Spatial Sampling Scheme Research Articles

Far-field directivity estimation with a cube-shaped array of 256 MEMS microphones

The far-field directivity function (FFDF) of a sound source characterises the angular dependence of the acoustic fields far away from this source. This function can be estimated by performing a spherical wave expansion (SWE) of the sound field from pressure measurements distributed around the source. The truncation order of the SWE is a critical parameter that depends on the number of measurement points and on the spatial sampling scheme used for the measurements. Unfortunately, for irregular sampling schemes, no theoretical result allows to determine a truncation order. In this work, a surrounding cuboid microphone array composed of 256 MEMS microphones is deployed. A cross-validation framework is used in order to determine an optimal truncation order for the SWE of the field radiated by a test source. The quality of the reconstructed field is assessed on the frequency range 100-5000 Hz. Finally, the estimated SWEs and far-field directivities are compared to an analytical model of the test source.

Using VHR satellite imagery, OBIA and landscape metrics to improve mosquito surveillance in urban areas

Surveillance is critical to efficiently control and prevent mosquito-borne diseases such as Dengue. Surveillance relies on sampling the target region for arthropod vectors over time. However, in most cases the sampling framework is ad hoc and relies only on expert opinion. We sought to improve the efficiency of mosquito surveillance in Córdoba (Argentina) by designing a spatial sampling scheme within complex urban areas that would optimize ovitrap collections. We classified a very high resolution (VHR) satellite image following an object based (OBIA) approach and estimated several landscape metrics over which we applied a k-means clustering. The objective was to identify an optimal distribution for the ovitrap network characterizing the urban coverage of the city at three types of territorial units: neighbourhoods, census tracts and Thiessen polygons around health care facilities. We distributed 150 ovitraps throughout the city based on the identified environmental groups and compared results with the current strategy used by the Ministry of Health. Stratified ovitrap distributions for census tracts or Thiessen polygons performed best compared to the current strategy in terms of environmental variability covered, i.e., relevant environmental groups are either subsampled or oversampled in the current distribution. Because of the general availability of these environmental data sets and algorithms, the approach could be applied in most urban areas where vector borne disease control is challenging.

An Insight into the Warping Spatial Sampling Method in Subsurface Radar Imaging and Its Experimental Validation

In this paper, we are concerned with microwave subsurface imaging achieved by inverting the linearized scattering operator arising from the Born approximation. In particular, we consider the important question of reducing the required data to achieve imaging. This can help to reduce the radar system’s cost and complexity and mitigate the imaging algorithm’s computational burden and the needed storage resources. To cope with these issues, in the framework of a multi-monostatic/multi-frequency configuration, we introduce a new spatial sampling scheme, named the warping method, that allows for a significant reduction in spatial measurements compared to other literature approaches. The basic idea is to introduce some variable transformations that “warp” the measurement space so that the reconstruction point-spread function obtained by adjoint inversion is recast as a Fourier-like transformation, which provides insights into how to achieve the sampling. In our previous contributions, we focused on presenting and checking the theoretical background with simple numerical examples. In this contribution, we briefly review the key components of the warping method and present its experimental validation by considering a realistic subsurface scattering scenario for the case of a buried water pipe. Essentially, we show that the latter succeeds in reducing the number of data compared to other approaches in the literature, without significantly affecting the reconstruction results.

Inverse Models for Estimating the Initial Condition of Spatio-Temporal Advection-Diffusion Processes

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This article investigates an important class of inverse problems—the estimation of the initial condition of a spatio-temporal advection-diffusion process using spatially sparse data streams. Three spatial sampling schemes are considered, including irregular, nonuniform and shifted uniform sampling. The irregular sampling scheme is the general scenario, while computationally efficient solutions are available in the spectral domain for nonuniform and shifted uniform sampling. For each sampling scheme, the inverse problem is formulated as a regularized convex optimization problem that minimizes the distance between forward model outputs and observations. The optimization problem is solved by the Alternating Direction Method of Multipliers algorithm, which also handles the situation when a linear inequality constraint (e.g., non-negativity) is imposed on the model output. Numerical examples are presented, code is made available on GitHub, and discussions are provided to generate some useful insights of the proposed inverse modeling approaches.

