Nonuniform Spatial Sampling Research Articles

Non-uniform spatial sampling by individuals in midge swarms.

Individual animals engaged in collective behaviour can interchange their relative positions on a wide range of time scales. In situations where some regions of the group are more desirable, it is thought that more fit individuals will preferentially occupy the more favourable locations. However, this notion is difficult to test for animal groups like insect swarms that fluctuate rapidly and display little apparent structure. Here, we study the way that individuals in mating swarms of the non-biting midge Chironomus riparius sample the space available to them. We use Voronoi tessellation to define different regions of the swarm in a dynamic way, and show that midges indeed sample the swarm non-uniformly. However, individuals that preferentially reside in the interior or exterior of the swarm do not display statistically distinct flight behaviour, suggesting that differences in fitness must be assessed in a different way. Nevertheless, our results indicate that midge swarms are not random configurations of individuals but rather possess non-trivial internal structure.

MVHANet: multi-view hierarchical aggregation network for skeleton-based hand gesture recognition

Skeleton-based gesture recognition (SHGR) is a very challenging task due to the complex articulated topology of hands. Previous works often learn hand characteristics from a single observation viewpoint. However, the various context information hidden in multiple viewpoints is disregarded. To resolve this issue, we propose a novel multi-view hierarchical aggregation network for SHGR. Firstly, two-dimensional non-uniform spatial sampling, a novel strategy forming extrinsic parameter distributions of virtual cameras, is presented to enumerate viewpoints to observe hand skeletons. Afterward, we adopt coordinate transformation to generate multi-view hand skeletons and employ a multi-branch convolutional neural networks to further extract the multi-view features. Furthermore, we exploit a novel hierarchical aggregation network including hierarchical attention architecture and global context modeling to fuse the multi-view features for final classification. Experiments on three benchmarked datasets demonstrate that our work can be competitive with the state-of-the-art methods.

Algorithm to Correct Measurement Offsets Introduced by Inactive Elements of Transducer Arrays in Ultrasonic Flow Metering

Ultrasonic flow meters (UFMs) based on transducer arrays offer several advantages. With electronic beam steering, it is possible to tune the steering angle of the beam for optimal signal-tonoise ratio (SNR) upon reception. Moreover, multiple beams can be generated to propagate through different travel paths, covering a wider section of the flow profile. Furthermore, in a clamp-on configuration, UFMs based on transducer arrays can perform self-calibration. In this manner, userinput is minimized and measurement repeatability is increased. In practice, transducer array elements may break down. This could happen due to aging, exposure to rough environments, and/or rough mechanical contact. As a consequence of inactive array elements, the measured transit time difference contains two offsets. One offset originates from non-uniform spatial sampling of the generated wavefield. Another offset originates from the ill-defined beam propagating through a travel path different from the intended one. In this paper, an algorithm is proposed that corrects for both of these offsets. The algorithm also performs a filtering operation in the frequency-wavenumber domain of all spurious (i.e., flow-insensitive) wave modes. The advantage of implementing the proposed algorithm is demonstrated on simulations and measurements, showing improved accuracy and precision of the transit time differences compared to the values obtained when the algorithm is not applied. The proposed algorithm can be implemented in both in-line and clamp-on configuration of UFMs based on transducer arrays.

Theoretical formulation/development of signal sampling with an equal arc length using the frame theorem

Nonuniform sampling with equal arc length intervals can be found in shape measurements with contact sensor arrays. In this study, the conditions of nonuniform spatial sampling with an equal arc length interval are derived from two frame theorems. First, for general nonuniform sampling, the condition is that the equal arc length interval of the sensors should be less than frac{1}{4Omega }. Second, for strictly increasing sampling (the sampling point set is strictly increasing), the condition is that the equal arc length interval of the sensors should be less than frac{1}{2Omega }. The Omega is the maximum frequency of the detected object. For the latter, if the sampling frequency is more than twice the sampling frequency required, the reconstruction error (RRMSE and MRE) is less than 5%. If the sampling frequency is more than 2.5 times, the reconstruction error is less than 3%. The simulation and the application test are carried out, and the results show that a sensor array with equal arc length interval can reconstruct the detected object with high accuracy.

