Linear Processing Of Nonuniformly Sampled Signals: A Fourier Analysis

Dealing with visualizations containing large data set is a challenging issue and, in the field of information visualization, almost every visual technique reveals its drawback when visualizing large number of items. To deal with this problem we introduce a formal environment, modeling in a virtual space the image features we are interested in (e.g, absolute and relative density, clusters, etc.) and we define some metrics able to characterize the image decay. Such metrics drive our automatic techniques (i.e., not uniform sampling) rescuing the image features and making them visible to the user. In This work we focus on 2D scatter-plots, devising a novel non uniform data sampling strategy able to preserve in an effective way relative densities.

This paper presents an ultra-low-power non-uniform sampling scheme using a derivative-based algorithm that can maintain a comparable accuracy to other non-uniform sampling schemes but with less complexity and lower power consumption. In this method, the change in the derivative of the signal above certain threshold values is used to identify high signal activity for retention of the significant points of the signal. The scheme is implemented using simple building blocks that calculate and compare the change in approximate real-time derivative to a tunable threshed value that can be adjusted to obtain the desired Compression Factor (CF) and Post-Reconstruction Signal-to-Noise plus Distortion Ratio (PR-SNDR) for different signal types. Fabricated in TSMC's <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.13 \mu \text{m}$ </tex-math></inline-formula> CMOS technology and tested with real-world biomedical signals, the proposed Derivative Dependent Sampling (DDS) system consumes a maximum power of 155 nW while achieving a CF of more than 6 for an Electrocardiography (ECG) signal. By adding the proposed DDS block to a data acquisition and processing system, the non-uniform sampling can reduce the power dissipation of the entire system.

A nonuniform sampling scheme is described for measuring the mutual intensity of the wave field produced in a plane a distance z from a spatially incoherent, three-dimensional source object. Both uniform and nonuniform sampling are analyzed and discussed in detail, and comparisons of the two schemes are made. It is shown that nonuniform sampling requires fewer measurements than uniform sampling to specify the coherence function. Additionally, the smallest separation required between measurement points is larger for the nonuniform case.

Nonuniform sampling (NUS) strategies are developed for acquiring highly resolved 1,1-ADEQUATE spectra, in both conventional and homodecoupled (HD) variants with improved sensitivity. Specifically, the quantile-directed and Poisson gap methods were critically compared for distributing the samples nonuniformly, and the quantile schedules were further optimized for weighting. Both maximum entropy and iterative soft thresholding spectral estimation algorithms were evaluated. All NUS approaches were robust when the degree of data reduction is moderate, on the order of a 50% reduction of sampling points. Further sampling reduction by NUS is facilitated by using weighted schedules designed by the quantile method, which also suppresses sampling noise well. Seed independence and the ability to specify the sample weighting in quantile scheduling are important in optimizing NUS for 1,1-ADEQUATE data acquisition. Using NUS yields an improvement in sensitivity, while also making longer evolution times accessible that would be difficult or impractical to attain by uniform sampling. Theoretical predictions for the sensitivity enhancements in these experiments are in the range of 5-20%; NUS is shown to disambiguate weak signals, reveal some n JCC correlations obscured by noise, and improve signal strength relative to uniform sampling in the same experimental time. This work presents sample schedule development for applying NUS to challenging experiments. The schedules developed here are made available for general use and should facilitate the broader utilization of ADEQUATE experiments (including 1,1-, 1,n-, and HD- variants) for challenging structure elucidation problems.

A proper monitoring of stochastic systems is the control charts of statistical process control and drift in characteristics of output may be due to one or several assignable causes. Although many research works have been done on the economic design of control charts with single assignable cause, the economic statistical design of T^2 control chart under Weibull shock model with multiple assignable causes and considering multivariate Taguchi loss function has not been presented yet. Using Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values ??of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with Taguchi loss function has a lower cost than single assignable cause model and integrated model with non-uniform sampling has a lower cost than that with uniform sampling.

As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. Scenedesmus obliquus, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.

Many target tracking subsystems have the ability to schedule their own data rates; essentially they can order new information whenever they need it, and the cost is in terms of the sensor resource. But among the unmanaged schemes, uniform sampling, in which a new measurement is requested periodically and regularly, is the most commonly-used sampling scheme; deliberately nonuniform schemes are seldom given serious consideration. In this paper, however, we show that such schemes may have been discarded prematurely: a nonuniform sampling can have its benefits. Specifically, the nonuniform and uniform sampling schemes are compared for two kind of trackers: the probabilistic data association filter (PDAF), which updates its track based on a single scan of information at a time; and N-D assignment (an optimization-based implementation of the multi-hypothesis tracker (MHT)), in which the sliding window involves many scans of observations. We find that given the ground rule of maintenance of the same overall scan rate (i.e., the same sensor effort) uniform sampling is always optimal for the single-scan tracker in the sense of track life. However, nonuniform sampling can outperform uniform sampling if a more sophisticated multi-scan tracker is used, particularly when 1) the target has a high process noise, and/or 2) the false alarm density is high, and/or 3) the probability of detection is high.

In decision support applications, the ability to provide fast approximate answers to aggregation queries is desirable. One commonly-used technique for approximate query answering is sampling. For many aggregation queries, appropriately constructed biased (non-uniform) samples can provide more accurate approximations than a uniform sample. The optimal type of bias, however, varies from query to query. In this paper, we describe an approximate query processing technique that dynamically constructs an appropriately biased sample for each query by combining samples selected from a family of non-uniform samples that are constructed during a pre-processing phase. We show that dynamic selection of appropriate portions of previously constructed samples can provide more accurate approximate answers than static, non-adaptive usage of uniform or non-uniform samples.

