Sampling Theorem Research Articles

Dynamic modeling and analysis of discontinuous wave propagation in a rod

The wave propagation in an impacting rod is instant and nearly discontinuous, which remains a challenging problem for both dynamic modeling and experimental test. This paper presents an Enriched Finite Element Method (Enriched FEM) with controllable dispersion error to accurately and efficiently model the discontinuous wave propagation. The Enriched FEM approximates the displacement solutions based on a linear interpolation enriched with a series of harmonic functions. The paper focuses on the dispersion error of the enriched finite element from spatial-temporal discretization and the sampling theorem of the enriched finite element with different cutoff numbers, and then gives a simple quantitative criterion on the interdependent relationship between the size of mesh and time step so as to reduce the numerical dispersion error. In addition, the paper presents the experimental study on the wave propagation of an elastic rod colliding with a rigid wall. The experimental results explicitly show the incidence and reflection of the stress wave in the rod in the contact duration. They also indicate that the amplitude of the strain almost does not decay with the wave propagation along the rod. The numerical results based on the Hertzian contact model are in good agreement with the experimental observations, especially at wave interfaces.

Embracing off-the-grid samples

Many empirical studies suggest that samples of continuous-time signals taken at locations randomly deviated from an equispaced grid (i.e., off-the-grid) can benefit signal acquisition, e.g., undersampling and anti-aliasing. However, explicit statements of such advantages and their respective conditions are scarce in the literature. This paper provides some insight on this topic when the sampling positions are known, with grid deviations generated i.i.d. from a variety distributions. By solving a square-root LASSO decoder with an interpolation kernel we demonstrate the capabilities of nonuniform samples for compressive sampling, an effective paradigm for undersampling and anti-aliasing. For functions in the Wiener algebra that admit a discrete s-sparse representation in some transform domain, we show that O(spolylogN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(s{{\\,\\mathrm{poly\\,\\hspace{-2pt}log}\\,}}N)$$\\end{document} random off-the-grid samples are sufficient to recover an accurate N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{N}{2}$$\\end{document}-bandlimited approximation of the signal. For sparse signals (i.e., s≪N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s \\ll N$$\\end{document}), this sampling complexity is a great reduction in comparison to equispaced sampling where O(N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(N)$$\\end{document} measurements are needed for the same quality of reconstruction (Nyquist–Shannon sampling theorem). We further consider noise attenuation via oversampling (relative to a desired bandwidth), a standard technique with limited theoretical understanding when the sampling positions are non-equispaced. By solving a least squares problem, we show that O(NlogN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(N\\log N)$$\\end{document} i.i.d. randomly deviated samples provide an accurate N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{N}{2}$$\\end{document}-bandlimited approximation of the signal with suppression of the noise energy by a factor ∼1log(N).\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim \\frac{1}{\\sqrt{\\log (N)}}.$$\\end{document}

Frequency Response Enhanced Quantitative Vibration Detection Using Fading-Free Coherent $\varphi$-OTDR With Randomized Sampling

A frequency response enhanced quantitative vibration detection scheme for interference fading suppressed coherent phase-sensitive optical time domain reflectometry (ϕ-OTDR) is proposed and demonstrated. By utilizing randomized sampling, the proposed scheme not only breaks the inherent limitation between the sensing range and the maximum detectable frequency in conventional ϕ-OTDR systems, but also allows for quantitative measurement of the vibration amplitude by tracking the peak intensity of the discrete Fourier transformation spectrum of the phase signals. The operation principle and the measurement accuracy are mathematically analyzed through the frequency spectrum estimator unbiasedness and the estimation standard deviation, which provides a comprehensive guidance for parameter configuration in practical applications. For proof of concept, quantitative detection of vibration signals up to 384 kHz is realized over a 5.4 km fiber, while the conventional solutions only reach 18.5 kHz as restricted by the Nyquist sampling theorem. The proposed sensing scheme paves the way to enable ultra-high frequency quantitative vibration detection using ϕ-OTDR.