Correction of Dropped Frames in High-resolution Push-broom Hyperspectral Images for Cultural Heritage

Dropped frames can occur in line-scan cameras, which result in non-uniform spatial sampling of the scene. A dropped frame occurs when data from an image sensor is not successfully recorded. When mosaicking multiple line-scan images, such as in high-resolution imaging, this can cause misalignment. Much previous work to identify dropped frames in video prioritises fast computation over high accuracy, whereas in heritage imaging, high accuracy is often preferred over short computation time. Two approaches to identify the position of dropped frames are presented, both using the A* search algorithm to correct dropped frames. One method aligns overlapping sections of push-broom images and the other aligns the push-broom image to a lower resolution reference image. The two methods are compared across a range of test images, and the method aligning overlapping sections is shown to perform better than the method using a reference image under most circumstances. The overlap method was applied to hyperspectral images acquired of La Ghirlandata, an 1873 oil on canvas painting by D. G. Rossetti, enabling a high-resolution hyperspectral image mosaic to be produced. The resulting composite image is 10,875 \( \times \) 14,697 pixels each with 500 spectral bands from 400–2,500 nm. This corresponds to a spatial resolution of \( 80 \,\mathrm{\upmu }\mathrm{m} \) and a spectral resolution of 3–6 nm.

Detecting aliasing and artifact free co-seismic and tsunamigenic ionospheric perturbations using GPS

• Nonuniform spatial sampling and polynomial misfits introduce aliasing and artifacts in ionospheric perturbations obtained using GPS. • Spatio-Periodic Leveling Algorithm (SPLA) is efficient in removing such aliasing and artifacts. • SPLA detects 50% more perturbations compare to conventional methods and increases SNR up to 149%. • SPLA efficiently detects perturbations at low elevations and removes the need of elevation cut-off. Ionospheric perturbations induced by tsunamis and earthquakes can be used for tsunami early warning and remote sensing of earthquakes, provided the perturbations are characterized properly to distinguish them from the ones caused by other sources. The ionospheric perturbations are increasingly being obtained from Global Positioning System (GPS) based Total Electron Content (TEC) measurements sampled at uniform time intervals. However, the sampling is not uniform in space. The nonuniform spatial sampling along the GPS satellite tracks introduces aliasing if it is not accounted while computing the ionospheric perturbations. All the methods hitherto used to detect the co-seismic and tsunamigenic ionospheric perturbations did not account the nonuniform spatial sampling while computing these perturbations. In addition, the residual approach used to obtain the perturbations by detrending the TEC time series using high-order polynomial fit introduces artifacts. These aliasing and artifacts corrupt amplitude, Signal-to-Noise Ratio (SNR), phase, and frequency of ionospheric perturbations which are vital to distinguish the perturbations induced by tsunamis and earthquakes from the rest. We show that Spatio-Periodic Leveling Algorithm (SPLA) successfully removes such aliasing and artifacts. The efficiency of SPLA in removing the aliases and artifacts is validated under two simulated scenarios, and using GPS observations carried out during two natural disasters – the 2004 Indian Ocean tsunami and the 2015 Nepal-Gorkha earthquake. We, further, studied the severity of aliasing and artifacts on co-seismic and tsunamigenic perturbations by analyzing its characteristics employing SNR, spatiotemporal, and wavelet analyses. The results reveal that removal of aliasing and artifacts using SPLA i) increases the SNR up to ∼149% compared to the residual method and ∼39% compared to the differential method, ii) distinctly resolves signals from sharp static variations, and iii) detects 50% more co-seismic ionospheric perturbations and 25% more tsunami-induced ionospheric perturbations in the two events studied. Cross-correlation of the perturbation time series obtained using the residual method and SPLA reveals that aliasing and artifacts shift the time of occurrence by −7.64 minutes to +4.21 minutes. Further, the results show that the SPLA efficiently detects the ionospheric perturbations at low elevation angles, thereby removes the need of applying elevation cut-off and increases the area of ionospheric exploration of a GPS receiver.

