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The amount of data collected for sensing tasks in scientific computing is based on the Shannon-Nyquist sampling theorem proposed in the 1940s. Sensor data generation will surpass 73 trillion GB by 2025 as we increase the high-fidelity digitization of the physical world. Skyrocketing data infrastructure costs and time to maintain and compute on all this data are increasingly common. To address this, we introduce a selective learning approach, where the amount of data collected is problem dependent. We develop novel shift-invariant and spectrally stable neural networks to solve real-time sensing problems formulated as classification or regression problems. We demonstrate that (i) less data can be collected while preserving information, and (ii) test accuracy improves with data augmentation (size of training data), rather than by collecting more than a certain fraction of raw data, unlike information theoretic approaches. While sampling at Nyquist rates, every data point does not have to be resolved at Nyquist and the network learns the amount of data to be collected. This has significant implications (orders of magnitude reduction) on the amount of data collected, computation, power, time, bandwidth, and latency required for several embedded applications ranging from low earth orbit economy to unmanned underwater vehicles. [ABSTRACT FROM AUTHOR]

Given M ≥ 2 distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD)—a parameter that quantifies the difference between the M distributions. The population KMD, which takes values between 0 and 1, is 0 if and only if all the M distributions are the same, and 1 if and only if all the distributions are mutually singular. Moreover, KMD possesses many properties commonly associated with f-divergences such as the data processing inequality and invariance under bijective transformations. The sample estimate of KMD, based on independent observations from the M distributions, can be computed in near linear time (up to logarithmic factors) using k-nearest neighbor graphs (for k ≥ 1 fixed). We develop an easily implementable test for the equality of M distributions based on the sample KMD that is consistent against all alternatives where at least two distributions are not equal. We prove central limit theorems for the sample KMD, and provide a complete characterization of the asymptotic power of the test, as well as its detection threshold. The usefulness of our measure is demonstrated via real and synthetic data examples; our method is also implemented in an R package. for this article are available online. [ABSTRACT FROM AUTHOR]

Stochastic root-finding problems are fundamental in the fields of operations research and data science. However, when the root-finding problem involves rare events, crude Monte Carlo can be prohibitively inefficient. Importance sampling (IS) is a commonly used approach, but selecting a good IS parameter requires knowledge of the problem's solution, which creates a circular challenge. In "Adaptive Importance Sampling for Efficient Stochastic Root Finding and Quantile Estimation," He, Jiang, Lam, and Fu propose an adaptive IS approach to untie this circularity. The adaptive IS simultaneously estimates the root and the IS parameters, and can be embedded in sample average approximation–type algorithms and stochastic approximation–type algorithms. They provide theoretical analysis on strong consistency and asymptotic normality of the resulting estimators, and show the benefit of adaptivity from a worst-case perspective. They also provide specialized analyses on extreme quantile estimation under milder conditions. In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance sampling can be employed to drive down the sampling error to a desirable level. However, selecting a good importance sampler requires knowledge of the solution to the problem at hand, which is the goal to begin with and thus forms a circular challenge. We investigate the use of adaptive importance sampling to untie this circularity. Our procedure sequentially updates the importance sampler to reach the optimal sampler and the optimal solution simultaneously, and can be embedded in both sample-average-approximation-type algorithms and stochastic-approximation-type algorithms. Our theoretical analysis establishes strong consistency and asymptotic normality of the resulting estimators. We also demonstrate, via a minimax perspective, the key role of using adaptivity in controlling asymptotic errors. Finally, we illustrate the effectiveness of our approach via numerical experiments. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72293562, 72121001, and 72171060], the National Science Foundation [Grants CAREER CMMI-1834710 and IIS-1849280], and the Air Force Office of Scientific Research [Grant FA95502010211]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2023.2484. [ABSTRACT FROM AUTHOR]

The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and optics. This paper investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited functions in the OLCT and offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark's interpolation formulas, we derive the sampling theorems for bandlimited functions in the OLCT and OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity. [ABSTRACT FROM AUTHOR]

In this study, we defined a kind of Fourier expansion of set-valued square-integrable functions. In fact, we have seen that the classical Fourier basis also constitutes a basis for the Hilbert quasilinear space L 2 (− π , π , Ω (C)) of Ω (C) -valued square-integrable functions, where Ω (C) is the class of all compact subsets of complex numbers. Furthermore, we defined the quasi-Paley–Wiener space, Q P W , using the Fourier transform defined for set-valued functions and thus we showed that the sequence s i n c. − k k ∈ Z form also a basis for Q P W . We call this result Shannon's sampling theorem for set-valued functions. Finally, we gave an application based on this theorem. [ABSTRACT FROM AUTHOR]

An accurate treatment of electronic spectra in large systems with a technique such as time-dependent density functional theory is computationally challenging. Due to the Nyquist sampling theorem, direct real-time simulations must be prohibitively long to achieve suitably sharp resolution in frequency space. Super-resolution techniques such as compressed sensing and MUSIC assume only a small number of excitations contribute to the spectrum, which fails in large molecular systems where the number of excitations is typically very large. We present an approach that combines exact short-time dynamics with approximate frequency space methods to capture large narrow features embedded in a dense manifold of smaller nearby peaks. We show that our approach can accurately capture narrow features and a broad quasi-continuum of states simultaneously, even when the features overlap in frequency. Our approach is able to reduce the required simulation time to achieve reasonable accuracy by a factor of 20-40 with respect to standard Fourier analysis and shows promise for accurately predicting the whole spectrum of large molecules and materials. Calculating electronic spectra of large systems is computationally challenging. Here, the authors combine exact short-time dynamics with approximate frequency space methods to capture narrow features embedded in a dense manifold of smaller peaks. [ABSTRACT FROM AUTHOR]

Abstract We consider a general case of a magnetotelluric (MT) study to reveal three-dimensional (3D) distribution of the electrical conductivity within the Earth based on measurements of electromagnetic (EM) fields by a two-dimensional (2D) array. Such an MT array observation can be regarded as a spatially discrete sampling of the MT responses (impedances), and each observation site can be regarded as a sampling point. This means that MT array measurements must follow the Nyquist–Shannon sampling theorem. This paper discusses how the sampling theorem is applied to MT array studies and what kind of consideration is required in the application on the basis of synthetic model calculations, with special attention to spatial resolutions. With an aid of the EM scattering theory and the sampling theorem, we can show that an observation array resolves some features of the MT impedance but does not others. We call the resolvable and unresolvable features the MT signal and noise, respectively. This study introduces the spatial Fourier transform of array MT data (impedances) which helps us investigating sampling effects of lateral heterogeneity from a different angle (in the wavenumber domain). Shallow heterogeneities cause a sharp spatial change of impedance elements near structural boundaries. High wavenumber Fourier components are required to describe such a feature, which means the site spacing must be sufficiently short to be able to resolve such features. Otherwise, a set of array MT data will suffer from aliasing, which is one of the typical causes of MT distortion (MT geologic noise). Conversely, a signal due to a deep-seated conductivity anomaly will have more reduced amplitude at higher wavenumbers, which means focused imaging of such an anomaly is generally difficult. Finally, it is suggested to properly consider the sampling theorem in an observation array design, so as to have best performance in resolving MT signals. Graphical abstract