Analysis of Sparse Signal Sequences under Compressive Sampling Techniques for Different Measurement Matrices

Introduction:: A more modern, extremely applicable method for signal acquisition is compression sensing. It permits effective data sampling at a rate that is significantly lower than what the Nyquist theorem suggests. Compressive sensing has a number of benefits, including a muchreduced demand for sensory devices, a smaller memory storage need, a greater data transfer rate, and significantly lower power usage. Compressive sensing has been employed in a variety of applications because of all these benefits. Neuro-signal acquisition is a domain in which compressive sensing has applications in the medical industry. Methods:: The novel methods discussed in this article are FFT-based CoSaMP (FFTCoSaMP), DCT-based CoSaMP(DCTCoSaMP) and DWT-based CoSaMP (DWTCoSaMP) based on sparse signal sequences / dictionaries by means of Transform Techniques, where CoSaMP stands for Compressive Sampling Matching Pursuit with respect to Objective Quality Assessment Algorithms like PSNR, SSIM and RMSE, where CoSaMP stands for Compressive Sampling Matching Pursuit. Results: DWTCoSaMP is giving the PSNR values of 40.26 db, for DCTCoSaMP and FFTCoSaMP, PSNR is 36.76 db and 34.76 db. For DWTCoSaMP, SSIM value is 0.8164, and for DCTCoSaMP and FTCoSaMP, SSIM 0.719 and 0.5625 respectively. Finally, for DWTCoSaMP, RMSE value is 0.442, and for DCTCoSaMP and FFTCoSaMP, SSIM 0.44 and 0.4425, respectively. Conclusion:: Among Compressed sampling techniques DWTCoSaMP, DCTCoSaMP and FFTCoSaMP discussed in this paper, DWTCoSaMP reveals the best results.

An efficient optimization of measurement matrix for compressive sensing

Compressive sensing (CS) is a new paradigm for signal acquisition and reconstruction, which can reconstruct the signal at less than the Nyquist sampling rate. The sampling of the signal occurs through a measurement matrix (MM); thus, MM generation is significant in the context of the CS framework. In this paper, an optimization algorithm is introduced for the generation of the MM of CS based on Restricted Isometric Property (RIP) mandates that eigenvalues of the sensing matrix fall within an interval also minimizes the mutual coherence of the sensing matrix (i.e. the product of the MM and sparsifying matrix). A novel gradient-based iterative optimization method is used to reduce the eigenvalues of the sensing matrix by SVD decomposition. Meanwhile, the proposed algorithm can also reduce the operational complexity. Experimental results and analysis prove that the optimized MM reduces the maximum mutual and average mutual coherence between the MM and the sparsifying basis, which shows the effectiveness of the proposed algorithm over some state-of-art works.

Bioimpedance spectroscopy measurement method based on multisine excitation and integer-period undersampling

Bioimpedance spectroscopy (BIS) is a detection technology that uses the bioimpedance characteristics of human tissues and their changes to analyze their physiological and pathological status, and is widely used in clinical and scientific research applications. Traditional BIS measurement must satisfy the Nyquist sampling theorem so as to ensure that the measurement signal has no frequency aliasing, but at the same time the sampling frequency and the number of sampling points will be increased, which will increase the computation and hardware costs. This paper proposes a novel BIS measurement method based on multisine excitation and integer-period undersampling (IPUS) technology. Firstly, the multisine-based IPUS theory is deduced, and the BIS measurement principle based on multisine excitation and IPUS technology is introduced. Secondly, a BIS measurement system based on a field-programmable gate array + analog-to-digital converter + digital-to-analog converter architecture is designed, and multisine excitation with 32 pseudo-logarithmically distributed frequency components in the range of 2–997 kHz is generated. Comparative BIS measurement experiments on three RC three-element models are carried out under the Nyquist sampling condition (sampling frequency fs = 2.56 MHz) and under the IPUS condition (fs = 512 kHz), respectively. Experimental results show that the mean amplitude error of BIS measurement under the Nyquist sampling condition is 0.80% (±1.19% SD), while the mean amplitude error under the IPUS condition is 1.02% (±1.13% SD). Moreover, the signal-to-noise ratio (SNR z ) is calculated in 40 repeated BIS measurements, where the mean SNR z is 63.60 dB under the IPUS condition, similar to the value of 62.77 dB under the Nyquist sampling condition. The proposed multisine-based IPUS theory and its implementation method in this paper can complete a BIS measurement with only one fundamental period, and the sampling frequency and sampling point requirements are lower than for Nyquist sampling, laying a theoretical and technical foundation for a BIS measurement system with reduced hardware and computation requirements.

Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples

We establish convergence analysis for Hermite-type interpolations for L^{2} ( mathbb {R})-entire functions of exponential type whose linear canonical transforms (LCT) are compactly supported. The results bridges the theoretical gap in implementing the derivative sampling theorems for band-limited signals in the LCT domain. Both complex analysis and real analysis techniques are established to derive the convergence analysis. The truncation error is also investigated and rigorous estimates for it are given. Nevertheless, the convergence rate is O(1/sqrt{N}), which is slow. Consequently the work on regularization techniques is required.

Statistical analysis of hypersonic glide vehicle radar cross section

AbstractThe capability to design, manufacture and test Hypersonic Glide Vehicles (HGVs) has been demonstrated by a number of nations, and they are increasingly forming part of military inventories, potentially offering capabilities highly unique to this technology. This article reports the simulated Monostatic Radar Cross Section of a generic HGV in five frequency ranges, HF, VHF, UHF, L, and S‐bands associated with different radar types. Full spherical datasets of complex co‐ and cross‐polar data are synthesised so that backscatter resulting from illumination by r.f./microwave energy of linear or circular polarisation can subsequently be computed from the raw dataset. Circular polarisation is commonly employed by ground‐based Ballistic Missile Early Warning Systems and Space Object Surveillance and Identification radars to avoid polarisation mis‐match losses resulting from ionospheric Faraday rotation effects. The data was generated using Ansys' Finite Element Solver at 10, 150 and 430 MHz, with the Geometric Optics/Physical Optics based SBR+ solver employed for 1.3 and 3 GHz data. All data was produced at below the Nyquist sampling interval relevant to the target's electrical size. These datasets were then imported into a Matlab routine which extracted data over limited angular ranges associated with the likely radar line‐of‐sight in particular scenarios, typically having a standard deviation of ±10° about the direction of flight, applying either a Gaussian or Uniform sampling distribution as part of a Monte Carlo analysis. These extracted data were then used to form histograms giving the probability of sampling particular RCS values. Probability density functions and cumulative distribution functions were then fitted, to aid in the representation of statistical target fluctuations for each band and angular sampling range. The HGV exists in either the ‘Rayleigh’, ‘resonance’ or ‘optical’ scattering regimes, depending on its relative electrical size. The results suggest that for this target shape at HF and VHF cases a simple Swerling 0 (fluctuation invariant) approximation is adequate in most instances, whilst a Gamma distribution may be applied for UHF band cases. At L and S‐band a Beta distribution was found to provide a good fit to the available data.

Dynamic Predictive Sampling Analog to Digital Converter for Sparse Signal Sensing

This paper presents a dynamic predictive sampling (DPS) based analog-to-digital converter (ADC) that provides a non-uniform sampling of input analog continuous-time signals. The processing unit generates a dynamic prediction of the input signal using two prior-quantized samplings to compute digital values of an upper threshold and a lower threshold. The digital threshold values are converted to analog thresholds to form a tracking window. A dynamic comparator compares the input analog signal with the tracking window to determine if the prediction is successful. A counter records timestamps between the unsuccessful predictions, which are the selected sampling points for quantization. No quantization is performed for successfully predicted sampling points so that the data throughput and power can be saved. The proposed circuits were designed as a 10-bit ADC using 0.18 micro CMOS process sampling at 1 kHz. The results show that the proposed system can achieve a data compression factor of 6.17 and a power saving factor of 31% compared to a Nyquist rate SAR ADC for ECG monitoring.