Compressive-sensing based damped multi-mode extraction with nonuniform spatial sampling

Multi-mode extraction is an important technique providing essential information for waveguide model validation and waveguide condition assessment. In this paper, an extraction method for damped multi-modes is proposed using randomly distributed nonuniform spatial samples. It addresses the problems of the conventional measurement method using uniform sampling, such as high sampling rate and large sample numbers. The proposed method is based on enhanced matrix completion (EMaC) which constructs a Hankel matrix by spatial signal. Using the measured nonuniform spatial samples, EMaC uses nuclear norm compressive sensing (CS) to reconstruct all entries of the Hankel matrix, from which the spatial signal is recovered and modes with their wavenumbers and attenuations are extracted. The bounds in terms of minimum sample numbers, spectrum separation and reconstruction error are analyzed by theory and quantified by simulations. Using the simulated data of a thin Titanium plate waveguide and the experimental data of a water-filled steel pipeline, the proposed method is shown to extract damped multi-modes using just 25% of the whole uniform samples set. The accuracy of wavenumber and attenuation estimates of the proposed method are found to be similar to the conventional method using uniform samples.

A Multi-Level Non-Uniform Spatial Sampling Method for Accuracy Assessment of Remote Sensing Image Classification Results

Accuracy assessment of classification results has important significance for the application of remote sensing images, which can be achieved by sampling methods. However, the existing sampling methods either ignore spatial correlation or do not consider spatial heterogeneity. Here, we proposed a multi-level non-uniform spatial sampling method (MNSS) for the accuracy assessment of classification results. Taking the remote sensing image of Kobo Askov, Texas, USA, as an example, the classification result of this image was obtained by Support Vector Machine (SVM) classifier. In the proposed MNSS, the studied spatial region was zoned from high to low resolution based on the features of spatial correlation. Then, the sampling rate of each zone was deduced from the low to high resolution based on the spatial heterogeneity. Finally, the positions of sample points were allocated in each zone, and the classification results of the sample points were obtained. We also used other sampling methods, including a random sampling method (SRS), stratified sampling method (SS), and spatial sampling of the gray level co-occurrence matrix method (GLCM), to obtain the classification results of the sample points (2-m resolution). Five categories of ground objects in the same region were used as the ground truth data. We than calculated the overall accuracy, Kappa coefficient, producer accuracy, and user accuracy to estimate the accuracy of the classification results. The results showed that MNSS was the strictest inspection method as shown by the minimum value of accuracy. Moreover, MNSS overcame the shortcoming of SRS, which did not consider the spatial correlation of sample points, and overcame the shortcomings of SS and GLCM, which had redundant information between sample points. This paper proposes a novel sampling method for the accuracy assessment of classification results of remote sensing images.

Detecting ionospheric disturbances using GPS without aliasing caused by non-uniform spatial sampling: Algorithm, validation and illustration

Ionospheric disturbance (ID) detected using GPS based Total Electron Content (TEC) measurements are widely used to study the morphology and dynamics of the ionosphere, and its impact on radio communication and satellite based navigation. The IDs normally derived as rate of change of TEC (ROT) between consecutive ionospheric pierce points at uniform time interval implicitly results in non-uniform spatial sampling along the GPS satellite tracks. The non-uniform spatial sampling introduces aliasing in ROT. These aliasing corrupt amplitude and Signal-to-Noise Ratio (SNR) of the detected IDs. In this study, we propose a Spatio-Periodic Leveling Algorithm (SPLA) to remove such aliasing. Efficiency of the proposed algorithm was tested by simulating the IDs along a satellite track and validated with GPS observations carried out during 2015 St. Patrick's day geomagnetic storm. Spatiotemporal, and SNR analyses of simulated and observed IDs reveal that the SPLA is (i) efficient in removing the aliases, (ii) increases the SNR on an average of 99.5% compared to ROT, (iii) removes the need of applying elevation cut-off, and (iv) expands the area of coverage up to 65%.

