Optimal Sampling Strategy Research Articles

Optimal sampling strategy for probability estimation: An application to the Agricultural Quarantine Inspection Monitoring program.

Imported agricultural pests can cause substantial damage to agriculture, food security, and ecosystems. In the United States, the Agricultural Quarantine Inspection Monitoring (AQIM) program conducts random sampling to estimate the probabilities that cargo and passengers arriving at ports of entry carry pests. Assessing these risks accurately is critical to enable effective policies and operational procedures. This study introduces a pathway-level analysis with an objective function aligned with AQIM's goal, offering a new perspective compared to the current container-by-container approach, which relies on heuristics to set inspection rates. We formulate an optimization model that minimizes the mean squared error of the probability estimates that AQIM obtains. The central decision-making tradeoff that the model explores is whether it is preferable to sample more arriving containers (and fewer boxes per container) or more boxes per container (and fewer containers), given limited resources. We first derive an analytical solution for the optimal sampling strategy by leveraging several approximations. Then, we apply our model to a numerical case study of maritime cargo sampling at the Port of Long Beach. Across a wide range of parameter settings, the optimal strategy samples more containers (but fewer boxes per container) than the current AQIM protocol. The difference between the two strategies and the accuracy improvement with the optimal approach are larger if the pest statuses of boxes in the same container are more strongly correlated. We recommend that AQIM record box-level (beyond only container-level) inspection data, which could be used to estimate this correlation and other modelparameters.

Quantification of contaminant mass discharge and uncertainties: Method and challenges in application at contaminated sites

Contaminant mass discharge (CMD) estimation involves combining multilevel concentration and flow measurements to quantify the contaminant mass passing through a control plane downgradient of a point source. However, geological heterogeneities and limited data introduce uncertainties that complicate CMD estimation and risk assessment. Although CMD is increasingly used in groundwater management, methods for quantifying and handling these uncertainties are still needed. This study develops and tests a CMD estimation method based on Bayesian geostatistics to quantify CMD uncertainties using data from a control plane perpendicular to the contaminant plume.By combining geostatistical conditional simulations of the spatial concentration distribution with the flow, an ensemble of CMD realizations is generated, from which a cumulative distribution function is derived. A key element of this approach is the use of a macrodispersive transport model to simulate the spatial concentration trend. This ensures that the estimated concentration reflects the expected physical behavior of the contaminant plume while also allowing the integration of site-specific conceptual information.The method is applicable to plumes with dissolved contaminants, such as chlorinated solvents, petroleum hydrocarbons, Per- and polyfluoroalkyl substances (PFAS) and pesticides. Site-specific conceptual understanding is used to inform the prior probability density functions of the structural model parameters and to define acceptable simulated concentration limits. We applied the method at three sites contaminated with chlorinated ethenes, demonstrating its robustness across varying information levels and data availability.Our results shows that strong site-specific conceptual knowledge and high sampling density constrain the CMD uncertainty (CV = 21 %) and results in estimated model parameters and a spatial concentration distribution that agrees well with the conceptual model. For a site with less data and limited conceptual knowledge, CMD and concentration distribution estimates are still feasible, though with higher uncertainty (CV = 41 %). Extending the method to account for multiple source zones and complex plume migration improved parameter identification and reduced the 95 % CMD confidence interval by 11 % ([4950–8750] to [5090–8480] g yr−1), while also providing a spatial concentration distribution in better agreement with the plume conceptualization.This study highlights the importance of integrating site-specific conceptual knowledge in CMD estimation, particularly for less-sampled sites. The method can furthermore assist in identifying remediation targets, evaluating remedial effectiveness, and optimizing sampling strategies.