A Novel Spatial Sampling Scheme for DOA Estimation With Movable Arbitrary Sparse Arrays

Sparse arrays have been an important concept in the study of direction of arrival (DOA) estimation since they can obtain the number of degrees of freedom (DOFs) is much larger than that of the number of physical sensors. However, the missing lags in the difference co-array reduce the DOF that is expected. Recently, array motion has received considerable attention, since this operation can fill the missing lags, increase the DOF, and enlarge the array aperture without adding extra physical sensors. In this study, we investigate the DOA estimation of array mounted on a moving platform and propose the condition and corresponding spatial sampling scheme that can result in a complete consecutive difference co-array. Specifically, we first explore the general expression of the synthetic array, which is generated by collecting the sampling data of a moving array at different times. After that, the closed-form expression for the difference co-array corresponding to the synthetic array is derived. Thirdly, we introduce the condition that must be satisfied to generate a hole-free difference co-array for movable arbitrary arrays. Then, based on this condition, we develop a non-uniform sampling method that can fill all the missing lags and lead to a fully consecutive difference co-array regardless of the physical geometry, which can therefore improve uniform DOFs (uDOFs). Finally, several classical arrays, including uniform linear array, coprime array, nested array, etc., are adopted to apply the proposed sampling scheme, and the closed-form expressions of the resulting uDOFs are analyzed in detail. Numerical simulations are presented to illustrate the effectiveness and superiority of the proposed sampling scheme in DOA estimation performance.

Spatial Sampling in Monostatic Radar Imaging

This letter deals with microwave imaging via a migration-like inversion method. The aim is the determination of a spatial sampling scheme which allows to collect as low as possible spatial measurements and to preserve the point-spread function features and hence, the achievable performance in the reconstructions. To keep math simple and to more easily illustrate the theoretical arguments, the study is developed for a 2-D monostatic scalar configuration and a homogeneous background medium. It is shown that the new sampling scheme requires much fewer samples than the standard literature results and that the samples must be nonuniformly deployed across the measurement domain.

The Effect of Spatial Resolution and Temporal Sampling Schemes on the Measurement Error for a Moon-Based Earth Radiation Observatory

The Moon-Based Earth Radiation Observatory (MERO) is a new platform, which is expected to advance current Earth radiation budget (ERB) research with better observations. For the instrument design of a MERO system, ascertaining the spatial resolution and sampling scheme is important. However, current knowledge about this is still limited. Here we proposed a simulation method for the MERO-measured Earth top of atmosphere (TOA) outgoing shortwave radiation (OSR) and outgoing longwave radiation (OLR) fluxes and constructed the “true” Earth TOA OSR and OLR fluxes based on the Clouds and Earth’s Radiant Energy System (CERES) data. Then we used them to reveal the effects of spatial resolution and temporal scheme (sampling interval and the temporal sampling sequence) on the measurement error of a MERO. Our results indicate that the spatial sampling error in the unit of percentage reduces linearly as the spatial resolution varies from 1000 km to 100 km; the rate is 2.5%/100 km for the Earth TOA OSR flux, which is higher than that (1%/100 km) of the TOA OLR flux. Besides, this rate becomes larger when the spatial resolution is finer than 40 km. It is also demonstrated that a sampling temporal sequence of starting time of 64 min with a sampling interval of 90 min is the optimal sampling scheme that results in the least temporal sampling error for the MERO system with a 40 km spatial resolution, note that this conclusion depends on the temporal resolution and quality of the data used to construct the “true” Earth TOA OSR and OLR fluxes. The proposed method and derived results in this study could facilitate the ascertainment of the optimal spatial resolution and sampling scheme of a MERO system under certain manufacturing budget and measurement error limit.