Quadratically Constrained Ambiguity Suppression Algorithm for APC/Multichannel SAR Systems With Nonuniform Spatial Sampling

The azimuth phase coding (APC) technique is known for its very low implementation complexity and its effectiveness for point and distributed ambiguities in conventional synthetic aperture radar (SAR) systems. In recent years, as an extension, the APC technique has been briefly discussed for multichannel SAR systems. However, the properties of the APC technique are no longer guaranteed in the multichannel SAR systems based on the digital beamforming (DBF) on-receive, and only a slight APC gain in the suppression of the range ambiguity can be obtained. In this article, we first provide a more thorough analysis for an APC-multichannel SAR system with respect to a uniform pulse-repetition frequency (PRF). Then, the APC/multichannel SAR system with nonuniform spatial sampling is briefly discussed, and an improved reconstruction approach based on a quadratically constrained optimization model is proposed to increase greatly the APC gain with respect to existing multichannel reconstruction algorithms. This proposed approach allows the minimization of the range ambiguity with a given azimuth-ambiguity constraint. In particular, for some specific PRFs, the proposed method permits a cancellation of the odd-order range ambiguity. Finally, simulation experiments are performed to verify the advantages and effectiveness of the proposed approach.

On Long‐Term SABER CO2 Trends and Effects Due to Nonuniform Space and Time Sampling

AbstractThe Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument on board the TIMED satellite has been continuously operating for more than 16 years, since 2002, monitoring the CO2 concentration on nearly a global scale in the middle and upper atmosphere (from 65 km up to 110 km). A recent reanalysis (Qian et al., 2017, https://doi.org/10.1002/2016JA023825) concluded that different deseasonalizing methodologies may have a strong impact on long‐term trend analysis, ultimately yielding different altitude profiles of the global mean CO2 trend. In this work, we aim to understand how the nonuniform spatial and temporal sampling inherent in the SABER CO2 data set affects the determination of the long‐term trends. In addition, our goal is to disentangle reported differences in SABER CO2 trends due to different time averaging windows and methodologies used for trend estimation. The Whole Atmosphere Community Climate Model is used for synthetic studies of the time series. We demonstrate that, due to the time varying data gaps and nonuniform sampling of local times, different time binning of the SABER CO2 data may indeed bias the long‐term trend estimation. We show and discuss how the 60‐day averaging reduces the bias in relative trends. We also conclude that different deseasonalizing methodologies (averaged over the same temporal bins) yield negligible differences on the trend determination. Taking this into account the global mean CO2 relative trend does not deviate statistically from the tropospheric value below 1 × 10−3 mb (90 km). Above about 90 km, there is a positive slope in the global CO2 trend profile, but with substantially reduced magnitude for 60‐day binned data.

The impact of nonuniform sampling on stratospheric ozone trends derived from occultation instruments.

This paper applies a recently developed technique for deriving long-term trends in ozone from sparsely sampled data sets to multiple occultation instruments simultaneously without the need for homogenization. The technique can compensate for the nonuniform temporal, spatial, and diurnal sampling of the different instruments and can also be used to account for biases and drifts between instruments. These problems have been noted in recent international assessments as being a primary source of uncertainty that clouds the significance of derived trends. Results show potential "recovery" trends of ∼2-3 % decade-1 in the upper stratosphere at midlatitudes, which are similar to other studies, and also how sampling biases present in these data sets can create differences in derived recovery trends of up to ∼1 % decade-1 if not properly accounted for. Limitations inherent to all techniques (e.g., relative instrument drifts) and their impacts (e.g., trend differences up to ∼2 % decade-1) are also described and a potential path forward towards resolution is presented.

Modified Multichannel Reconstruction Method of SAR With Highly Nonuniform Spatial Sampling

The traditional filter bank algorithm (FBA) for a multichannel synthetic aperture radar (SAR) system can provide an unambiguous recovery. However, the FBA may result in a seriously signal-to-noise ratio (SNR) loss or might even fail to reconstruct the spectrum if there is highly nonuniform sampling in azimuth. It is the general case because pulse repetition frequency (PRF) cannot be selected flexibly for spaceborne imaging system. In this paper, a new algorithm for processing highly nonuniform sampled SAR data to improve the SNR is presented. The proposed method is based on the operation of ambiguity-index screening (AIS) and the minimum mean square error (MMSE) criterion. It can be utilized to reconstruct the spectrum even in the presence of highly nonuniform sampling or coinciding sampling. The approach can significantly improve the SNR especially for the highly nonuniform sampling, and the azimuth ambiguity-to-signal ratio obtained by the proposed method is superior to the traditional one for a wide range of PRF. The proposed algorithm is validated by the simulated data and the real two-channel radar raw data acquired by C-band airborne SAR system with a bandwidth of 210 MHz, which is designed by the Department of Space Microwave Remote Sensing System, Institute of Electronics, Chinese Academy of Sciences.