For time division multiplexing multiple input multiple output (TDM MIMO) millimeter wave radar, the measurement of target range, velocity and other parameters depends on the phase of the received Intermediate Frequency (IF) signal. The coupling between range and velocity phases occurs when measuring moving targets, leading to inevitable errors in calculating range and velocity from the phase, which in turn affects measurement accuracy. Traditional two-dimensional fast fourier transform (2D FFT) estimation errors are particularly pronounced at high velocity, significantly impacting measurement accuracy. Additionally, due to limitations imposed by the Nyquist sampling theorem, there is a restricted range for velocity measurements that can result in aliasing. In this study, we propose a method to address the coupling of range and velocity based on the original signal as well as a method for velocity compensation to resolve aliasing issues. Our research findings demonstrate that this approach effectively reduces errors in measuring ranges and velocities of high-velocity moving targets while efficiently de-aliasing velocities. [ABSTRACT FROM AUTHOR]

We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can be uniquely recovered, up to global sign, from its multiwavelet frame coefficients \[ \{\lvert \mathcal {W}_{\phi _i} f(\alpha ^{m}\beta n,\alpha ^{m}) \rvert : i\in \{1,2,3\}, m,n\in \mathbb {Z}\} \] for every \alpha >1,\beta >0 with \beta \ln (\alpha)\leq 4\pi /(1+4p), p>0, when the three wavelets \phi _i are suitable linear combinations of the Poisson wavelet P_p of order p and its Hilbert transform \mathscr {H}P_p. For complex-valued signals we find that this is not possible for any choice of the parameters \alpha >1,\beta >0, and for any window. In contrast to the existing literature on wavelet sign retrieval, our uniqueness results do not require any bandlimiting constraints or other a priori knowledge on the real-valued signals to guarantee their unique recovery from the absolute values of their wavelet coefficients. [ABSTRACT FROM AUTHOR]

As one of the most widely used spread spectrum techniques, the frequency-hopping spread spectrum (FHSS) has been widely adopted in both civilian and military secure communications. In this technique, the carrier frequency of the signal hops pseudo-randomly over a large range, compared to the baseband. To capture an FHSS signal, conventional non-cooperative receivers without knowledge of the carrier have to operate at a high sampling rate covering the entire FHSS hopping range, according to the Nyquist sampling theorem. In this paper, we propose an adaptive compressed method for joint carrier and direction of arrival (DOA) estimations of FHSS signals, enabling subsequent non-cooperative processing. The compressed measurement kernels (i.e., non-zero entries in the sensing matrix) have been adaptively designed based on the posterior knowledge of the signal and task-specific information optimization. Moreover, a deep neural network has been designed to ensure the efficiency of the measurement kernel design process. Finally, the signal carrier and DOA are estimated based on the measurement data. Through simulations, the performance of the adaptively designed measurement kernels is proved to be improved over the random measurement kernels. In addition, the proposed method is shown to outperform the compressed methods in the literature. [ABSTRACT FROM AUTHOR]

Introduction: In the 1950s and 1960s, John Senders carried out a number of influential experiments on the monitoring of multidegree-of-freedom systems. In these experiments, participants were tasked with detecting events (threshold crossings) for multiple dials, each presenting a signal with different bandwidth. Senders’ analyses showed a nearly linear relationship between signal bandwidth and the amount of attention paid to the dial, and he argued that humans sample according to bandwidth, in line with the Nyquist–Shannon sampling theorem. Objective: The current study tested whether humans indeed sample the dials based on bandwidth alone or whether they also use salient peripheral cues. Methods: A dial-monitoring task was performed by 33 participants. In half of the trials, a gaze-contingent window was used that blocked peripheral vision. Results: The results showed that, without peripheral vision, humans do not effectively distribute their attention across the dials. The findings also suggest that, when given full view, humans can detect the speed of the dial using their peripheral vision. Conclusion: It is concluded that salience and bandwidth are both drivers of distributed visual attention in a dialmonitoring task. [ABSTRACT FROM AUTHOR]

Objectives of our study are to develop a procedure for intertemporal comparison of both technical and cost efficiency and estimate farm efficiency for the Korean rice industry from 2003 to 2017. The newly developed base‐year procedure excludes frontier shift and price effects from the standard procedure for intertemporal comparison. An adjusted central limit theorem for sample T‐tests is applied to avoid potential bias from efficiency scores by the Data Envelope Analysis. Our empirical results show that the two procedures yield different scores and trends. The standard approach indicates declining efficiency, while the base‐year method shows overall improvement in farm efficiency. [ABSTRACT FROM AUTHOR]

We consider a general case of a magnetotelluric (MT) study to reveal three-dimensional (3D) distribution of the electrical conductivity within the Earth based on measurements of electromagnetic (EM) fields by a two-dimensional (2D) array. Such an MT array observation can be regarded as a spatially discrete sampling of the MT responses (impedances), and each observation site can be regarded as a sampling point. This means that MT array measurements must follow the Nyquist–Shannon sampling theorem. This paper discusses how the sampling theorem is applied to MT array studies and what kind of consideration is required in the application on the basis of synthetic model calculations, with special attention to spatial resolutions. With an aid of the EM scattering theory and the sampling theorem, we can show that an observation array resolves some features of the MT impedance but does not others. We call the resolvable and unresolvable features the MT signal and noise, respectively. This study introduces the spatial Fourier transform of array MT data (impedances) which helps us investigating sampling effects of lateral heterogeneity from a different angle (in the wavenumber domain). Shallow heterogeneities cause a sharp spatial change of impedance elements near structural boundaries. High wavenumber Fourier components are required to describe such a feature, which means the site spacing must be sufficiently short to be able to resolve such features. Otherwise, a set of array MT data will suffer from aliasing, which is one of the typical causes of MT distortion (MT geologic noise). Conversely, a signal due to a deep-seated conductivity anomaly will have more reduced amplitude at higher wavenumbers, which means focused imaging of such an anomaly is generally difficult. Finally, it is suggested to properly consider the sampling theorem in an observation array design, so as to have best performance in resolving MT signals. [ABSTRACT FROM AUTHOR]