Exploring optimal sampling strategy of testate amoebae as hydrological bioindicators in UK upland peatlands

Many modified or degraded blanket bogs in the UK have been undergoing restoration by different rewetting strategies. While testate amoebae (TA), well-known as hydrology-sensitive species, have been increasingly applied to assess and monitor peatland restoration success, we still do not know the most appropriate sampling strategy of TA in heather-dominated peatlands. In this study, TA communities were taken from two modified blanket bog sites and one intact border mire across a strong hydrological gradient to explore the optimal sampling strategy. The results showed that: 1) TA communities from Sphagnum moss performed better to indicate the hydrological gradient of peatland habitats than other plant types (i.e., other mosses, heather and sedge litter), among which the dominant and second abundant Sphagnum moss species had similar performance as combined all Sphagnum moss did; 2) there was a clear and marked vertical separation in TA community composition, living status and species-specific niche preference; and 3) TA species richness and density incrementally increased from March to next January although median species richness decreased from September to the following January; by contrast, the average number of encysted TA was much higher in June and January than in March and September, which highlights the capability of TA to form cysts in response to extreme hot/dry and cold weather and this change may also suggest a non-negligible influence on ecosystem processes (e.g., C-cycling). Considering sampling cost and practicality, this study in heather-dominated peatlands recommends sampling the entire segment/length of the dominant Sphagnum moss from relatively flat (lawn) positions (although more studies are needed for microtopographic investigation) during the autumn or early winter as a simple but effective sampling strategy to assess the potential of TA as hydrological bioindicators or when using them to monitor the restoration (rewetting) success.

Towards large-scale single-shot millimeter-wave imaging for low-cost security inspection

Millimeter-Wave (MMW) imaging is a promising technique for contactless security inspection. However, the high cost of requisite large-scale antenna arrays hinders its widespread application in high-throughput scenarios. Here, we report a large-scale single-shot MMW imaging framework, achieving low-cost high-fidelity security inspection. We first analyzed the statistical ranking of each array element through 1934 full-sampled MMW echoes. The highest-ranked elements are preferentially selected based on the ranking, building the experimentally optimal sparse sampling strategy that reduces antenna array cost by one order of magnitude. Additionally, we derived an untrained interpretable learning scheme, realizing robust and accurate MMW image reconstruction from sparsely sampled echoes. Last, we developed a neural network for automatic object detection, and experimentally demonstrated successful detection of concealed centimeter-sized targets using 10% sparse array, whereas all the other contemporary approaches failed at such a low sampling ratio. With the strong detection ability and order-of-magnitude cost reduction, we anticipate that this technique provides a practical way for large-scale single-shot MMW imaging.

Monitoring resilience in bursts

The possibility to anticipate critical transitions through detecting loss of resilience has attracted attention in many fields. Resilience indicators rely on the mathematical concept of critical slowing down, which means that a system recovers more slowly from external perturbations when it gets closer to tipping point. This decrease in recovery rate can be reflected in rising autocorrelation and variance in data. To test whether resilience is changing, resilience indicators are often calculated using a moving window in long, continuous time series of the system. However, for some systems, it may be more feasible to collect several high-resolution time series in short periods of time, i.e., in bursts. Resilience indicators can then be calculated to detect a change of resilience between such bursts. Here, we compare the performance of both methods using simulated data and showcase the possible use of bursts in a case study using mood data to anticipate depression in a patient. With the same number of data points, the burst approach outperformed the moving window method, suggesting that it is possible to downsample the continuous time series and still signal an upcoming transition. We suggest guidelines to design an optimal sampling strategy. Our results imply that using bursts of data instead of continuous time series may improve the capacity to detect changes in resilience. This method is promising for a variety of fields, such as human health, epidemiology, or ecology, where continuous monitoring can be costly or unfeasible.

Optimizing pseudo-spiral sampling for abdominal DCE MRI using a digital anthropomorphic phantom.

