Irregular Sampling Schemes 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.

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.

Testing for Endogeneity of Irregular Sampling Schemes

Testing for Endogeneity of Irregular Sampling Schemes

Testing for Endogeneity of Irregular Sampling Schemes

Testing for Endogeneity of Irregular Sampling Schemes

Sampling Analysis and Processing Approach for Distributed SAR Constellations With Along-Track Baselines

In the constant strive for improving the capacity of next-generation spaceborne SARs while containing the increase in system complexity, distributed along-track constellations operated below Nyquist appear as one of the most promising solutions for delivering metric resolution imagery over swaths of hundreds of kilometers. In the operation of multistatic SAR constellations, however, sampling singularities typically result in dramatic noise scaling and the impossibility to recover the entire Doppler bandwidth unambiguously. We investigate in this article the likelihood of these singularities in the case of along-track distributed constellations and justify the use of irregular sampling schemes to reduce the percentage of invalid samples of an acquisition. This article also presents a bistatic polychromatic reconstruction algorithm, which is used for the evaluation of the performance of along-track distributed constellations. With all these elements, the performance of along-track multistatic systems is assessed by means of a Monte Carlo analysis and conclusions on the scaling numbers of the constellations are drawn. Based on the performance investigations, an exemplary distributed L-band SAR constellation is proposed as a corollary of this article.

Probe-corrected near-field to far-field transformation using multiple spherical wave expansions

AbstractNear-field to far-field transformations constitute a powerful antenna characterization technique for near-field measurement scenarios. In this paper, a near-field to far-field transformation technique based on multiple spherical wave expansions (SWEs) is presented. Thanks to its iterative matrix inversion nature, the approach performs the transformation of fields measured on arbitrary surfaces. Also, irregular sampling schemes can be incorporated. The proposed algorithm is based on modeling the antenna fields with not one, but several SWEs distributed over its geometry. Due to the high number of SWEs, their truncation number can be arbitrarily reduced. Working with expansions of low order allows us to incorporate the probe correction in the transformation in a very simple way, accepting any type of probe and orientation. Only the probe far-field pattern is used, thus working with its full SWE is avoided. The algorithm is validated using simulated field data as well as measurements of real antennas.

Detecting dominant changes in irregularly sampled multivariate water quality data sets

Abstract. Time series of groundwater and stream water quality often exhibit substantial temporal and spatial variability, whereas typical existing monitoring data sets, e.g. from environmental agencies, are usually characterized by relatively low sampling frequency and irregular sampling in space and/or time. This complicates the differentiation between anthropogenic influence and natural variability as well as the detection of changes in water quality which indicate changes in single drivers. We suggest the new term “dominant changes” for changes in multivariate water quality data which concern (1) multiple variables, (2) multiple sites and (3) long-term patterns and present an exploratory framework for the detection of such dominant changes in data sets with irregular sampling in space and time. Firstly, a non-linear dimension-reduction technique was used to summarize the dominant spatiotemporal dynamics in the multivariate water quality data set in a few components. Those were used to derive hypotheses on the dominant drivers influencing water quality. Secondly, different sampling sites were compared with respect to median component values. Thirdly, time series of the components at single sites were analysed for long-term patterns. We tested the approach with a joint stream water and groundwater data set quality consisting of 1572 samples, each comprising sixteen variables, sampled with a spatially and temporally irregular sampling scheme at 29 sites in northeast Germany from 1998 to 2009. The first four components were interpreted as (1) an agriculturally induced enhancement of the natural background level of solute concentration, (2) a redox sequence from reducing conditions in deep groundwater to post-oxic conditions in shallow groundwater and oxic conditions in stream water, (3) a mixing ratio of deep and shallow groundwater to the streamflow and (4) sporadic events of slurry application in the agricultural practice. Dominant changes were observed for the first two components. The changing intensity of the first component was interpreted as response to the temporal variability of the thickness of the unsaturated zone. A steady increase in the second component at most stream water sites pointed towards progressing depletion of the denitrification capacity of the deep aquifer.

EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY AND RELATED PROCESSES

We derive nonparametric efficiency bounds for regular estimators of integrated smooth transformations of instantaneous variances, in particular, integrated power variance. We find that realized variance attains the efficiency bound for integrated variance under both regular and irregular sampling schemes. For estimating higher powers such as integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds, when observation times are equidistant. Moreover, the estimator in Jacod and Rosenbaum (2013), whose efficiency was documented for the submodel assuming constant volatility, is efficient also for nonconstant volatility paths. When the observation times are possibly random but predictable, we provide an estimator, similar to that of Kristensen (2010), which can get arbitrarily close to the nonparametric bound. Finally, parametric information about the functional form of volatility leads to a lower efficiency bound, unless the volatility process is piecewise constant.