Photoacoustic imaging (PAI) is a rapidly developing emerging non-invasive biomedical imaging technique that combines the strong contrast from optical absorption imaging and the high resolution from acoustic imaging. Abnormal biological tissues (such as tumors and inflammation) generate different levels of thermal expansion after absorbing optical energy, producing distinct acoustic signals from normal tissues. This technique can detect small tissue lesions in biological tissues and has demonstrated significant potential for applications in tumor research, melanoma detection, and cardiovascular disease diagnosis. During the process of collecting photoacoustic signals in a PAI system, various factors can influence the signals, such as absorption, scattering, and attenuation in biological tissues. A single ultrasound transducer cannot provide sufficient information to reconstruct high-precision photoacoustic images. To obtain more accurate and clear image reconstruction results, PAI systems typically use a large number of ultrasound transducers to collect multi-channel signals from different angles and positions, thereby acquiring more information about the photoacoustic signals. Therefore, to reconstruct high-quality photoacoustic images, PAI systems require a significant number of measurement signals, which can result in substantial hardware and time costs. Compressed sensing is an algorithm that breaks through the Nyquist sampling theorem and can reconstruct the original signal with a small number of measurement signals. PAI based on compressed sensing has made breakthroughs over the past decade, enabling the reconstruction of low artifacts and high-quality images with a small number of photoacoustic measurement signals, improving time efficiency, and reducing hardware costs. This article provides a detailed introduction to PAI based on compressed sensing, such as the physical transmission model-based compressed sensing method, two-stage reconstruction-based compressed sensing method, and single-pixel camera-based compressed sensing method. Challenges and future perspectives of compressed sensing-based PAI are also discussed. [ABSTRACT FROM AUTHOR]

This paper studies the continuous-time behavior of sampled-data control systems. In these systems, a discrete-time control law is applied to a continuous-time system model using sampling and zero-order hold. Traditionally, sampled-data systems are modeled in discrete-time, and thus, the intersample dynamics cannot be examined. This paper shows that the classical methods (such as the d2c function of MATLAB) for obtaining continuous-time models can be inaccurate between the sampling instants, even when Shannon's sampling theorem is satisfied. In this paper, a new method is also presented which can be used to characterize the continuous-time dynamics of sampled-data control systems. The new continuous-time system model including the intersample behavior is derived analytically from the discrete-time model, and the results are verified by simulations. [ABSTRACT FROM AUTHOR]

One of the most important issues in the linear control subject is to obtain eigenvalues of the system to study the stability of a system. It is needed to identify the sign of eigenvalues but not the value of it. To fulfil this, there are different methods such as Routh stability criterion, Lyapunov's method and Nyquist stability criterion. In this research, we will present the most simple one to determine the sign of eigenvalues and we shall discuss and explain different types of stability. Also, we will discuss some special cases that cross a controversial mission, and a new method is proposed to calculate the stability of systems, which we call the Lyapunov-Routh method (composition of Lyapunov and Routh method). [ABSTRACT FROM AUTHOR]

High-pixel-number synchrotron radiation computed tomography (CT) has the advantages of high sensitivity, high resolution, and a large field of view. It has been widely used in biomedicine, cultural heritage research, non-destructive testing, and other fields. The Nyquist sampling theorem states that when the detector's pixels per row are increased, it requires more CT projections, resulting in a lengthened CT scan time and increased radiation damage. Sparse-view CT can significantly reduce radiation damage and improve the projection data acquisition speed. However, there is insufficient sparse projection data, and the slices reconstructed show aliasing artifacts. Currently, aliasing artifact correction processes more medical CT images, and the number of pixels of such images is small (mainly 512 × 512 pixels). This paper presents an aliasing artifact correction algorithm based on deep learning for synchrotron radiation CT with a high pixel number ( 1728 × 1728 pixels). This method crops high-pixel-number CT images with aliasing artifacts into patches with overlapping features. During the network training process, a convolutional neural network is utilized to enhance the details of the patches, after which the patches are reintegrated into a new CT slice. Subsequently, the network parameters are updated to optimize the new CT slice that closely approximates the full-view slice. To align with practical application requirements, the neural network is trained using only three samples to optimize network parameters and applied successfully to untrained samples for aliasing artifact correction. Comparative analysis with typical deep learning aliasing artifact correction algorithms demonstrates the superior ability of our method to correct aliasing artifacts while preserving image details more effectively. Furthermore, the effect of aliasing artifact correction at varying levels of projection sparsity is investigated, revealing a positive correlation between image quality after deep learning processing and the number of projections. However, the trade-off between rapid experimentation and artifact correction remains a critical consideration. [ABSTRACT FROM AUTHOR]

Traditional bridge health monitoring methods that necessitate sensor installation are not only costly but also time-consuming. In contrast, utilizing smartphone data collected from vehicles as they traverse bridges offers an efficient and cost-effective alternative. This paper introduces a cutting-edge damage detection framework for indirect monitoring of bridge structures, leveraging a substantial volume of acceleration data collected from smartphones in vehicles passing over the bridge. Our innovative approach addresses the challenge of collecting and transmitting high-frequency data while preserving smartphone battery life and data plans through the integration of compressed sensing (CS) into the crowdsensing-based monitoring framework. CS employs random sampling and signal recovery from a significantly reduced number of samples compared to the requirements of the Nyquist–Shannon sampling theorem. In the proposed framework, acceleration signals from vehicles are initially acquired using smartphone sensors, undergo compression, and are then transmitted for signal reconstruction. Subsequently, feature extraction and dimensionality reduction are performed using Mel-frequency cepstral coefficients and principal component analysis. Damage indexes are computed based on the dissimilarity between probability distribution functions utilizing the Wasserstein distance metric. The efficacy of the proposed methodology in bridge monitoring has been substantiated through the utilization of numerical models and a lab-scale bridge. Furthermore, the feasibility of implementing the framework in a real-world application has been investigated, leveraging the smartphone data from 102 vehicle trips on the Golden Gate Bridge. The results demonstrate that damage detection using the reconstructed signals obtained through compressed sensing achieves comparable performance to that obtained with the original data sampled at the Nyquist measurement sampling rate. However, it is observed that to retain severity information within the signals for accurate damage severity identification, the compression level should be limited to 20%. These findings affirm that compressed sensing significantly reduces the data collection requirements for crowdsensing-based monitoring applications, without compromising the accuracy of damage detection while preserving essential damage-sensitive information within the dataset. [ABSTRACT FROM AUTHOR]