For reliable DCE MRI parameter estimation, k-space undersampling is essential to meet resolution, coverage, and signal-to-noise requirements. Pseudo-spiral (PS) sampling achieves this by sampling k-space on a Cartesian grid following a spiral trajectory. The goal was to optimize PS k-space sampling patterns for abdomin al DCE MRI. The optimal PS k-space sampling pattern was determined using an anthropomorphic digital phantom. Contrast agent inflow was simulated in the liver, spleen, pancreas, and pancreatic ductal adenocarcinoma (PDAC). A total of 704 variable sampling and reconstruction approaches were created using three algorithms using different parametrizations to control sampling density, halfscan and compressed sensing regularization. The sampling patterns were evaluated based on image quality scores and the accuracy and precision of the DCE pharmacokinetic parameters. The best and worst strategies were assessed in vivo in five healthy volunteers without contrast agent administration. The best strategy was tested in a DCE scan of a PDAC patient. The best PS reconstruction was found to be PS-diffuse based, with quadratic distribution of readouts on a spiral, without random shuffling, halfscan factor of 0.8, and total variation regularization of 0.05 in the spatial and temporal domains. The best scoring strategy showed sharper images with less prominent artifacts in healthy volunteers compared to the worst strategy. Our suggested DCE sampling strategy also showed high quality DCE images in the PDAC patient. Using an anthropomorphic digital phantom, we identified an optimal PS sampling strategy for abdominal DCE MRI, and demonstrated feasibility in a PDAC patient.

Sampling for Remote Estimation of the Wiener Process over an Unreliable Channel

In this paper, we study a sampling problem where a source takes samples from a Wiener process and transmits them through a wireless channel to a remote estimator. Due to channel fading, interference, and potential collisions, the packet transmissions are unreliable and could take random time durations. Our objective is to devise an optimal causal sampling policy that minimizes the long-term average mean square estimation error. This optimal sampling problem is a recursive optimal stopping problem, which is generally quite difficult to solve. However, we prove that the optimal sampling strategy is, in fact, a simple threshold policy where a new sample is taken whenever the instantaneous estimation error exceeds a threshold. This threshold remains a constant value that does not vary over time. By exploring the structure properties of the recursive optimal stopping problem, a low-complexity iterative algorithm is developed to compute the optimal threshold. This work generalizes previous research by incorporating both transmission errors and random transmission times into remote estimation. Numerical simulations are provided to compare our optimal policy with the zero-wait and age-optimal policies.

Fisher information for smart sampling in time-domain spectroscopy.

Time-domain spectroscopy encompasses a wide range of techniques, such as Fourier-transform infrared, pump-probe, Fourier-transform Raman, and two-dimensional electronic spectroscopies. These methods enable various applications, such as molecule characterization, excited state dynamics studies, or spectral classification. Typically, these techniques rarely use sampling schemes that exploit the prior knowledge scientists typically have before the actual experiment. Indeed, not all sampling coordinates carry the same amount of information, and a careful selection of the sampling points may notably affect the resulting performance. In this work, we rationalize, with examples, the various advantages of using an optimal sampling scheme tailored to the specific experimental characteristics and/or expected results. We show that using a sampling scheme optimizing the Fisher information minimizes the variance of the desired parameters. This can greatly improve, for example, spectral classifications and multidimensional spectroscopy. We demonstrate how smart sampling may reduce the acquisition time of an experiment by one to two orders of magnitude, while still providing a similar level of information.

Optimal sampling of spatial patterns improves deep learning-based early warning signals of critical transitions.

Complex spatio-temporal systems like lakes, forests and climate systems exhibit alternative stable states. In such systems, as the threshold value of the driver is crossed, the system may experience a sudden (discontinuous) transition or smooth (continuous) transition to an undesired steady state. Theories predict that changes in the structure of the underlying spatial patterns precede such transitions. While there has been a large body of research on identifying early warning signals of critical transitions, the problem of forecasting the type of transitions (sudden versus smooth) remains an open challenge. We address this gap by developing an advanced machine learning (ML) toolkit that serves as an early warning indicator of spatio-temporal critical transitions, Spatial Early Warning Signal Network (S-EWSNet). ML models typically resemble a black box and do not allow envisioning what the model learns in discerning the labels. Here, instead of naively relying upon the deep learning model, we let the deep neural network learn the latent features characteristic of transitions via an optimal sampling strategy (OSS) of spatial patterns. The S-EWSNet is trained on data from a stochastic cellular automata model deploying the OSS, providing an early warning indicator of transitions while detecting its type in simulated and empirical samples.