Identification of linear continuous-time systems under irregular and random output sampling

This paper considers the problem of identifiability and parameter estimation of single-input–single-output, linear, time-invariant, stable, continuous-time systems under irregular and random sampling schemes. Conditions for system identifiability are established under inputs of exponential polynomial types and a tight bound on sampling density. Identification algorithms of Gauss–Newton iterative types are developed to generate convergent estimates. When the sampled output is corrupted by observation noises, input design, sampling times, and convergent algorithms are intertwined. Persistent excitation (PE) conditions for strongly convergent algorithms are derived. Unlike the traditional identification, the PE conditions under irregular and random sampling involve both sampling times and input values. Under the given PE conditions, iterative and recursive algorithms are developed to estimate the original continuous-time system parameters. The corresponding convergence results are obtained. Several simulation examples are provided to verify the theoretical results.

Identifiability and Parameter Estimation of Linear Continuous-time Systems under Irregular and Random Sampling

This paper considers the problem of identifiability and parameter estimation of single-input-single-output, linear, time-invariant, stable, continuous-time systems under irregular and random sampling schemes. Conditions for system identifiability are established under inputs of exponential polynomial types and a tight bound on sampling density. Identification algorithms of Gauss-Newton iterative types are developed to generate convergent estimate sequences. When the sampled output is corrupted by observation noises, input design, sampling times, and convergent algorithms are intertwined. Persistent excitation (PE) conditions for strongly convergent algorithms are derived. Unlike the traditional identification, the PE conditions under irregular and random sampling involve both sampling times and input values. Under the given PE conditions, iterative and recursive algorithms are developed to estimate the original continuous-time system parameters. The corresponding convergence results are obtained. Several simulation examples are displayed to verify the theoretical results.

Joint state and event observers for linear switching systems under irregular sampling

Joint estimation of states and events in linear regime-switching systems is studied under irregular sampling schemes which stem from improved sampling and quantization methods for efficient utility of communication resources. Joint observability and sampling complexity are established, extending Shannon’s sampling theorem and our recent results on sampling complexity to joint estimation problems. Observer design and convergence analysis are conducted for systems under noisy observations. It is shown that our algorithms converge strongly with an error bound of the order O(1/N). Simulation examples are included to illustrate potential usages of the algorithms.

Joint State and Event Observers for Irregularly Sampled Switching Systems

Joint estimation of states and events in linear regime-switching systems is studied under irregular sampling schemes which stem from improved sampling and quantization methods for efficient utility of communication resources. Joint observability and sampling complexity are established. Observer design and convergence analysis are developed for systems under noisy observations. It is shown that our algorithms converge strongly and guarantee a convergence rate of magnitude O(1/N).

State and event estimation for regime-switching systems under irregular and random sampling schemes

Estimation of states and events in randomly switching systems is studied under irregular and random sampling schemes. Probabilistic characterization of observability is presented under various sampling schemes and regime-switching processes. The characterization is derived on the basis of our recent results on sampling complexity for system observability. Observer design and algorithms are developed. 1. Introduction. This paper investigates estimation of states and events in ran- domly switching systems under various sampling schemes. The problems are typically studied under the names of regime-switching systems, hybrid systems, discrete-event systems, etc. Typically, such systems involve communication channels whose power and bandwidth limitations make it desirable to reduce resource consumption in sam- pling and quantization. It was shown in (29, 30) that traditional periodic sampling is inefficient in utility of such resources. More efficient sampling/quantiz ation schemes introduced in (29, 30) lead naturally to irregular sampling (also known as non-uniform or non-periodic sampling). Irregular and random sampling may occur also due to event triggered sampling (3, 22) or communication uncertainty and interruptions (9). When a system switches its dynamics, it introduces an event which is itself a dy- namic process whose state space is a finite set and its state also needs to be estimated. State estimation of linear dynamic systems is a traditional topic that has been well studied (14). Independently, observability of events has been studied extensively in discrete event systems (15, 18). References (25, 26) contain more recent studies on observability of sampled systems. Joint identification of states and events has been studied in hybrid systems (20, 25). Studies on fundamental properties of non-uniform sampling remain an active area of research, see (6) and the references therein for some recent work in this area. Some related results on identification, state estimation, and fault detection using binary or quantized outputs can be found in (13, 26, 31, 32, 35). This paper studies some fundamental issues in joint estimation of states and events when the events are stochastic processes. The main issues are: What are the conditions for observability? How many sampling points are needed to ensure

Consistent Estimation of Non-bandlimited Spectral Density From Uniformly Spaced Samples

In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular (uniform) sampling. A major reason for this preference is the well-known problem of inconsistency of estimators based on regular sampling, when the underlying power spectral density is not bandlimited. It is argued in this paper that, in consideration of a large sample property like consistency, it is natural to allow the sampling rate to go to infinity as the sample size goes to infinity. Through appropriate asymptotic calculations under this scenario, it is shown that the smoothed periodogram based on regularly spaced data is a consistent estimator of the spectral density, even when the latter is not band-limited. It transpires that, under similar assumptions, the estimators based on uniformly sampled and Poisson-sampled data have about the same rate of convergence. Apart from providing this reassuring message, the paper also gives a guideline for practitioners regarding appropriate choice of the sampling rate. Theoretical calculations for large samples and Monte-Carlo simulations for small samples indicate that the smoothed periodogram based on uniformly sampled data have less variance and more bias than its counterpart based on Poisson sampled data.