Comparative evaluation of interpolation methods for the directivity of musical instruments

Measurements of the directivity of acoustic sound sources must be interpolated in almost all cases, either for spatial upsampling to higher resolution representations of the data, for spatial resampling to another sampling grid, or for use in simulations of sound propagation. The performance of different interpolation techniques applied to sparsely sampled directivity measurements depends on the sampling grid used but also on the radiation pattern of the sources themselves. Therefore, we evaluated three established approaches for interpolation from a low-resolution sampling grid using high-resolution measurements of a representative sample of musical instruments as a reference. The smallest global error on average occurs for thin plate pseudo-spline interpolation. For interpolation based on spherical harmonics (SH) decomposition, the SH order and the spatial sampling scheme applied have a strong and difficult to predict influence on the quality of the interpolation. The piece-wise linear, spherical triangular interpolation provides almost as good results as the first-order spline approach, albeit with on average 20 times higher computational effort. Therefore, for spatial interpolation of sparsely sampled directivity measurements of musical instruments, the thin plate pseudo-spline method applied to absolute-valued data is recommended and, if necessary, a subsequent modeling of the phase.

Automatic fish measurement using a camera and a 3D sensor applied to a long-term experiment

Abstract The fish monitoring effort has been increasing over the past years, due to conservation and management requests demanding more accurate data and consequently raising costs. This is an important challenge especially for remote and disperse locations where fish sampling poses unbearable costs, leading to limited spatial sampling schemes, limited data on rare and occasional landed species, and erroneous and biased observations. In this article, we propose a new autonomous system that can be installed on monitoring spots or on board fishing vessels, which is able to remotely acquire all the landed or captured fish and measure it automatically without any physical interaction. The system uses (i) a camera and a 3D sensor to obtain a complete XYZ reading of the fish and (ii) a convolutional neural network, trained for a representative set of species to detect and measure the individuals visible in a box. The system was validated in real conditions, using continuous observations of the landed fish in three islands of the Azores Archipelago, for 2 years. The aim of this article is to provide an overview of the measuring system and an analysis of the sampled data, by comparing the results of the proposed method with the traditional sampling methodology for a given period.

When, Who, and How to Sample: Designing Practical Surveillance for 7 Neglected Tropical Diseases as We Approach Elimination.

As neglected tropical disease programs look to consolidate the successes of moving towards elimination, we need to understand the dynamics of transmission at low prevalence to inform surveillance strategies for detecting elimination and resurgence. In this special collection, modelling insights are used to highlight drivers of local elimination, evaluate strategies for detecting resurgence, and show the importance of rational spatial sampling schemes for several neglected tropical diseases (specifically schistosomiasis, soil-transmitted helminths, lymphatic filariasis, trachoma, onchocerciasis, visceral leishmaniasis, and gambiense sleeping sickness).

Spectrum Cartography via Coupled Block-Term Tensor Decomposition

Spectrum cartography aims at estimating power propagation patterns over a geographical region across multiple frequency bands (i.e., a radio map)---from limited samples taken sparsely over the region. Classic cartography methods are mostly concerned with recovering the aggregate radio frequency (RF) information while ignoring the constituents of the radio map---but fine-grained emitter-level RF information is of great interest. In addition, many existing cartography methods work explicitly or implicitly assume random spatial sampling schemes that may be difficult to implement, due to legal/privacy/security issues. The theoretical aspects (e.g., identifiability of the radio map) of many existing methods are also unclear. In this work, we propose a joint radio map recovery and disaggregation method that is based on coupled block-term tensor decomposition. Our method guarantees identifiability of the individual radio map of \textit{each emitter} (thereby that of the aggregate radio map as well), under realistic conditions. The identifiability result holds under a large variety of geographical sampling patterns, including a number of pragmatic systematic sampling strategies. We also propose effective optimization algorithms to carry out the formulated radio map disaggregation problems. Extensive simulations are employed to showcase the effectiveness of the proposed approach.