Observing And Characterizing Infragravity Waves Through Different Sampling Devices: A Case-Study Off The Belgian Coast

Infragravity waves are surface waves with relatively longer periods in comparison to periods of the spectrum-dominant gravity waves. They are characterized by oscillations between 20 and 300 seconds (0.0033 Hz < f < 0.05 Hz), amplitudes that range from a few millimeters to tens of centimeters, and wavelengths of kilometers (Munk, 1950; Holman and Bowen, 1982; Ardhuin et al., 2014). Their forcing is linked to, amongst others, nonlinear interaction between sea swell waves, varying wave heights causing the breaking point of the waves to vary with height, and height variation of incoming waves (Bertin et al., 2018). Infragravity waves play an important role in coastal dynamics (Svendsen, 2005) and have been reported to trigger nearshore hazards such as beach and dune erosion (de Vries et al. 2008; Roelvink et al., 2009), development of seiches in harbors (Melito et al., 2006; Cuomo and Guza, 2017), wave-driven coastal inundation (Gent, 2001; Stockdon et al., 2006), and ice shelves collapsing (Bromirski et al., 2010). Therefore, revealing infragravity wave characteristics is of utmost importance to understand their potential to generate hazards in a certain region, especially at sites strongly influenced by human occupation and activities. Their consideration in coastal safety planning can avoid damages, as several locations have already experienced in the past (Yamanaka et al., 2019). Implementing optimal sampling strategies for observing and characterizing infragravity waves might be challenging. By nature, these waves are hard to measure accurately due to their low amplitude. Their evolving characteristics in an environment marked by pronounced bathymetric features, such as the sand bank systems off the Belgian coast, add a degree of complexity that requires testing of different approaches, and at different sites. Within this context, this work first revisits observational approaches, instrumentation, logistics, and sampling techniques that have been used to study this phenomenon on the Belgian Coast. The advantages, challenges and limitations of different approaches are discussed, and best practices for collecting high-quality data in the field are addressed. To do so, this study explores multi-sensor in situ deployments conducted at four selected sites off the Belgian coast (Figure 1) (Nieuwpoort, Raversijde (inshore and offshore Stroombank), and Trapegeer) within the context of the “Influence of infragravity sea waves during storms on the hydro- and morphodynamic processes along hybrid soft-hard coastal defence structures with a shallow foreshore” project, an FWO-funded initiative being conducted in collaboration between UGent, VLIZ, and KULeuven and with support of Agency for Coastal and Maritime Services (AMDK). More specifically, field observations were conducted using multipurpose mooring frames equipped both with (i) Acoustic Doppler Current Profiles (ADCPs) to sample pressure (0.1% FS), current, and sea surface elevation through acoustic surface tracking and (ii) high-accuracy quartz pressure sensors (accuracy 0.01 % FS). Both ADCPs and pressure sensors were set to measure continuously at 4 Hz being, therefore, able to capture both infra- and gravity waves. Furthermore, the moorings were collocated with standard wave buoys from AMDK. Data was collected continuously for about 3 months, covering storm and calm wave conditions. Finally, the measurements from ADCPs (pressure and acoustic) and pressure sensors were compared and used to derive the infragravity wave characteristics, as well as cross-validated against wave buoy data.

Combined discrete Fourier transform method for azimuthal acoustic mode analysis

Modal analysis is an effective and prevalent method for analysing and diagnosing oscillatory systems. In this study, a combined discrete Fourier transform (cDFT) method was developed in addition to the discrete Fourier transform (DFT) method and solving equation (SE) method for azimuthal acoustic mode analysis to utilize the advantages of both methods. cDFT transforms the original sampling matrix equation into a sparse matrix equation by using the aliasing property of the DFT and obtains the modal spectrum results by solving the sparse matrix equation. In this study, the relative accuracy and computational complexity of modal analysis are further demonstrated. The cDFT method improves the calculation speed by grouping the DFT and solving the sparse matrix while simultaneously influencing the relative accuracy of the analysis results by changing the condition number of the sampling matrix. Applications of the cDFT method in terms of robustness to sensor failure and constrained sampling scheme optimisation are also presented. The cDFT method broadens the sampling limitations of DFT and enhances the sampling flexibility and robustness to sensor failure. Further, it can be used to determine the optimal sampling and analysis scheme according to the actual constraints, accuracy, and speed requirements, as well as the expectations of the future state of the measurement system.