The fractional Fourier transform (FRFT) is a generalized form of the Fourier transform (FT), it is another important class of time–frequency analysis tool in signal processing. In this paper, we study the two-dimensional (2D) FRFT in the polar coordinates setting. First, Parseval theorem of the 2D FRFT in the polar coordinates is obtained. Then, according to the relationship between 2D FRFT and fractional Hankel transform (FRHT), the convolution theorem for the 2D FRFT in polar coordinates is obtained. It shows that the FRFT of the convolution of two functions is the product of their respective FRFTs. Moreover, the fast algorithm for the convolution theorem of the 2D FRFT is discussed. Finally, the sampling theorem for signal is explored. [ABSTRACT FROM AUTHOR]

Sound field separation techniques are an advancing tool for extracting a target sound field from a mixed sound field. However, the methods bear a high measurement cost due to the restriction of the sampling theorem. In this study, a sound field separation method based on sparse sampling is established. The method initially utilizes dictionary learning to generate a sparse basis of the sound field. Then, a mixed sound field can be precisely recovered from sparse sampling of sound pressure and the target sound field can be extracted based on the recovered sound field by means of the theory of equivalent source method. The method is validated by numerical simulations. Compared to sound field separation based on the equivalent source method, the proposed method has advantage in terms of both the accuracy and the stability for sparse sampling. [ABSTRACT FROM AUTHOR]

A novel compressive sensing (CS) synthetic-aperture radar (SAR) called AgileSAR has been proposed to increase swath width for sparse scenes while preserving azimuthal resolution. AgileSAR overcomes the limitation of the Nyquist sampling theorem so that it has a small amount of data and low system complexity. However, traditional CS optimization-based algorithms suffer from manual tuning and pre-definition of optimization parameters, and they generally involve high time and computational complexity for AgileSAR imaging. To address these issues, a pseudo- L 0 -norm fast iterative shrinkage algorithm network (pseudo- L 0 -norm FISTA-net) is proposed for AgileSAR imaging via the deep unfolding network in this paper. Firstly, a pseudo- L 0 -norm regularization model is built by taking an approximately fair penalization rule based on Bayesian estimation. Then, we unfold the operation process of FISTA into a data-driven deep network to solve the pseudo- L 0 -norm regularization model. The network's parameters are automatically learned, and the learned network significantly increases imaging speed, so that it can improve the accuracy and efficiency of AgileSAR imaging. In addition, the nonlinearly sparsifying transform can learn more target details than the traditional sparsifying transform. Finally, the simulated and data experiments demonstrate the superiority and efficiency of the pseudo- L 0 -norm FISTA-net for AgileSAR imaging. [ABSTRACT FROM AUTHOR]

Pulse Wave Velocity (PWV) analysis is valuable for assessing arterial stiffness and cardiovascular health and potentially for estimating blood pressure cufflessly. However, conventional PWV analysis from two transducers spaced closely poses challenges in data management, battery life, and developing the device for continuous real-time applications together along an artery, which typically need data to be recorded at high sampling rates. Specifically, although a pulse signal consists of low-frequency components when used for applications such as determining heart rate, the pulse transit time for transducers near each other along an artery takes place in the millisecond range, typically needing a high sampling rate. To overcome this issue, in this study, we present a novel approach that leverages the Nyquist–Shannon sampling theorem and reconstruction techniques for signals produced by bioimpedance transducers closely spaced along a radial artery. Specifically, we recorded bioimpedance artery pulse signals at a low sampling rate, reducing the data size and subsequently algorithmically reconstructing these signals at a higher sampling rate. We were able to retain vital transit time information and achieved enhanced precision that is comparable to the traditional high-rate sampling method. Our research demonstrates the viability of the algorithmic method for enabling PWV analysis from low-sampling-rate data, overcoming the constraints of conventional approaches. This technique has the potential to contribute to the development of cardiovascular health monitoring and diagnosis using closely spaced wearable devices for real-time and low-resource PWV assessment, enhancing patient care and cardiovascular disease management. [ABSTRACT FROM AUTHOR]

Abstract In this paper, fast algorithms for the extrapolation of band-limited signals are presented by the sampling theorem and Fourier series in the case of over sampling. Assume the band-limited signal is known in a finite interval. We update the signal outside the interval by the Shannon sampling theorem in the case of over sampling. Then we obtain a fast algorithm in the form of Fourier series instead of the Fourier transform in the Papoulis–Gerchberg algorithm. Gibbs phenomena is analyzed in the method. An algorithm is presented to control the Gibbs phenomena, and some examples are given in the experimental results.

An effective near-field to far-field transformation using a reduced number of near-field measurements collected via a spherical scan over the upper hemisphere, due to the presence of a flat metallic ground, is devised in this paper. Such a transformation relies on the non-redundant sampling representations of electromagnetic fields and exploits the image principle to properly account for the metallic ground, supposed to be of infinite extent and realised by perfectly conducting material. The sampling representation of the probe voltage over the upper hemisphere is developed by modelling the antenna under test and its image by a very adaptable convex surface, which is able to fit as much as possible the geometry of any kind of antenna, thus minimising the volumetric redundancy and, accordingly, the number of required samples as well as the measurement time. Then, the use of a two-dimensional optimal sampling interpolation algorithm allows the reconstruction of the voltage value at each sampling point of the spherical grid required by the classical near-field-to-far-field transformation developed by Hansen. Numerical examples proving the effectiveness of the developed sampling representation and related near-field-to-far-field transformation techniques are reported. [ABSTRACT FROM AUTHOR]

Data reconstruction is the most essential step in seismic data processing. Although the compressed sensing (CS) theory breaks through the Nyquist sampling theorem, we previously proved that the CS-based reconstruction of spatially irregular seismic data could not fully meet the theoretical requirements, resulting in low reconstruction accuracy. Although deep learning (DL) has great potential in mining features from data and accelerating the process, it faces challenges in earth science such as limited labels and poor generalizability. To improve the generalizability of deep neural network (DNN) in reconstructing seismic data in the actual situation of limited labeling, this paper proposes a method called CSDNN that combines model-driven CS and data-driven DNN to reconstruct the spatially irregular seismic data. By physically constraining neural networks, this method increases the generalizability of the network and improves the insufficient reconstruction caused by the inability to sample randomly in the whole data definition domain. Experiments on the synthetic and field seismic data show that the CSDNN reconstruction method achieves better performance compared with the conventional CS method and DNN method, including those with low sampling rates, which verifies the feasibility, effectiveness and generalizability of this approach. [ABSTRACT FROM AUTHOR]