Effects of mitigation of pixel cross-talk in the encoding of complex fields using the double-phase method

We report on unwanted effects of pixel cross-talk and its mitigation on the experimental realization of the double-phase method with phase-only spatial light modulators. We experimentally demonstrate that a generalized sampling scheme can reduce nonuniform phase modulation due to the pixel cross-talk phenomenon and, consequently, improve the quality of amplitude and phase images obtained with this encoding method. To corroborate our proposal, several experiments to reconstruct amplitude-only as well as fully independent amplitude and phase patterns under different spatial sampling schemes were carried out. We also show how a convenient implementation of the well-known polarization-based phase-shifting technique can be employed to measure the encoded complex field using only a conventional CMOS camera.

Signal-Level Models of Pointwise Electromagnetic Exposure for Millimeter Wave Communication

Electromagnetic exposure from wireless devices is strictly regulated around the world to ensure the safety of consumers. Recent studies have demonstrated that multi-antenna systems can leverage signal-level exposure models to jointly mitigate user radiation absorption and achieve high data rates. This is especially important for millimeter wave technologies, which are susceptible to power back-off techniques due to high propagation and blockage losses. However, prior models require significant overhead in the form of exposure measurements to compute model parameters and cannot be easily modified to predict electromagnetic absorption in different testing configurations. This article proposes methods to approximate the characteristic matrix of a quadratic model for two exposure measures in the millimeter wave band: incident power density and surface specific absorption rate (SAR). The presented models can be calculated with a small number of parameters and can be altered to account for mutual coupling, near-field effects, and changes in the exposure scenario. Spatial sampling schemes based on these models are derived to determine how many testing points are necessary to estimate exposure in a region within a specified margin of error. Software simulation results with half-wave dipoles validate the accuracy of the proposed models in a millimeter wave scenario.

Automated survey design for blended acquisition with irregular spatial sampling via the integration of a metaheuristic and deep learning

Blended acquisition along with efficient detector and source geometries allows for a cost-effective operation. The outcome of subsequent deblending and data reconstruction is of primary importance in determining the technical success of this manner of data acquisition. Despite its advantages over conventional seismic surveys, finding optimum survey parameters is a difficult task. Although incorporating irregularity into spatial sampling and blending schemes leads to effective deblending and data reconstruction, it inherently provides a significantly large problem space. We have developed a survey-design workflow to provide acquisition parameters that account for the source blending as well as the spatial sampling of detectors and sources in an automated manner. Our method involves an iterative scheme to derive the survey parameters that lead to optimum deblending and data reconstruction quality. The approach deals jointly with deblending and data-reconstruction via a sparse inversion in the frequency-wavenumber domain coupled with constraints based on causality and coherency. The residue from this process is subsequently used to update the survey parameters by integrating a genetic algorithm and a convolutional neural network (CNN). Bioinspired operators enable the simultaneous update of the blending and sampling operators. To relate the choice of survey parameters to the performance of deblending and data reconstruction, we have used a CNN. The applied network architecture successfully rejects suboptimal solutions among newly generated ones from genetic operators. Consequently, only optimal ones are fed into the subsequent step, making our approach computationally affordable. We apply our workflow to design a seismic survey that incorporates the dispersed source array concept. A comparison among different survey-design strategies highlights the ability of the method to effectively derive optimum solutions. The resultant acquisition scenario derived from our approach yields a notable enhancement of deblending and data reconstruction quality attributed solely to the choice of survey parameters.