Antimicrobial residues in meat from chickens in Northeast Vietnam: analytical validation and pilot study for sampling optimisation

Antimicrobials used in chicken farming for therapeutic and/or prophylactic purposes may result in unacceptable levels of edible residues, if withdrawal periods are not respected. To evaluate the risk in Vietnam, we validated an analytical method to detect antimicrobial residues from chicken meat samples and carried out a pilot cross-sectional study to identify optimal sampling strategies. A total of 45 raw meat samples were collected from 4 markets, 1 slaughterhouse and 4 farms (5 per site) in Northern Vietnam, between March and April 2021. Farmers were asked about antimicrobials used during sampled production cycles (5 chickens sampled per batch). Samples were analysed using liquid chromatography-tandem mass spectrometry for the presence of 68 antimicrobials at a pre-defined validation concentration. 7 compounds were identified from 4 classes (tetracyclines, sulphonamides, macrolides, and fluoroquinolones). In markets, where the source of sampled chickens was unknown, a diverse pool of residual antimicrobials was detected in 20% (4/20) of the meat samples. No residues were detected in samples from the slaughterhouse. No residues were detected in chickens from the one farm that reported using antimicrobials, whereas sulfadimethoxine, doxycycline and tilmicosin residues were identified from the other 3 farms reporting no antimicrobial use. The probability of detecting antimicrobial residues present in a flock based on sampling a single chicken was estimated at 0.93 (highest density interval 0.735–0.997). The preliminary results suggest a disparity between farmers’ reports on antimicrobial drug use and actual usage, and that the analysis of a single sample per farm has a high probability of detecting antimicrobial residues, if present.

Analysis of the Yellow River water and sediment monitoring data

Abstract Graphics are drawn about the sediment content, water flow, and water level of the Yellow River with time. A cluster scatter plot of sand content is made with changes over time. Using variance analysis of a factor, it is concluded that sediment content is affected by two variables month and year. By studying the changing pattern of water-sand flux, the timing diagram of the water and sediment flux of the Yellow River with time is drawn. The flux of water and sand is predicted for the next two years. According to the prediction results, the optimal sampling and monitoring scheme is developed.

A spatio-temporal model of multi-marker antimalarial resistance.

The emergence and spread of drug-resistant Plasmodium falciparum parasites have hindered efforts to eliminate malaria. Monitoring the spread of drug resistance is vital, as drug resistance can lead to widespread treatment failure. We develop a Bayesian model to produce spatio-temporal maps that depict the spread of drug resistance, and apply our methods for the antimalarial sulfadoxine-pyrimethamine. We infer from genetic count data the prevalences over space and time of various malaria parasite haplotypes associated with drug resistance. Previous work has focused on inferring the prevalence of individual molecular markers. In reality, combinations of mutations at multiple markers confer varying degrees of drug resistance to the parasite, indicating that multiple markers should be modelled together. However, the reporting of genetic count data is often inconsistent as some studies report haplotype counts, whereas some studies report mutation counts of individual markers separately. In response, we introduce a latent multinomial Gaussian process model to handle partially reported spatio-temporal count data. As drug-resistant mutations are often used as a proxy for treatment efficacy, point estimates from our spatio-temporal maps can help inform antimalarial drug policies, whereas the uncertainties from our maps can help with optimizing sampling strategies for future monitoring of drug resistance.

DNA Barcoding in Species Delimitation: From Genetic Distances to Integrative Taxonomy.