Gabor phase retrieval is the problem of recovering a signal from the absolute values of Gabor transform, which has turned into a very active research area. In the paper, we define a generalized Paley–Wiener space, which is obtained by applying the special affine Fourier transform to L p ([ - B , B ]) (2 ≤ p ≤ ∞) and provide the uniqueness of the Gabor phase retrieval in the generalized Paley–Wiener space. When the window function ψ is the inverse special affine Fourier transform of ϕ = 2 1 4 e - π x 2 , we show that every signal in the generalized Paley–Wiener space can be uniquely recovered, up to a global sign, from its the magnitudes of Gabor measurement sampled on a rectangular lattice. Recently, Grohs, Liehr and Wellershoff studied the Gabor phase retrieval problems in the conventional Paley–Wiener space. The paper extends their results to the generalized Paley–Wiener space. Since the generalized Paley–Wiener space includes a broader class of signals, our results expand the applied range of the Gabor phase retrieval. [ABSTRACT FROM AUTHOR]

The existing ultrasonic thickness measurement systems require high sampling frequencies for echo signal acquisition, leading to complex circuit designs and high costs. Moreover, extracting the characteristics of ultrasonic echo signals for accurate thickness measurement poses significant challenges. To address these issues, this paper proposes a method that utilizes conventional sampling frequencies to acquire high-frequency ultrasonic echo signals, overcoming the limitations of high-frequency data acquisition imposed by the Nyquist–Shannon sampling theorem. By employing an improved sampling reconstruction technique, the multi-cycle sampling signals are reconstructed and rearranged within a single cycle, effectively increasing the equivalent sampling frequency. Additionally, a combination of coarse estimation using fast Fourier transform (FFT) and precise phase extraction using the moving sine fitting algorithm is proposed for accurate thickness measurement, resolving the limitations of common thickness measurement methods such as peak detection, envelope detection, and Hilbert autocorrelation in terms of low measurement accuracy. Experimental results obtained from thickness measurements on 45 steel ultrasonic test blocks within the range of 3 mm to 20 mm indicate a measurement error of ±0.01 mm, while for thicknesses ranging from 1 mm to 50 mm, the measurement error is ±0.05 mm. [ABSTRACT FROM AUTHOR]

Compressive sampling (CS) is a novel signal processing paradigm whereby the data compression is performed simultaneously with the sampling, by measuring some linear functionals of original signals in the analog domain. Once the signal is sparse sufficiently under some bases, it is strictly guaranteed to stably decompress/reconstruct the original one from significantly fewer measurements than that required by the sampling theorem, bringing considerable practical convenience. In the field of civil engineering, there are massive application scenarios for CS, as many civil engineering problems can be formulated as sparse inverse problems with linear measurements. In recent years, CS has gained extensive theoretical developments and many practical applications in civil engineering. Inevitable modelling and measurement uncertainties have motivated the Bayesian probabilistic perspective into the inverse problem of CS reconstruction. Furthermore, the advancement of deep learning techniques for efficient representation has also contributed to the elimination of the strict assumption of sparsity in CS. This paper reviews the advancements and applications of CS in civil engineering, focusing on challenges arising from data acquisition and analysis. The reviewed theories also have applicability to inverse problems in broader scientific fields. [ABSTRACT FROM AUTHOR]

In this paper, fast algorithms for the extrapolation of band-limited signals are presented by the sampling theorem and Fourier series in the case of over sampling. Assume the band-limited signal is known in a finite interval. We update the signal outside the interval by the Shannon sampling theorem in the case of over sampling. Then we obtain a fast algorithm in the form of Fourier series instead of the Fourier transform in the Papoulis–Gerchberg algorithm. Gibbs phenomena is analyzed in the method. An algorithm is presented to control the Gibbs phenomena, and some examples are given in the experimental results. [ABSTRACT FROM AUTHOR]

Compressive sensing and arbitrary sampling are techniques of data volume reduction challenging the Shannon sampling theorem and expected to provide efficient storage while preserving original information. Irregularity of sampling is either a result of intentional optimization of a sampling grid or stems from sporadic occurrence or intermittent observability of a phenomenon. Quantitative comparison of irregular patterns similarity is usually preceded by a projection to a regular sampling space. In this paper, we study methods for direct comparison of time series in their original non-uniform grids. We also propose a linear graph to be a representation of the non-uniform signal and apply the Mutual Graph Approximation (MGA) method as a metric to infer the degree of similarity of the considered patterns. The MGA was implemented together with four state-of-the-art methods and tested with example speech signals and electrocardiograms projected to bandwidth-related and random sampling grids. Our results show that the performance of the proposed MGA method is comparable to most accurate (correlation of 0.964 vs. Frechet: 0.962 and Kleinberg: 0.934 for speech signals) and to less computationally expensive state-of-the-art distance metrics (both MGA and Hausdorf: O (L 1 + L 2) ). Moreover, direct comparison of non-uniform signals can be equivalent to cross-correlation of resampled signals (correlation of 0.964 vs. resampled: 0.960 for speech signals, and 0.956 vs. 0.966 for electrocardiograms) in applications as signal classification in both accuracy and computational complexity. Finally, the bandwidth-based resampling model plays a substantial role; usage of random grid is the primary cause of inaccuracy (correlation of 0.960 vs. for random sampling grid: 0.900 for speech signals, and 0.966 vs. 0.878, respectively, for electrocardiograms). These figures indicate that the proposed MGA method can be used as a simple yet effective tool for scoring similarity of signals directly in non-uniform sampling grids. [ABSTRACT FROM AUTHOR]

The multi-resolution analysis (MRA) associated with quadratic phase Fourier transform (QPFT) serves as a tool to construct orthogonal bases of the L 2 (R) . Consequently, it assumes a pivotal role in facilitating potential applications of QPFT. Inspired by the sampling theorem applicable to band-limited signals in the QPFT domain, this paper formulates the development of the MRA linked with QPFT. Subsequently, we develop a method for constructing orthogonal bases for L 2 (R) , followed by some examples. [ABSTRACT FROM AUTHOR]

In sampling theory, it is a popular trend to use auxiliary information to obtain more efficient estimators for the population parameters to increase the precision of the estimator. Estimators obtained using auxiliary information are supposed to be more efficient than the estimators obtained without using auxiliary information. The ratio, regression, product and difference methods take advantage of the auxiliary information at the estimation stage. Therefore, this study considered a generalized class of log-type estimators of finite population mean based on correlation coefficient as the proposed estimator for estimating the population mean of the study variable. It has been shown that the generalized class of log-type estimators has lesser mean square errors (MSEs) under the optimum values of the characterizing scalar as compared to some of the commonly used related estimators available in the literature. Further, an extension of the proposed generalized class of log-type estimators using multiple auxiliary variables such as coefficient of variation (CX), coefficient of kurtosis (b2(x)), and correlation coefficient (ρxy). have also base initiated in this dissertation. The expressions for the properties of the proposed family of estimators, that is; Bias and Mean Square Error (MSE), were derived to the first degree of approximation. We also obtained the optimum Mean Square Error (MSEopt.), and theoretical comparisons were made with the related existing estimators in literature. Following theoretical comparisons, it was demonstrated that the proposed family of estimators was more efficient than various related existing estimators compared with, under the obtained conditions. [ABSTRACT FROM AUTHOR]