Statistical estimation of Lévy-type stochastic volatility models

Volatility clustering and leverage are two of the most prominent stylized features of the dynamics of asset prices. In order to incorporate these features as well as the typical fat-tails of the log return distributions, several types of exponential Levy models driven by random clocks have been proposed in the literature. These models constitute a viable alternative to the classical stochastic volatility approach based on SDEs driven by Wiener processes. This paper has two main objectives. First, using threshold type estimators based on high-frequency discrete observations of the process, we consider the recovery problem of the underlying random clock of the process. We show consistency of our estimator in the mean-square sense, extending former results in the literature for more general Levy processes and for irregular sampling schemes. Secondly, we illustrate empirically the estimation of the random clock, the Blumenthal-Geetor index of jump activity, and the spectral Levy measure of the process using real intraday high-frequency data.

Distance-based eigenvector maps (DBEM) to analyse metapopulation structure with irregular sampling

Characterizing spatial patterns due to ecological processes is a major issue for analysing and predicting species distributions. Grasping the non-linear nature of population dynamics over networks of discrete suitable sites is here central, as very specific signatures are expected. In the line of promising results from Fourier analysis of metapopulation maps, we found distance-based eigenvector maps (DBEM) to help disentangle the respective signatures of habitat and metapopulation structuring, with the great advantage of being applicable to irregular sampling schemes, a common feature of ecological surveys. A smoothing procedure was required to obtain the distinguishable signatures, and this may be a critical issue for investigating non-contingent and reliable patterns in spatial ecology.

DISSECTING THE SPATIAL STRUCTURE OF ECOLOGICAL DATA AT MULTIPLE SCALES

Spatial structures may not only result from ecological interactions, they may also play an essential functional role in organizing the interactions. Modeling spatial patterns at multiple spatial and temporal scales is thus a crucial step to understand the functioning of ecological communities. PCNM (principal coordinates of neighbor matrices) analysis achieves a spectral decomposition of the spatial relationships among the sampling sites, creating variables that correspond to all the spatial scales that can be perceived in a given data set. The analysis then finds the scales to which a data table of interest responds. The significant PCNM variables can be directly interpreted in terms of spatial scales, or included in a procedure of variation decomposition with respect to spatial and environmental components. This paper presents four applications of PCNM analysis to ecological data representing combinations of: transect or surface data, regular or irregular sampling schemes, univariate or multivariate data. The data sets include Amazonian ferns, tropical marine zooplankton, chlorophyll in a marine lagoon, and oribatid mites in a peat bog. In each case, new ecological knowledge was obtained through PCNM analysis.

Local relapse and systemic recurrence in breast cancer patients. Are they related?

A survey of radon concentration in the soil gas was carried out on a single geological formation: the Monsal Dale Limestone, to the South of the village of Biggin in Derbyshire (England): a ‘radon affected area’. An irregular sampling scheme was used with the interval between sampling points varying from 50 m to 250 m. Ninety-three dosimeters were placed at a depth of 50 cm in the soil over an area of 4 km2 to measure the soil radon concentration. The values were found to range between 3 kBq m−3 and 35 kBq m−3, with a mean value of 13.03 ± 7.60 kBq m−3. The ‘variogram’ of Regionalized Variable Theory showed that there is spatial autocorrelation in the variation of radon over the surveyed area within the lithological unit, and also that a considerable proportion of the variation is occurring over distances less than the smallest sampling interval of 50 m. The ‘kriged’ map of radon shows that there is a distinctive pattern in its variation with an apparent inverse relation between radon concentration and elevation.

New irregular sampling coding method for transmitting images progressively

Transmitting images over channels of low capacity is an important issue relating to networks. The authors propose a new progressive image transmission (PIT) method based on the irregular sampling coding scheme. In the proposed method, the original image is first sampled using the irregular sampling scheme and the resulting samples are divided into several segments for the purpose of progressive image transmission. Therefore, each segment of the samples is further encoded and then transmitted to the receiver in each phase. At the receiver, the well known four-nearest-neighbour (4NN) algorithm is employed to reconstruct the rough image during each phase. According to the experimental results, the image quality is better in each transmission phase than the image quality for the related methods, i.e. FRM, TSVQ and SMTSVQ. Moreover, in the first phase, the difference in PSNR between this method and SMTSVQ is up to 2.8 dB. Therefore, the proposed method is more effective than the other methods described previously.

An adaptive irregular sampling algorithm and its application to image coding

Abstract A novel irregular and nonuniform sampling scheme for image data is presented in this paper. Its main characteristics are the particular distribution of the samples along image edges and in textured areas, which is obtained following a multiresolution approach, and the low computational complexity. As an example of application, an image coding system is proposed which, thanks to both the peculiar sample distribution and a suitably designed interpolation scheme, yields good subjective quality images at low bit rates, avoiding the annoying artefacts which are typical of block-based coding techniques as JPEG.