Geographical Information Science (GIS), spatial sampling and sediment variability examined using a case of manslaughter

Abstract The body of a missing person was found adjacent to a 3 km long sand-covered forest track in an upland area of Northern Ireland (UK). Geological trace evidence in the form of sand was found in the passenger footwell and on the foot pedals of a vehicle belonging to the last known associates of the deceased. A Geographical Information Science (GIS) methodology was used to integrate regional geological and soil databases to confirm the provenance of the sand and to find geographical locations for control (or alibi) samples. To complement the forensic examination in the case, 77 samples were taken at the scene in order to test whether such a collection assists knowledge of the scene, or whether fewer, targeted samples at access points to the body would have sufficed. The results demonstrate the potential applications of a GIS approach and show the usefulness of employing a spatial sampling scheme to understand the degree of local variability between samples. The findings from this study demonstrated that fewer samples would have been sufficient to associate the questioned items with the scene, yet would not have demonstrated how other areas of the track could be progressively excluded from comparison.

UAV-Enabled Spatial Data Sampling in Large-Scale IoT Systems Using Denoising Autoencoder Neural Network

Internet of Things (IoT) technology has been pervasively applied to environmental monitoring, due to the advantages of low cost and flexible deployment of IoT enabled systems. In many large-scale IoT systems, accurate and efficient data sampling and reconstruction is among the most critical requirements, since this can relieve the data rate of trunk link for data uploading while ensure data accuracy. To address the related challenges, we have proposed an unmanned aerial vehicle (UAV) enabled spatial data sampling scheme in this paper using denoising autoencoder (DAE) neural network. More specifically, a UAV-enabled edge-cloud collaborative IoT system architecture is first developed for data processing in large-scale IoT monitoring systems, where UAV is utilized as mobile edge computing device. Based on this system architecture, the UAV-enabled spatial data sampling scheme is further proposed, where the wireless sensor nodes of large-scale IoT systems are clustered by a newly developed bounded-size $\boldsymbol K$ -means clustering algorithm. A neural network model, i.e., DAE, is applied to each cluster for data sampling and reconstruction, by exploitation of both linear and nonlinear spatial correlation among data samples. Simulations have been conducted and the results indicate that the proposed scheme has improved data reconstruction accuracy under the sampling ratio without introducing extra complexity, as compared to the compressive sensing-based method.

Evaluating ecosystem effects of climate change on tropical island streams using high spatial and temporal resolution sampling regimes.

Climate change is expected to alter precipitation patterns worldwide, which will affect streamflow in riverine ecosystems. It is vital to understand the impacts of projected flow variations, especially in tropical regions where the effects of climate change are expected to be one of the earliest to emerge. Space-for-time substitutions have been successful at predicting effects of climate change in terrestrial systems by using a spatial gradient to mimic the projected temporal change. However, concerns have been raised that the spatial variability in these models might not reflect the temporal variability. We utilized a well-constrained rainfall gradient on Hawaii Island to determine (a) how predicted decreases in flow and increases in flow variability affect stream food resources and consumers and (b) if using a high temporal (monthly, four streams) or a high spatial (annual, eight streams) resolution sampling scheme would alter the results of a space-for-time substitution. Declines in benthic and suspended resource quantity (10- to 40-fold) and quality (shift from macrophyte to leaf litter dominated) contributed to 35-fold decreases in macroinvertebrate biomass with predicted changes in the magnitude and variability in the flow. Invertebrate composition switched from caddisflies and damselflies to taxa with faster turnover rates (mosquitoes, copepods). Changes in resource and consumer composition patterns were stronger with high temporal resolution sampling. However, trends and ranges of results did not differ between the two sampling regimes, indicating that a suitable, well-constrained spatial gradient is an appropriate tool for examining temporal change. Our study is the first to investigate resource to community wide effects of climate change on tropical streams on a spatial and temporal scale. We determined that predicted flow alterations would decrease stream resource and consumer quantity and quality, which can alter stream function, as well as biomass and habitat for freshwater, marine, and terrestrial consumers dependent on these resources.