Spectrum aliasing occurs in signal echoes when the sampling frequency does not comply with the Nyquist Sampling Theorem. In this scenario, the extraction of micro-motion parameters becomes challenging. This paper proposes a spectral de-aliasing method for micro-motion signals based on a complex-valued U-Net network. Zero interpolation is employed to insert zeros into the echo, effectively increasing the sampling frequency. After zero interpolation, the micro-motion signal contains both real micro-motion signal frequency components and new frequency components. Short-Time Fourier Transform (STFT) is then applied to transform the zero-interpolated echo from the time domain to the time–frequency domain. Furthermore, a complex-valued U-Net training model is utilized to eliminate redundant frequency components generated by zero interpolation, thereby achieving the frequency reconstruction of micro-motion signal echoes. Finally, the training models are employed to process the measured data. The theoretical analysis, simulations, and experimental results demonstrate that this method is robust and feasible, and is capable of addressing the problem of micro-motion signal echo spectrum aliasing in narrowband radar. [ABSTRACT FROM AUTHOR]

Background: Biologgers have contributed greatly to studies of animal movement, behaviours and physiology. Accelerometers, among the various on-board sensors of biologgers, have mainly been used for animal behaviour classification and energy expenditure estimation. However, a general principle for the combined sampling duration and frequency for different taxa is lacking. In this study, we evaluated whether Nyquist–Shannon sampling theorem applies to accelerometer-based classification of animal behaviour and energy expenditure approximation. To evaluate the influence of accelerometer sampling frequency on behaviour classification, we annotated accelerometer data from seven European pied flycatchers (Ficedula hypoleuca) freely moving in aviaries. We also used simulated data to systematically evaluate the combined effect of sampling duration and sampling frequency on the performance of estimating signal frequency and amplitude. Results: We found that a sampling frequency higher than Nyquist frequency at 100 Hz was needed to classify fast, short-burst behavioural movements of pied flycatcher, such as swallowing food with a mean frequency of 28 Hz. In contrast, high frequency movements with longer durations such as flight could be characterized adequately using much lower sampling frequency of 12.5 Hz. To identify rapid transient prey catching manoeuvres within these flight bouts, again a high frequency sampling at 100 Hz was needed. For both the experimental data of the flycatchers and the simulated data, the combination of sampling frequency and sampling duration affected the accuracy of signal frequency and amplitude estimation. For long sampling durations, the sampling frequency equal to the Nyquist frequency was adequate for accurate signal frequency and amplitude estimation. Accuracy declined with decreasing sampling duration, especially for signal amplitude estimation with up to 40% standard deviation of normalized amplitude difference. To accurately estimate signal amplitude at low sampling duration, a sampling frequency of four times the signal frequency was necessary (two times the Nyquist frequency). Conclusions: The appropriate sampling frequency of accelerometers depends on the objective of the specific study and the characteristics of the behaviour. For studies with no constraints on device battery and storage, a sampling frequency of at least two times the Nyquist frequency will achieve relative optimal representative of signal information (i.e., frequency and amplitude). For classification and energy expenditure estimation of short-burst behaviours, 1.4 times the Nyquist frequency of behaviour is required. [ABSTRACT FROM AUTHOR]

This paper examines various aspects related to digital signal processing in digital control circuits used in power electronics. The discussion focuses on several common issues, including the sampling rate of signals (including phenomena such as aliasing and synchronization), coherent sampling, jitter of sampling pulses, sequential versus simultaneous sampling in multichannel systems, signal resolution (including signal-to-noise ratio, noise-shaping circuits, and changes in sampling speed), interpolation and decimation, and the conversion of analog circuits into digital form. One of the key contributions of this paper is the introduction of a new formula for calculating the resultant signal-to-noise ratio for three-stage digital control circuits. By carefully considering and correcting for sources of error, it is possible to increase the signal-to-noise ratio and minimize distortion components. This, in turn, leads to improved output/input current and voltage parameters, which can have a positive impact on the overall quality of energy processing in power electronic circuits. [ABSTRACT FROM AUTHOR]

Single-pixel imaging (SPI) uses a single-pixel detector instead of a detector array with a lot of pixels in traditional imaging techniques to realize two-dimensional or even multi-dimensional imaging. For SPI using compressed sensing, the target to be imaged is illuminated by a series of patterns with spatial resolution, and then the reflected or transmitted intensity is compressively sampled by the single-pixel detector to reconstruct the target image while breaking the limitation of the Nyquist sampling theorem. Recently, in the area of signal processing using compressed sensing, many measurement matrices as well as reconstruction algorithms have been proposed. It is necessary to explore the application of these methods in SPI. Therefore, this paper reviews the concept of compressive sensing SPI and summarizes the main measurement matrices and reconstruction algorithms in compressive sensing. Further, the performance of their applications in SPI through simulations and experiments is explored in detail, and then their advantages and disadvantages are summarized. Finally, the prospect of compressive sensing with SPI is discussed. [ABSTRACT FROM AUTHOR]

This article proposes an optimization‐based approach to selecting the sampling periods for classes of linear time‐invariant (LTI) regulators in a cascaded multi‐rate control structure, to account for practical implementation on numeric systems. Starting from the Shannon‐Nyquist sampling theorem, which proposes the minimum required sampling frequency for completely recovering the original analog signal from its discrete samples, the scope of the sampling process, viewed from a control perspective, is to ensure asymptotic stability of the closed‐loop system, with the smallest possible degradation of the initially‐proposed performance indices as possible according to a set of well‐picked criteria. As such, a configurable optimization‐based approach is proposed, solved with the mixed‐integer artificial bee colony (MI‐ABC) algorithm, for selecting the sampling periods by specifying the emphasis between closed‐loop fidelity and ease of implementation, with an intuitive visualization method. The proposed solution is illustrated on two case studies, with emphasis on the construction of the proposed functionals and their practical implications. [ABSTRACT FROM AUTHOR]