Зчитування сигналів сенсорів із автоматичним вибором частоти дискретизації

The correct selection of sampling frequency when reading signals from sensors ensures high quality of digitized data and saves memory when storing such data. The complexity of automatic selection of the sampling frequency is explained by the fact that this frequency depends on the frequencies of the useful signal, which are not always known. Therefore, in the work the computer system for reading signals from temperature, humidity, and lighting sensors with automatic selection of the sampling frequency based on the Fourier spectrum analysis of the signals was developed. Signals from digital sensors (DHT22) are transmitted directly to the Raspberry Pi3 microcomputer. Signals from analog sensors (LM335M, light sensor) are fed to the Arduino Uno device. An algorithm for the analysis of Fourier spectra of one-dimensional signals has been developed, which is designed to determine the optimal sampling frequency and decimation coefficient of signals read from sensors. Based on the initial signals, their Fourier spectra are calculated, and by analyzing the spectra, the maximum frequency of the useful signal and the optimal sampling frequency are determined. Specified sampling frequency according to the sampling theorem is calculated as a double value of the maximum frequency of the useful signal. Decimation (thinning) of the signal is performed with a coefficient determined by the ratio of the initial and specified sampling frequencies. To assess the quality of the signal after decimation, the decimated values were interpolated by splines. The root mean square error of interpolation was calculated. Experimental testing of the developed tools for reading and analyzing signals from temperature, humidity and lighting sensors was carried out. In all considered cases, the sampling frequency is determined correctly. The resulting sampling rates can be used for decimation of signals or for subsequent reading of signals from sensors.

A Millimeter-Wave 3D Imaging Algorithm for MIMO Synthetic Aperture Radar.

Multiple-input-multiple-output synthetic aperture radar (MIMO-SAR) is being studied and applied in more and more scenarios. However, there is still a certain distance away from real-time imaging using advanced algorithms. The traditional backpropagation algorithm (BPA) multi-accumulation integration is unsuitable for dealing with large-size scanning data, and the wavenumber domain algorithm requires the array to satisfy Nyquist sampling law in azimuth to avoid aliasing in imaging reconstruction. Based on these issues, a novel 3D imaging method is proposed for MIMO-SAR. An appropriate transformation and inverse Fourier transform (FT) is carried out for the frequency domain; thus, accumulation in the wavenumber domain is not required, which is easy to implement. The computational complexity of the algorithm is much lower than BPA and has better generalizability than the wavenumber domain algorithm. Coherence factor (CF) is also introduced to achieve sidelobe suppression. Proof-of-principle experiments were also carried out in the 92.5 GHz band based on the MIMO-SAR prototype system. Both simulation and experimental results of different distributed targets show good performance of imaging and do not lose the quality of image reconstruction.

Delay sampling theorem: A criterion for the recovery of multitone signal

Periodic nonuniform sampling (PNS) is widely used in sub-Nyquist sampling schemes of multitone signals. However, what sampling pattern of PNS enables the signal to recover from the sub-Nyquist samples? Although this problem has been discussed in different schemes, the corresponding answers vary greatly. In this paper, we introduce the recurrent delay times to describe a PNS and provide a mathematical definition of signal recoverability from the perspective of delay. On this basis, we review the well-known Shannon–Nyquist sampling theorem and suggest a delay sampling theorem (DST) that a multitone signal bandlimited to [0,fmax] can be perfectly reconstructed from its periodic nonuniform samples when its minimum combined delay time τmin is not more than the Nyquist interval 1/2fmax. To explain and demonstrate the DST, subspace theory-based algorithms and active aliasing and de-aliasing algorithm (AADA) are proposed and used to recover the spectrum or waveform of multitone signals. The high consistency between practical and theoretical results evidently verifies the correctness of DST. In terms of sampling and recovery of multitone signal, DST extends the Shannon–Nyquist sampling theorem and naturally unifies several existing sampling strategies from the perspective of delay. DST provides a new guideline for the sub-Nyquist sampling of multitone signals. According to the DST criterion, we can optimize the sampling patterns to reduce cosets and improve the supremum frequency such that the reconstructed spectrum is alias-free. By generalizing the sampling theorem from the view of delay, DST opens many avenues for the development of multitone signal processing.