Wideband Microwave Camera for Real-Time 3-D Imaging

This paper presents a microwave camera design operating in the 20–30 GHz frequency range and capable of producing 3-D images at video frame rate (i.e., real-time), using synthetic aperture radar (SAR) technique. This microwave camera has the potential to provide real-time inspection and diagnosis capabilities in the nondestructive testing, biomedical and security applications, to name a few. The camera utilizes an array composed of a novel array element with built-in dual receivers at its radiating end. The dual receiver design has two significant features particularly important for SAR imaging, namely, it provides for nonuniform spatial sampling, and allows the use of antennas whose sizes are greater than half of the operating wavelength. The camera operates in the monostatic mode where each antenna in the array is used as the transmitting and receiving antenna. A major advantage of this real-time camera design is the simplicity of the microwave circuitry, which reduces the overall size, power consumption, and, cost and renders it portable. The detail design of this wideband microwave 3-D real-time camera is provided along with several images of diverse and complex targets to demonstrate its capabilities and functionality.

Sparse source localization using perturbed arrays via bi-affine modeling

Non-uniform spatial sampling geometries, such as nested and coprime arrays, are provably capable of localizing O(M2) sources using only M sensors. However, such guarantees require the physical locations of the sensors to satisfy certain constraints, as dictated by the corresponding array geometries. In this paper, we consider the scenario when these constraints may be violated, leading to unknown perturbations on the locations of sensors. Such perturbations can have detrimental effect on the performance of virtual array based direction-of-arrival (DOA) estimation algorithms, since the perturbed virtual array will no longer be a uniform linear array (ULA). We propose a novel self-calibration approach for underdetermined DOA estimation with such arrays, that makes extensive use of the redundancies (or repeated elements) in the virtual array. Assuming small perturbations, and a sparse grid-based model for the DOAs, we extract a novel “bi-affine” model (affine in the perturbation variable, and linear in the source powers) from the covariance matrix of the received signals. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers, from which the DOAs can be exactly recovered under suitable conditions. This reduction is derived for both ULA and a newly-introduced robust version of coprime arrays, when the covariance matrix of the received signals is exactly known. Our approach is compared and contrasted with recently developed algorithms for blind gain and phase calibration (BGPC), whose signal model is fundamentally different from ours. We also provide an iterative algorithm to jointly solve for the DOAs and perturbation values when we can only estimate the covariance matrix using a finite number of snapshots.

Reevaluation of stratospheric ozone trends from SAGE II data using a simultaneous temporal and spatial analysis

Abstract. This paper details a new method of regression for sparsely sampled data sets for use with time-series analysis, in particular the Stratospheric Aerosol and Gas Experiment (SAGE) II ozone data set. Non-uniform spatial, temporal, and diurnal sampling present in the data set result in biased values for the long-term trend if not accounted for. This new method is performed close to the native resolution of measurements and is a simultaneous temporal and spatial analysis that accounts for potential diurnal ozone variation. Results show biases, introduced by the way data are prepared for use with traditional methods, can be as high as 10%. Derived long-term changes show declines in ozone similar to other studies but very different trends in the presumed recovery period, with differences up to 2% per decade. The regression model allows for a variable turnaround time and reveals a hemispheric asymmetry in derived trends in the middle to upper stratosphere. Similar methodology is also applied to SAGE II aerosol optical depth data to create a new volcanic proxy that covers the SAGE II mission period. Ultimately this technique may be extensible towards the inclusion of multiple data sets without the need for homogenization.