X-ray tomography is often affected by noise and artifacts during the reconstruction process, such as detector offset, calibration errors, metal artifacts, etc. Conventional algorithms, including FDK and SART, are unable to satisfy the sampling theorem requirements for 3D reconstruction under sparse-view constraints, exacerbating the impact of noise and artifacts. This paper proposes a novel 3D reconstruction algorithm tailored to sparse-view cone-beam computed tomography (CBCT). Drawing upon compressed sensing theory, we incorporate the weighted Schatten p-norm minimization (WSNM) algorithm for 2D image denoising and the adaptive steepest descent projection onto convex sets (ASD-POCS) algorithm, which employs a total variation (TV) regularization term. These inclusions serve to reduce noise and ameliorate artifacts. Our proposed algorithm extends the WSNM approach into three-dimensional space and integrates the ASD-POCS algorithm, enabling 3D reconstruction with digital brain phantoms, clinical medical data, and real projections from our portable CBCT system. The performance of our algorithm surpasses traditional methods when evaluated using root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM) metrics. Furthermore, our approach demonstrates marked enhancements in artifact reduction and noise suppression. [ABSTRACT FROM AUTHOR]

In ecology, there is an emerging emphasis on the importance of capturing temperature variation at relevant scales. Temperature fluctuates continuously in nature but is sampled at discrete time points, so how often should ecologists measure temperature to capture its variation? A recent development in thermal ecology is the use of spectral analysis of temperature time series to determine at what frequencies important temperature fluctuations occur. Building on this, I borrow from signal processing theory to show how continuous thermal regimes can be effectively reconstructed from discrete, regular, measurements, and provide a rule of thumb for designing temperature sampling schemes that capture ecologically relevant temporal variation.I introduce sinc interpolation, a method for reconstructing continuous waveforms from discrete samples. Furthermore, I introduce the Nyquist–Shannon sampling theorem, which states that continuous complex waveforms can be perfectly sinc‐interpolated from discrete, regular, samples if sampling intervals are sufficiently short. To demonstrate the power of these concepts in an ecological context, I apply them to several published high‐resolved (15‐min intervals) temperature time series used for ecological predictions of insect development times. First, I use spectral analysis to illuminate the fluctuation frequencies that dominate the temperature data. Second, I employ sinc interpolation over artificially thinned versions of the temperature time series. Third, I compare interpolated temperatures with observed temperatures to demonstrate the Nyquist–Shannon sampling theorem and its relation to spectral analysis. Last, I repeat the ecological predictions using sinc‐interpolated temperatures.Daily, and less frequent, fluctuations dominated the variation in all the temperature time series. Therefore, in accordance with the Nyquist–Shannon sampling theorem, 11‐h measurement intervals consistently retrieved most 15‐min temperature variation. Moreover, previous predictions of insect development times were improved by using sinc‐interpolated, rather than averaged, temperatures.By identifying the highest frequency at which ecologically (or otherwise) relevant temperature fluctuations occur and applying the Nyquist–Shannon sampling theorem, ecologists (or others doing climate‐related research) can use sinc interpolation to produce remarkably accurate continuous thermal regimes from sparse but regular temperature measurements. Surprisingly, these concepts have remained largely unexplored in ecology despite their applicability, not least in thermal ecology. [ABSTRACT FROM AUTHOR]

Establishing discriminant validity has been a keystone of measurement validity in empirical marketing research for many decades. Without statistically showing that constructs have discriminant validity, contributions to marketing literature are likely to foster the proliferation of constructs that are operationally the same as other constructs already present in the literature, thus leading to confusion in the development of theory. This article addresses this concern by evaluating well-established methods for testing discriminant validity through the simulation of artificial datasets (containing varying levels of correlation between constructs, sample size, measurement error, and distribution skewness). The artificial data are applied to six commonly used approaches for testing the existence of discriminant validity. Results strongly suggest that several methods are much more likely than others to yield accurate assessments of whether discriminant validity exists, especially under specific conditions. Recommendations for practice in the assessment of discriminant validity are suggested. [ABSTRACT FROM AUTHOR]

The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is folded back into a low dynamic range measurement, avoiding the saturation problem. Since the non-bandlimited signal in the Fourier domain cannot be directly applied to its existing theory, the non-bandlimited signal in the Fourier domain may be bandlimited in the fractional Fourier domain. Therefore, this brief report studies the unlimited sampling problem of high dynamic non-bandlimited signals in the Fourier domain based on the fractional Fourier transform. Firstly, a mathematical signal model for unlimited sampling is proposed. Secondly, based on this mathematical model, the annihilation filtering method is used to estimate the arbitrary folding time. Finally, a novel fractional Fourier domain unlimited sampling theorem is obtained. The theory proves that, based on the folding characteristics of the self-reset ADC, the number of samples is not affected by the modulo threshold, and any folding time can be handled. [ABSTRACT FROM AUTHOR]

Background: Dynamic measurement and analysis of rotating components is an arduous and complex task that has always attracted great attention from the engineering community. Objective: In order to propose a low-cost, efficient, high-precision, and high temporal and spatial resolution rotating vibration measurement scheme, three-dimensional Digital Image Correlation (3D DIC) combined with down-sampling technology is employed. Two defects of this scheme hinder its wide application: the additional initial shape function estimation in rotation correlation of DIC and the cumbersome experimental operation process of traditional down-sampling. Therefore, an extension of down-sampling technology and a comparative study on efficient initial value estimation algorithms were researched. Methods: Comparative experiments of extended down-sampling proposed in this paper and high-frequency sampling were carried out on a rotating disc for its vibration Operational Deflection Shapes (ODSs) measurement. During the data processing procedure, an efficient initial value estimation algorithm is recommended by comparing the efficiency and accuracy of Fourier-Mellin Transform-based (FMT-based), Scale Invariant Feature Transform-based (SIFT-based), and Hough Transform-based (HT-based) algorithms. Results: The experimental results indicate that the FMT-based algorithm is the most efficient, and its estimation accuracy guarantees accurate and efficient convergence of the sub-pixel iteration process, though slightly lower than that of the SIFT-based algorithm; The harmonic response and natural response ODSs of the disc were obtained in the high-frequency sampling experiment, and the corresponding harmonic response ODSs were obtained in the extended down-sampling experiment. The precision of the amplitude of obtained ODSs is on the order of submicron. Conclusions: The proposed extended down-sampling technology has been verified to circumvent the limitation of the Nyquist-Shannon sampling theorem, and accurately restore different orders of harmonic response ODSs with sampling once at a low frequency. Combined with extended down-sampling technology, 3D DIC becomes an efficient, submicron precision, full-field rotating vibration measurement scheme with high temporal and spatial resolution using low-cost conventional cameras. Simultaneously, the FMT-based rotation parameters estimation algorithm can efficiently provide accurate initial value estimation for 3D DIC. [ABSTRACT FROM AUTHOR]