Over the past two decades, DNA barcoding has become the most popular exploration approach in molecular taxonomy, whether for identification, discovery, delimitation, or description of species. The present contribution focuses on the utility of DNA barcoding for taxonomic research activities related to species delimitation, emphasizing the following aspects:(1) To what extent DNA barcoding can be a valuable ally for fundamental taxonomic research, (2) its methodological and theoretical limitations, (3) the conceptual background and practical use of pairwise distances between DNA barcode sequences in taxonomy, and (4) the different ways in which DNA barcoding can be combined with complementary means of investigation within a broader integrative framework. In this chapter, we recall and discuss the key conceptual advances that have led to the so-called renaissance of taxonomy, elaboratea detailed glossary for the terms specific to this discipline (see Glossary in Chap. 35 ), and propose a newly designed step-by-step species delimitation protocol starting from DNA barcode data that includes stepsfrom the preliminary elaboration of an optimal sampling strategy to the final decision-making process which potentially leads to nomenclatural changes.

Effect of varying hydrologic regime on seasonal total maximum daily loads (TDML) in an agricultural watershed

Rising hypoxia due to the eutrophication of riverine ecosystems is primarily caused by the transport of nutrients. The majority of existing TMDL models cannot be efficienty applied to represent nutrient concentrations in riverine ecosystems having varying flow regimes due to seasonal differences. Accurate TMDL assessment requires nutrient loads and suspended matter estimation under varying flow regimes with minimal uncertainty. Though a large database can enhance accuracy, it can be resource intensive. This study presents the design of an innovative modeling strategy to optimize the use of existing datasets to effectively represent streamflow-load dynamics while minimizing uncertainty. The study developed an approach to assess TMDLs using six different flux models and kriging techniques (i) to enhance the accuracy of nutrient load estimation under different hydrologic regimes (flow stratifications) and (ii) to derive an optimal modeling strategy and sampling scheme for minimizing uncertainty. The flux models account for uncertainty in load prediction across varying flow strata, and the deployment of multiple load calculation procedures. Further, the proposed flux approach allows the determination of load exceedance under different TMDL scenarios aimed at minimizing uncertainty to achieve reliable load predictions. The study employed a 10-year dataset (2009–2018) consisting of daily flow data (m3/sec) and weekly data (mg/L) for nitrogen (N), phosphorus (P) and total suspended solids (TSS) concentrations in three distinct agricultural sites in+ the Minnesota River Watershed. The outcomes were analyzed geospatially in a Geographic Information System (GIS) environment using the kriging interpolation technique. The study recommends (i) triple stratification of flows to obtain accurate load estimates, and (ii) an optimal sampling scheme for nitrogen and phosphorous with 30.6 % and 49.8 % datapoints from high flow strata. The study outcomes are expected to contribute to the planning of economically and technically sound combinations of best management practices (BMPs) required for achieving total maximum daily loads (TMDL) in a watershed.

Getting to the Root of Tree Soil Microbiome Sampling

Microbiomes play critical roles in host functioning and, therefore, there is increasing interest in the microbiome assembly of plants. However, sampling strategies for long-lived perennial trees need to be standardized to produce robust data that accurately represent the microbiome over time. This issue is currently unresolved because there is little evidence indicating which portion of perennial tree species (e.g., root region or surrounding soil) is the best to sample to produce the most accurate measure of microbiome communities. Our aim was to sample different compartments of a plant's belowground microbiome to identify the optimal sampling strategy to account for the microbial community present. We found that the structure of the microbial community depends most strongly on the environment (site) and compartment of sample collected (bulk soil, rhizosphere, or rhizoplane), rather than the depth or cardinal direction of the sample. We also found that the microbial community increased in diversity with increased distance from the tree within the rhizoplane and rhizosphere. The data presented here provide systematic evidence for a pragmatic and robust sampling regime that was tested and validated across different environments and soil types while controlling for host genotype. This sampling regime will enable effective partitioning of root compartments when studying the microbiome associated with perennial tree species, allowing targeted questions about the microbiome to be explored with greater accuracy.