Super-Bandwidth Two-Step Phase-Shifting Off-Axis Digital Holography by Optimizing Two-Dimensional Spatial Frequency Sampling Scheme

The presence of the auto correlation and twin cross correlation noises restrict the available spatial bandwidth of the holographic microscopy to much less than the available bandwidth of the digital sensor. Therefore, in order to record the same image area as conventional 2D intensity imaging techniques, several images should be taken. We present two-step phase-shifting off-axis digital holography with maximum space-bandwidth product for three-dimensional (3D) digital holography. Removing the autocorrelation term using a two-step phase-shifting technique significantly increases the available bandwidth for off-axis interferometry. An optimizing super-diagonal two-dimensional (2D) spatial frequency sampling scheme at the sub-Nyquist frequency is employed for performing off-axis interferometry in the absence of the autocorrelation term. The spatial bandwidth of the proposed two-step phase-shifting technique is 400% of that in square scheme off-axis digital holography. Experimental results demonstrate the feasibility of this technique in extracting the 3D morphology of transparent microscopic objects with a larger bandwidth.

Sampling Design of Synthetic Volume Arrays for Three-Dimensional Microwave Imaging

In this paper, sampling design of three-dimensional (3-D) synthetic array (i.e., synthetic volume array) for microwave imaging is considered. Generally, the spatial sampling criteria for one- or two-dimensional arrays can be determined based on some narrowband/ultrawideband array theories. However, for 3-D arrays, where antennas are located in a volume instead of over a surface, these existing array theories are no longer straightforwardly applicable. To address the spatial sampling problem of 3-D arrays, we formulate it as a sensor/observation selection problem in this paper. Although some selection approaches exist and are conveniently applicable to small-scale problems, they are either less efficient or provide less optimal results for selection problems with data dimensions of hundreds or even thousands which is typical for microwave imaging. To get the (near-) optimal spatial sampling scheme for 3-D arrays, a greedy algorithm named clustered maximal projection on minimal eigenspace (CMPME) is proposed to select the most informative sampling positions based on some optimality criteria. This algorithm attempts to select the fewest sampling positions by considering an error threshold for the estimated images. Moreover, it has higher computational efficiency compared to the existing approaches. Finally, its effectiveness and selection performances are demonstrated through some imaging examples.

Toward measuring biogeochemistry within the stream‐groundwater interface at the network scale: An initial assessment of two spatial sampling strategies

AbstractIt is important to understand how point measurements across spatially heterogeneous ecosystems are scaled to represent these systems. Stream biogeochemistry presents an illustrative example because water quality concerns within stream networks and recipient water bodies motivate heterogeneous watershed studies. Measurements of the stream water‐groundwater (SW‐GW) interface (i.e., the shallow stream subsurface) are well‐documented for point‐scale sampling density measurements (i.e., cm2–m2 features), but poorly characterized for network‐scale sampling density measurements (i.e., km2; stream reaches and networks). Sampling the SW‐GW interface is more time and labor intensive than surface water sampling, meaning sample point selection must be made with care for network‐scale analyses. In this study, we endeavor to determine which of two common spatial sampling schemes is appropriate for characterizing SW‐GW interface biogeochemistry across a third‐order stream network, focusing on dissolved organic carbon. The first scheme, called Local Sampling, focuses on characterizing small‐scale (< 10 m2) variability produced by the local physical and biogeochemical heterogeneity, with fewer points across the stream network. The second scheme, called Longitudinal Sampling, has approximately the same number of measurements distributed over many more points across the stream network with less local variability characterization. This comparison reveals that selection of a Local Sampling versus a Longitudinal Sampling scheme influences the biogeochemical pattern interpretation at the stream network scale. Additionally, this study found that increasing observation efforts at the local scale added limited information for reach‐ to network‐scale biogeochemical patterns, suggesting that emphasis should be placed on characterizing variability across broader spatial scales with the Longitudinal Sampling approach.