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

A proper method of monitoring a stochastic system is to use the control charts of statistical process control in which a drift in characteristics of output may be due to one or several assignable causes. In the establishment of X charts in statistical process control, an assumption is made that there is no correlation within the samples. However, in practice, there are many cases where the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. Using three di erent loss functions in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Although some research works have considered the economic design of control charts under single assignable cause and correlated data, the economic statistical design of X control chart for multiple assignable causes and correlated data under Weibull shock model with three di erent loss functions have not been presented yet. Based on the optimization of the average cost per unit of time and taking into account the di erent combination values of Weibull distribution parameters, optimal design values of sample size, sampling interval and control limit coecient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with correlated samples with non-uniform sampling integrated with three di erent loss functions has a lower cost than the model with uniform sampling.

A unified approach to the representation and processing of a class of images which are not bandlimited but belong to the space of locally bandlimited signals is presented. A nonuniform sampling theorem (Clark et al, 1985) for functions belonging to this space is extended, and a class of nonstationary stochastic processes is considered. The space of locally bandlimited signals is shown to be a reproducing-kernel space. A generalized projection theorem can therefore be applied, yielding either a continuous or a discrete projection filter. The former can be used for image conditioning prior to nonuniform sampling, while the latter provides a general tool for image representation by nonuniform sampling schemes. The problem of finding the local bandwidth of a given signal, in order to generate an optimal sampling scheme, is addressed in the context of signal representation in the combined position-frequency space. The stochastic estimation of parameters which characterize the local bandwidth is discussed. Bounds on the error resulting from the utilization of nonexact position-varying signal parameters are derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We consider the problem of reconstructing a 2D bandlimited signal from its nonuniform samples taken in polar coordinates. We introduce two nonuniform sampling strategies in polar coordinates and develop algorithms for reconstructing the signal from these samples. The proposed methods collect nonuniform samples along concentric circles or radial lines, where the circles or lines are nonuniformly distributed. We then apply these methods to the problem of reconstruction of tomographic images and show through simulations that they result in a higher quality of reconstruction with respect to the traditionally used algorithms.

The accuracy of measurement-driven mobile coverage maps depends on the quality, density and pattern of the signal strength observations. Thus, identifying an efficient measurement data collection methodology is essential, especially when considering the cost associated with the measurement collection approaches (e.g., drive tests, crowd approaches). We propose ZipWeave, a novel measurement data collection and fusion framework for building efficient and reliable measurement-based mobile coverage maps. ZipWeave incorporates a novel nonuniform sampling strategy to achieve reliable coverage maps with reduced sample size. Assuming prior knowledge of the propagation characteristics of the region of interest, we first examine the potential gains of this non-uniform sampling strategy in different cases via a measurement-based statistical analysis methodology; this involves irregular spatial tessellation of the region of interest into sub-regions with internally similar radio propagation characteristics and sampling based on these sub-regions. We then present a practical form of ZipWeave nonuniform sampling strategy that can be used even without any prior information. In all our evaluations, we show that the ZipWeave non-uniform sampling approach reduces the samples by half compared to the common systematic-random sampling, while maintaining similar accuracy. Moreover, we show that the other key feature of ZipWeave to combine high-quality controlled measurements (that present limited geographic footprint similar to drive tests) with crowdsourced measurements (that cover a wider footprint) leads to more reliable mobile coverage maps overall.

The acquisition of high-quality multi-dimensional nuclear magnetic resonance (NMR) spectra can be accelerated through the implementation of non-uniform sampling (NUS) and the employment of reconstruction method. However, the optimization of the NUS scheme and the reconstruction method have been performed independently up to now. This results in a weakened relationship between the NUS scheme and the reconstruction method and thus suboptimal reconstructed spectra, leading to shortcomings such as lost peaks and artifacts. Here, a deep learning network for jointly optimized sampling and reconstruction, referred to as JOSR-Net, is proposed. It integrates the sampling sub-network and the reconstruction sub-network into a unified end-to-end framework, aiming to simultaneously optimize both the sampling scheme and the reconstruction of undersampled data during the training process. This enables the optimal co-adaptation between the NUS scheme and the reconstruction algorithm, ultimately achieving high quality spectral reconstruction. And the results on protein spectra demonstrate that the proposed method effectively learns optimal sampling schemes and achieves superior reconstruction performance, compared to both traditional reconstruction methods and current deep learning reconstruction methods.

The theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite-precision amplitude values. In this paper, we explore signal representation and recovery based on uniform amplitude sampling with assumed infinite precision timing information. The approach is based on the delta-ramp encoder which consists of applying a one-level level-crossing detector to the result of adding an appropriate sawtooth-like waveform to the input signal. The output samples are the time instants of these level crossings, thus representing a time-encoded version of the input signal. For theoretical purposes, this system can be equivalently analyzed by reversibly transforming through ramp addition a nonmonotonic input signal into a monotonic one, which is then uniformly sampled in amplitude. The monotonic function is then represented by the times at which the signal crosses a predefined and equally-spaced set of amplitude values. We refer to this technique as amplitude sampling. The time sequence generated can be interpreted alternatively as nonuniform time sampling of the original source signal. We derive duality and frequency-domain properties for the functions involved in the transformation. Iterative algorithms are proposed and implemented for recovery of the original source signal. As indicated in the simulations, the proposed iterative amplitude-sampling algorithm achieves a faster convergence rate than frame-based reconstruction for nonuniform sampling. The performance can also be improved by appropriate choice of the parameters while maintaining the same sampling density.