the scaling numbers of the constellations are drawn. Based on the performance investigations, an exemplary distributed L-band SAR constellation is proposed as a corollary of this article.

Graph Signal Processing for Geometric Data and Beyond: Theory and Applications

Geometric data acquired from real-world scenes, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , 2D depth images, 3D point clouds, and 4D dynamic point clouds, have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">etc</i> . Due to irregular sampling patterns of most geometric data, traditional image/video processing methodologies are limited, while Graph Signal Processing (GSP)—a fast-developing field in the signal processing community—enables processing signals that reside on irregular domains and plays a critical role in numerous applications of geometric data from low-level processing to high-level analysis. To further advance the research in this field, we provide the first timely and comprehensive overview of GSP methodologies for geometric data in a unified manner by bridging the connections between geometric data and graphs, among the various geometric data modalities, and with spectral/nodal graph filtering techniques. We also discuss the recently developed Graph Neural Networks (GNNs) and interpret the operation of these networks from the perspective of GSP. We conclude with a brief discussion of open problems and challenges.

Event-Triggered Communication-Based Control for Strict-Feedback Nonlinear Systems.

In this article, we shall investigate the event-triggered communication control problem for strict-feedback nonlinear systems with measurement outputs. First, two event-triggered communication schemes are designed. Based on both event-triggered schemes, the measurement output and control input signals are only transmitted at triggering time instants, which saves communication costs from the sensor to the controller and from the controller to the actuator. Meanwhile, Zeno behavior can be excluded under the proposed triggering schemes. Second, since the full-state information is not available to the controller, by developing an observer, the system state is estimated and a controller based on estimated state information is designed. Due to the irregular sampling of information communication and state estimation error affects each other, the parameters of the state observer, the controller, and the event-triggering mechanism should be jointly designed. It is proved that the closed-loop system state converges to the origin. Finally, a simulation example verifies the validity of the obtained theoretical result.

Reconstructing Signals from Aperture-Filtered Samples

Sampling plays a crucial role in remote sensing and signal analysis. In classic sampling theory, a signal is sampled at a uniform rate and at a minimum of twice the signal bandwidth. In practice, only finitely many samples of the signal are available and these can often only be obtained at irregular positions due to platform movement, scanning, pulsed operations, etc. In addition, often only local averages of the signal at these irregularly spaced locations can be measured, often with different apertures at different locations. We will use the one-to-one correspondence between the analog and discrete band-limited signal spaces established by the regular sampling theorem, and give a direct treatment of the discrete problem of irregular samplings. This problem is finite-dimensional and linear, easily accessible, and transparent. Its solution can be easily implemented and analyzed to solve engineering applications. We will see that—different from other approaches—only the number of samples, not their location or density, determine whether the signal can be recovered or not.