Out-of-Band Ambiguity Analysis of Nonuniformly Sampled SAR Signals

High-resolution and wide-swath synthetic aperture radar (SAR) images can be obtained by multichannel sampling. However, a nonoptimum pulse-repetition frequency is associated with a nonuniform spatial sampling in azimuth. A spectrum reconstruction algorithm and a filter group algorithm can be used to reconstruct the spectrum in azimuth with a nonuniform sampling. In this letter, a comparison of spectrum reconstruction algorithm and filter group algorithm is given. Through a transformation matrix, the relationship between out-of-band signals and the out-of-band signals after reconstruction is built. Furthermore, an equivalent spectrum after reconstruction is obtained, and simulation results proved that it is precise. From the equivalent spectrum, it shows that multichannel SAR can be seen as uniform sampling system but with a different original signal. Finally, channel imbalance is discussed. Simulation results have proved that the imbalance targets have the same location with corresponding ambiguous targets.

Optimum Signal Processing for Multichannel SAR: With Application to High-Resolution Wide-Swath Imaging

A new method for processing multichannel synthetic aperture radar (SAR) data to achieve desirable image characteristics is presented. The method is optimal because it is derived by minimizing a mean-square-error cost function and generalizes current methods for high-resolution wide-swath SAR signal processing. The proposed method is easily implementable, can support a wide range in the pulse repetition frequency (PRF), including cases with highly nonuniform spatial sampling, and is robust against PRFs where current projection techniques fail, cases where the PRF is ideally suited to clutter suppression. Point spread functions for the proposed algorithms are presented, and the theory and simulations are further corroborated by results using multichannel SAR data measured by RADARSAT-2. We demonstrate that, if RADARSAT-2 were able to illuminate a 250-km swath (300 km ground range), then, conceptually, the new method would be able to process the highly nonuniformly sampled data to provide an extremely wide mode at approximately 5-m azimuth resolution.

Optimum 2-D Nonuniform Spatial Sampling for Microwave SAR-Based NDE Imaging Systems

Microwave and millimeter-wave synthetic aperture radar (SAR)-based imaging techniques, which are used for nondestructive evaluation (NDE), have shown tremendous usefulness for the inspection of a wide variety of complex composite materials and structures. An important practical issue associated with these imaging techniques is the required criteria associated with the physical gathering of the imaging data. In previous work on uniform sampling optimization, it was shown that the (uniform) spatial sampling density should be higher than the Nyquist density if preservation of spatial resolution, as defined by the half-power width of an ideal point target, is of interest. Conversely, nonuniform sampling has shown to provide effective signal reconstruction even for average spatial sampling densities below the Nyquist density-a distinct advantage over uniform sampling. This paper presents a comprehensive study into the optimization of nonuniform sampling for microwave SAR-based NDE imaging using three typical reconstruction techniques for nonuniformly sampled data, including natural interpolation, area-weighted Fourier integration, and conjugate gradient residual error minimization methods. To study the efficacy of these reconstruction methods, simulations of a point target were performed for a range of target distances and a range of average spatial sample separations. Resulting SAR images from the reconstruction techniques are then analyzed and compared according to two metrics: error between an image and an ideal image and resolution as determined by the half-power width of a point target. This is followed by experimental results corroborating the simulation results. Finally, nonuniform sampling requirements, given a minimum metric performance, are generalized for a given imager aperture size.

Imaging the shallow crust with teleseismic receiver functions

SUMMARY Teleseismic receiver functions (RFs) represent an estimate of the site-response to incoming seismic energy. This technique has long been a staple of the global earthquake community, as RFs are sensitive to impedance contrasts associated with major discontinuities in the crust and upper mantle. However, there is substantial debate in the community concerning the lateral and vertical resolution limits possible using these methods due to limitations resulting from ambient noise and non-uniform spatial sampling of finite-frequency wave kernels. Here, we take advantage of data from the LaBarge Passive Seismic Experiment to examine these questions in more detail. We find (1) that RFs can provide a robust image of the near-surface (<5 km) structure; (2) that vertical resolution may exceed 500 m and (3) that our results compare favourably to nearby wells. These results indicate that RF analysis can provide high-resolution images of the shallow crust, which has potential value for hydrocarbon exploration.