A hardware prototype of wideband high‐dynamic range analog‐to‐digital converter

AbstractKey parameters of analog‐to‐digital converters (ADCs) are their sampling rate and dynamic range. Power consumption and cost of an ADC are directly proportional to the sampling rate; hence, it is desirable to keep it as low as possible. The dynamic range of an ADC also plays an important role, and ideally, it should be greater than the signal's; otherwise, the signal will be clipped. To avoid clipping, modulo folding can be used before sampling, followed by an unfolding algorithm to recover the true signal. Here, the authors present a modulo hardware prototype that can be used before sampling to avoid clipping. The authors’ modulo hardware operates prior to the sampling mechanism and can fold higher frequency signals compared to existing hardware. The authors present a detailed design of the hardware and also address key issues that arise during implementation. In terms of applications, the authors show the reconstruction of finite‐rate‐of‐innovation signals, which are beyond the dynamic range of the ADC. The authors’ system operates at six times below the Nyquist rate of the signal and can accommodate eight times larger signals than the ADC's dynamic range.

Criticality and Neuromorphic Sensing in a Single Memristor.

Resistive random access memory (RRAM) is an important technology for both data storage and neuromorphic computation, where the dynamics of nanoscale conductive filaments lies at the core of the technology. Here, we analyze the current noise of various silicon-based memristors that involves the creation of a percolation path at the intermediate phase of filament growth. Remarkably, we find that these atomic switching events follow scale-free avalanche dynamics with exponents satisfying the criteria for criticality. We further prove that the switching dynamics are universal and show little dependence on device sizes or material features. Utilizing criticality in memristors, we simulate the functionality of hair cells in auditory sensory systems by observing the frequency selectivity of input stimuli with tunable characteristic frequency. We further demonstrate a single-memristor-based sensing primitive for representation of input stimuli that exceeds the theoretical limits dictated by the Nyquist-Shannon theorem.

Sub-Nyquist sampling of sparse and correlated signals in array processing

This paper considers efficient sampling of simultaneously sparse and correlated (S&C) signals for automotive radar application. We propose an implementable sampling architecture for the acquisition of S&C at a sub-Nyquist rate. We prove a sampling theorem showing exact and stable reconstruction of the acquired signals even when the sampling rate is smaller than the Nyquist rate by orders of magnitude. Quantitatively, our results state that an ensemble M signals, composed of a-priori unknown latent R signals, each bandlimited to W/2 but only S-sparse in the Fourier domain, can be reconstructed exactly from compressive sampling only at a rate RSlogα⁡W samples per second. When R≪M and S≪W, this amounts to a significant reduction in sampling rate compared to the Nyquist rate of MW samples per second. This is the first result that presents an implementable sampling architecture and a sampling theorem for the compressive acquisition of S&C signals. We resort to a two-step algorithm to recover sparse and low-rank (S&L) matrix from a near optimal number of measurements. This result then translates into a signal reconstruction algorithm from a sub-Nyquist sampling rate.

Design and Implementation of a Multi-Channel Temperature Measurement System Based on LabVIEW

As computer technology and instrument technology advance rapidly, both virtual instrument and Lab-VIEW have significantly grown. LabVIEW is extensively employed in the industrial and academic sectors for developing data acquisition systems, instrument control software, and analysis software. This paper presents the design of a multi-channel temperature measurement system based on a single-chip CPU and LabVIEW. The system consists of analog-to-digital conversion modules, temperature measurement modules, and data acquisition modules. The system uses the Nyquist-Shannon sampling theorem and the advantages of various digital filter types to obtain temperature uncertainty, including the compensation uncertainty of the reference junction. The system is of high quality in measuring accuracy, stability, scalability and other aspects. The complete system was inspected and verified using a superconducting magnetic energy storage device (SMES). The results demonized the ease of construction, practicality and precise regulation of the system. These results also show that temperature measurement devices are less than 0.1°C absolute error and are highly accurate, making them valuable for applications that require precise temperature measurements.