Quantitative Analysis of Paleomagnetic Sampling Strategies

AbstractSampling strategies used in paleomagnetic studies play a crucial role in dictating the accuracy of our estimates of properties of the ancient geomagnetic field. However, there has been little quantitative analysis of optimal paleomagnetic sampling strategies and the community has instead defaulted to traditional practices that vary between laboratories. In this paper, we quantitatively evaluate the accuracy of alternative paleomagnetic sampling strategies through numerical experiments and an associated analytical framework. Our findings demonstrate a strong correspondence between the accuracy of an estimated paleopole position and the number of sites or independent readings of the time‐varying paleomagnetic field, whereas larger numbers of in‐site samples have a dwindling effect. This remains true even when a large proportion of the sample directions are spurious. This approach can be readily achieved in sedimentary sequences by distributing samples stratigraphically, considering each sample as an individual site. However, where the number of potential independent sites is inherently limited the collection of additional in‐site samples can improve the accuracy of the paleopole estimate (although with diminishing returns with increasing samples per site). Where an estimate of the magnitude of paleosecular variation is sought, multiple in‐site samples should be taken, but the optimal number is dependent on the expected fraction of outliers. The use of filters based on angular distance helps the accuracy of paleopole estimation, but leads to inaccurate estimates of paleosecular variation. We provide both analytical formulas and a series of interactive Jupyter notebooks allowing optimal sampling strategies to be developed from user‐informed expectations.

S2O-FSPI: Fourier single pixel imaging via sampling strategy optimization

It is necessary to artificially set the sampling strategy of Fourier single-pixel imaging (FSPI) to obtain more useful information of the image under the assumption that the image information is mainly concentrated in the low-frequency part of the spatial frequency domain. However, due to the empiricism sampling strategy, it is easy to sample the spatial frequencies with low contribution to image reconstruction, resulting in a waste of sampling resources. To solve this problem, a one-stage FSPI reconstruction network with sampling strategy optimization is designed to obtain the efficient sampling strategy and improve the reconstruction quality. The proposed one-stage FSPI reconstruction network contains the sampling strategy optimization module and reconstruction module, which are jointly trained to obtain high-quality reconstructed results and efficient sampling strategy simultaneously. Experiments and numerical simulations demonstrate the effectiveness of the proposed method. Moreover, the geometric topology of the optimal sampling strategy for FSPI reconstruction trained on various categories of datasets is summarized. It is found that the dataset with similar categories have the similar geometric topology of the optimal sampling strategy, which provides support for sampling strategy selection in subsequent Fourier single-pixel imaging studies.

How much is enough? Examining the sampling effort necessary to estimate mean eDNA concentrations in lentic systems

AbstractThe concentration of eDNA in an environment can provide important ecological information of relevance for management and conservation, but little research has explored optimizing sampling strategies to estimate mean eDNA concentrations in natural environments. Inter‐replicate eDNA concentrations often exhibit right‐skewed “clustered” or “clumped” distributions, likely due to the stochastic capture of large “aggregate” particles with high eDNA copy numbers. This has important potential implications for modeling the resulting sampling effort necessary to accurately quantify eDNA concentrations. In a previous study, 17–20 Brook Charr eDNA samples were collected from 28 lakes in Québec, Canada. We explored how variation in eDNA concentrations within a lake was affected by several habitat characteristics. We then conducted a power analysis to determine the sampling effort (“minimum n”) necessary to accurately quantify mean lake eDNA concentrations and, using simulations, explored how a bimodal distribution of eDNA particle copy count could affect inter‐replicate variability. The median sample size such that 90% of sample mean estimates were within 20% of the “true” mean was 12.5; a sample size of 20 was sufficient to quantify mean concentrations in 21/28 lakes. We found no evidence that temperature or lake size impacted sample variability. We also found that variance among replicates was non‐linearly related to mean lake eDNA concentration across years: variability was lowest at low and high concentrations and highest at intermediate concentrations. We hypothesize that this resulted from the stochastic capture of large “aggregate” particles at intermediate concentrations; at low concentrations, aggregates were likely rarely captured and at high concentrations may represent a consistent component of total eDNA. Simulations demonstrated that these patterns can emerge from some bimodal eDNA particle “size” distributions. Overall, we conclude that sampling efforts in many previous studies (notably including the authors' own) were potentially low, emphasizing the need to increase spatial replication in lentic surveys.