The spatial and spectral information contained in the hyperspectral image (HSI) make it widely used in many fields. However, the sharp increase of HSI data brings enormous pressure to the data storage and real‐time transmission. The research shows that hyperspectral compressive sensing (HCS) breaks through the bottleneck of the Nyquist sampling theorem, which can relieve the massive pressure on data storage and real‐time transmission. Existing HCS methods try to design advanced compression sampling matrix or reconstruction algorithms, but cannot connect the two through a unified framework. To further improve the image reconstruction quality, a novel codec space‐spectrum joint dense residual network (CDS2‐DResN) is proposed. The CDS2‐DResN is divided into block compression sampling part and reconstruction part. For block compression sampling, coded convolutional layer (CCL) is leveraged to compress and sample HSI. For measurements reconstruction, deconvolution layer is first leveraged to initially reconstruct HSI, and then build a space‐spectrum joint network to refine the initial reconstructed HSI. Moreover, the CCL and reconstruction network are optimized via a unified framework, which can simplify the pre‐processing and post‐processing process of HCS. Extensive experiments have shown that CDS2‐DResN has an excellent HCS reconstruction effect at measurement rates 0.25, 0.10, 0.04 and 0.01, respectively. [ABSTRACT FROM AUTHOR]

The Fresnel transform (FrT) is commonly used to describe the free-space propagation of optical waves. In this work, we present new definitions for the convolution, correlation and generalized shift operations based on the FrT. The generalized shift operation is defined by using simultaneous space and phase shifts. The generalized shift operation is useful for centred optical systems in the Fresnel domain (FrD) when the data distributions at the input plane of the optical system are shifted. The new convolution and correlation operations defined in terms of the FrT, the wavelength and the propagation distance, can be considered as a generalization of the usual convolution and correlation operations. The sampling theorem for distributions, whose resulting FrT has finite support, is formulated by using the new convolution operation introduced in this work and a new definition of the Dirac comb function. These new definitions and results could be applied to describe, design and implement optical processing systems related to the FrT. Finally, we present a centred optical systems used in holography and optical security systems that can be described or modelled by the new definitions of the operations proposed in this paper. [ABSTRACT FROM AUTHOR]

Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the p-dimensional Euclidean space. The asymptotic property of the sample MMD has been well studied when the dimension p is fixed using the theory of U-statistic. As motivated by the frequent use of MMD test for data of moderate/high dimension, we propose to investigate the behavior of the sample MMD in a high-dimensional environment and develop a new studentized test statistic. Specifically, we obtain the central limit theorems for the studentized sample MMD as both the dimension p and sample sizes n;m diverge to infinity. Our results hold for a wide range of kernels, including popular Gaussian and Laplacian kernels, and also cover energy distance as a special case. We also derive the explicit rate of convergence under mild assumptions and our results suggest that the accuracy of normal approximation can improve with dimensionality. Additionally, we provide a general theory on the power analysis under the alternative hypothesis and show that our proposed test can detect difference between two distributions in the moderately high dimensional regime. Numerical simulations demonstrate the effectiveness of our proposed test statistic and normal approximation. [ABSTRACT FROM AUTHOR]

Although various infrared imaging spectrometers have been studied, most of them are developed under the Nyquist sampling theorem, which severely burdens 3D data acquisition, storage, transmission, and processing, in terms of both hardware and software. Recently, computational imaging, which avoids direct imaging, has been investigated for its potential in the visible field. However, it has been rarely studied in the infrared domain, as it suffers from inconsistency in spectral response and reconstruction. To address this, we propose a novel mid-wave infrared snapshot compressive spectral imager (MWIR-SCSI). This design scheme provides a high degree of randomness in the measurement projection, which is more conducive to the reconstruction of image information and makes spectral correction implementable. Furthermore, leveraging the explainability of model-based algorithms and the high efficiency of deep learning algorithms, we designed a deep infrared denoising prior plug-in for the optimization algorithm to perform in terms of both imaging quality and reconstruction speed. The system calibration obtains 111 real coded masks, filling the gap between theory and practice. Experimental results on simulation datasets and real infrared scenarios prove the efficacy of the designed deep infrared denoising prior plug-in and the proposed acquisition architecture that acquires mid-infrared spectral images of 640 pixels × 512 pixels × 111 spectral channels at an acquisition frame rate of 50 fps. [ABSTRACT FROM AUTHOR]

This paper proposes a cumulative distribution modelling method for pavement performance indexes based on the sampling theorem and implements clustering analysis of similar road sections through the K-means algorithm. The results show that: (1) The modelling method proposed in this paper can convert discrete pavement performance data into a continuous function of pavement performance indexes and a continuous function of pavement performance cumulative distribution and achieve the acquisition of a large amount of pavement performance data. (2) Based on the cumulative distribution and K-means clustering, it is possible to understand the overall pavement performance status of the network and identify road sections with similar decay models and poor decay status for focused attention, which constructed the pavement performance evaluation system of the three-level system of road network–road section–unit road section. [ABSTRACT FROM AUTHOR]

Notion of optical flow literally refers to the displacements of intensity patterns. In that sense, extracting interested information from 2D scene is analogy to modulation/demodulation in random signal processing. To address the limitations presented in computer vision based on static image, we propose a novel metal component defect detection method, specified as the instance of turbine blade surface detection, using optical flow estimation.To start the specified pattern recognition in 2D presentation, we modulate the brightness constancy assumption equation as illumination varying model, by sampling the second image with function whose frequency was chosen according to the Nyquist sampling theorem, and a sinusoidal factor was introduced as an additive factor. This tunable channel based on 2D image transfers intensity features into optical modes. Then, we implement optical flow estimation on two sequential images. Experimental results reveal grayscale space shows completness in representing the optical modes of turbine blade with various kinds of surface characteristics. By modifying the index of information content, we propose quantitative index to evaluate the performance of our method. Evaluation reveals optical flow algorithm is qualified to examine defects on highly reflective turbine blade, and our method extends the application of optical flow. [ABSTRACT FROM AUTHOR]

Online crowdfunding, an innovative model based on " Internet + Finance ", is a hot spot for financing via Internet. Crowdfunding based on blockchain is an emerging economic phenomenon and becomes one of the most advanced risk financing strategies. However, crowdfunding transactions face security threats due to identity leaks, quantum attacks and the untraceable nature of blind signatures, which facilitate criminal activity. Different from the previous works, which ignored the importance of traceability, in this paper, we establish a blockchain-empowered secure crowdfunding architecture and propose an anti-quantum partially blind signature algorithm based on the verifiable identity of both sides. Specially, for one thing, the private key decided by user identity is generated by lattice-based sample matrix, and the privacy of user identity can be ensured and traced by the rejection sampling theorem. For another thing, we design an improved krill herd algorithm (IKHA) to increase the credit factor of fundraisers for dealing with project investment issues. The simulation evaluates the correctness and effectiveness of our theoretical analyses. Compared with the current popular schemes, the proposed IKH algorithm has a higher convergence speed and can optimize investment efficiency. [ABSTRACT FROM AUTHOR]