Sparsity-Driven Inverse Synthetic Aperture Radar Imaging Using Accelerated Meta-Heuristic Optimization

When the inverse synthetic aperture radar (ISAR) system have sparse aperture (SA) dataset, which are non-uniform and less than Nyquist sampling rate along the cross-range axis, it can significantly blur the ISAR image of target having complex motion. To overcome this, we propose an improved ISAR imaging method based on dictionary estimation using parametric signal reconstruction (DEPSR) using accelerated meta-heuristic optimization (MHO). The proposed method reconstructs a motion-compensated and full-aperture (FA) dataset from a sparse-aperture (SA) dataset using MHO, which can be accelerated by a graphics processing unit (GPU). After then, we can obtain the motion-compensated FA dataset and by using this, we can exploit the conventional range-Doppler (R-D) processing. Simulation and real-data-based ISAR imaging results validate the superiority of the proposed method in terms of image quality in comparison with conventional methods, such as simple R-D processing, basis pursuit denoising, and DEPSR. Particularly, the proposed method exhibits a significantly lower computational burden than that of the traditional DEPSR approach.

Dual-phase digital lock-in implementation based on Nyquist rate and sampling subtraction.

Lock-in amplifiers (LIA) are widely used in laboratory environments to detect low-amplitude signals buried in noise as well as real and imaginary parts of a complex quantity. They are based on the technique of synchronous detection, where the signal of interest is modulated into a desired frequency, sent to the medium or device to be analyzed, and captured by a detector. The detector scheme relies on the concept of phase-sensitive detection, generally resulting in two components: in-phase and quadrature. This article shows a very simple and low computational-cost way to implement a dual-phase LIA, using readily available microcontrollers, running a simple and fast algorithm. Three examples of signal detection are presented (sound wave signal, impedance meter, and weak signal recovery) to point out the flexibility and capabilities of the proposed methodology.

Compressive Sensing Strategy on Sparse Array to Accelerate Ultrasonic TFM Imaging

Phased array ultrasonic testing (PAUT) based on full matrix capture (FMC) has recently been gaining popularity in the scientific and nondestructive testing communities. FMC is a versatile acquisition method that collects all the transmitter-receiver combinations from a given array. Furthermore, when postprocessing FMC data using the total focusing method (TFM), high-resolution images are achieved for defect characterization. Today, the combination of FMC and TFM is becoming more widely available in commercial ultrasonic phased array controllers. However, executing the FMC-TFM method is data-intensive, as the amount of data collected and processed is proportional to the square of the number of elements of the probe. This shortcoming may be overcome using a sparsely populated array in transmission followed by an efficient compression using compressive sensing (CS) approaches. The method can therefore lead to a massive reduction of data and hardware requirements and ultimately accelerate TFM imaging. In the present work, a CS methodology was applied to experimental data measured from samples containing artificial flaws. The results demonstrated that the proposed CS method allowed a reduction of up to 80% in the volume of data while achieving adequate FMC data recovery. Such results indicate the possibility of recovering experimental FMC signals using sampling rates under the Nyquist theorem limit. The TFM images obtained from the FMC, CS-FMC, and sparse CS approaches were compared in terms of contrast-to-noise ratio (CNR). It was seen that the CS-FMC combination produced images comparable to those acquitted using the FMC. Implementation of sparse arrays improved CS reconstruction times by up to 11 folds and reduced the firing events by approximately 90%. Moreover, image formation was accelerated by 6.6 times at the cost of only minor image quality degradation relative to the FMC.

Algorithm Fusion for 3D Ground-Penetrating Radar Imaging with Field Examples

Numerous data processing algorithms are available for ground-penetrating radar (GPR) data processing. However, most of the existing processing algorithms are derived from Fourier theory and assume that the system is linear or that data are stationary, which may oversimplify the case. Some nonlinear algorithms are accessible for improvement but generally are for stationary and deterministic systems. To alleviate the dilemma, this study proposes an algorithm fusion scheme that employs standard linear techniques in conjunction with a newer nonlinear and non-stationary method. The linear techniques include linear filtering, migration, and interpolation. The newer method is mainly for nonlinear filtering and image reconstruction. The results can be demonstrated in a two-dimensional single profile (time–distance section) or a 3D visualization if survey lines fulfill the 3D Nyquist sample intervals requirement. Two controlled experiments were conducted to justify the proposed scheme. Then, a field study including two examples was carried out to demonstrate the feasibility of practical applications. Compared with conventional methods, the proposed algorithm fusion provides better visualization and integrative interpretation for GPR imaging.