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Abstract: Chromatographic detection responses are recorded digitally. A peak is represented ideally by a Guassian distribution. Raising a Guassian distribution to the power ‘n’ increases the height of the peak to that power, but decreases the standard deviation by √n. Hence there is an increasing disparity in detection responses as the signal moves from low level noise, with a corresponding decrease in peak width. This increases the S/N ratio and increases peak to peak resolution. The ramifications of these factors are that poor resolution in complex chromatographic data can be improved, and low signal responses embedded at near noise levels can be enhanced. The application of this data treatment process is potentially very useful in 2D-HPLC where sample dilution occurs between dimension, reducing signal response, and in the application of post-reaction detection methods, where band broadening is increased by virtue of reaction coils. In this work power functions applied to chromatographic data are discussed in the context of (a) complex separation problems, (b) 2D-HPLC separations, and (c) post-column reaction detectors. [ABSTRACT FROM AUTHOR]

Abstract: The regressive discrete Fourier series (RDFS) proposed in the early nineties can be used to smooth signals in one or two dimensions and to compute derivatives (e.g., spatial or time). This can be useful in applications where there is a need to compute derivatives of noisy data. The choice of the period and number of frequency lines of the Fourier series in the RDFS is empirical, based on the a priori information available about the data being treated. When the chosen period is larger that the data extension and the number of frequency lines increase, the RDFS may present numerical instability. In this paper a more robust RDFS is proposed to avoid such numerical instability. This robust version of the RDFS may be useful when a priori information is not available to guide the choice of the RDFS parameters. [Copyright &y& Elsevier]

Recent publications analyzing the influence of spatial smoothing on fMRI brain activation results demonstrated that smoothing may artificially combine activations from adjacent though functionally and anatomically distinct brain regions and that activation from large draining vessels may be smoothed into neighboring neuronal tissue. To investigate whether functional localizations may be artificially shifted by the smoothing procedure we performed replicability measurements. Localization centers of motor hand activations achieved during different conditions (isolated hand movements and simultaneous hand and chin movements) were compared with respect to smoothing effects. The voxel with the highest probability to represent a true positive activation was localized with a non-smoothed and a standard 4 × 4 × 6 mm smoothed correlational data analysis technique. Results show an increase of motor center aberrations between measurements by about 100% due to data smoothing indicating a statistically significant decrease in localization replicability. [Copyright &y& Elsevier]

Abstract: It is well-known that constrained Hebbian self-organization on multiple linear neural units leads to the same k-dimensional subspace spanned by the first k principal components. Not only the batch PCA algorithm has been widely applied in various fields since 1930s, but also a variety of adaptive algorithms have been proposed in the past two decades. However, most studies assume a known dimension k or determine it heuristically, though there exist a number of model selection criteria in the literature of statistics. Recently, criteria have also been obtained under the framework of Bayesian Ying–Yang (BYY) harmony learning. This paper further investigates the BYY criteria in comparison with existing typical criteria, including Akaike''s information criterion (AIC), the consistent Akaike''s information criterion (CAIC), the Bayesian inference criterion (BIC), and the cross-validation (CV) criterion. This comparative study is made via experiments not only on simulated data sets of different sample sizes, noise variances, data space dimensions, and subspace dimensions, but also on two real data sets from air pollution problem and sport track records, respectively. Experiments have shown that BIC outperforms AIC, CAIC, and CV while the BYY criteria are either comparable with or better than BIC. Therefore, BYY harmony learning is a more preferred tool for subspace dimension determination by further considering that the appropriate subspace dimension k can be automatically determined during implementing BYY harmony learning for the principal subspace while the selection of subspace dimension k by BIC, AIC, CAIC, and CV has to be made at the second stage based on a set of candidate subspaces with different dimensions which have to be obtained at the first stage of learning. [Copyright &y& Elsevier]

Three different least-squares methods for processing time-series of satellite sensor data are presented. The first method uses local polynomial functions and can be classified as an adaptive Savitzky–Golay filter. The other two methods are more clear cut least-squares methods, where data are fit to a basis of harmonic functions and asymmetric Gaussian functions, respectively. The methods incorporate qualitative information on cloud contamination from ancillary datasets. The resulting smooth curves are used for extracting seasonal parameters related to the growing seasons. The methods are implemented in a computer program, TIMESAT, and applied to NASA/NOAA Pathfinder AVHRR Land Normalized Difference Vegetation Index data over Africa, giving spatially coherent images of seasonal parameters such as beginnings and ends of growing seasons, seasonally integrated NDVI and seasonal amplitudes. Based on general principles, the TIMESAT program can be used also for other types of satellite-derived time-series data. [Copyright &y& Elsevier]

A new type of algebraic spline is used to derive a filter for smoothing or interpolating discrete data points. The spline is dependent on control parameters that specify the relative importance of data fitting and the derivatives of the spline. A general spline of arbitrary order is first formulated using matrix equations. We then focus on eighth-order splines because of the continuity of their first three derivatives (desirable for motor and robotics applications). The spline's matrix equations are rewritten to give a recursive filter that can be implemented in real time for lengthy data sequences. The filter is lowpass with a bandwidth that is dependent on the spline's control parameters. Numerical results, including a simple image processing application, show the tradeoffs that can be achieved using the algebraic splines. [ABSTRACT FROM AUTHOR]

Biophysical chemistry experiments, such as sedimentation-equilibrium analyses, require computational techniques to reduce the effects of random errors of the measurement process. The existing approaches have primarily relied on assumption of polynomial models and least-squares approximation. Such models by constraining the data to remove random fluctuations may distort the data and cause loss of information. The better the removal of random errors the greater is the likely introduction of systematic errors through the constraining fit itself. An alternative technique, reverse smoothing, is suggested that makes use of a more model-free approach of exponential smoothing of the first derivative. Exponential smoothing approaches have been generally unsatisfactory because they introduce significant data lag. The approaches given here compensates for the lag defect and appears promising for the smoothing of many experimental data sequences, including the macromolecular concentration data generated by sedimentation-equilibria experiments. Test results on simulated sedimentation-equilibrium data indicate that a 4-fold reduction in error may be typical over standard analyses techniques. [Copyright &y& Elsevier]

We are given univariate data that include random errors. We consider the problem of calculating a best approximation to the data by minimizing a strictly convex function of the errors subject to the condition that there are at most q sign changes in the sequence of the second divided differences of the approximation, where q is a prescribed integer. There are about O(nq) combinations of positions of sign changes, which make an exhaustive approach prohibitively expensive. However, Demetriou and Powell (Approximation Theory and Optimization, Cambridge University Press, Cambridge, 1997, pp. 109–132), have proved the remarkable property that there exists a partitioning of the data into (q+1) disjoint subsets such that the approximation may be calculated by a separate convex programming calculation on each subset. Based on this result, we provide a characterization theorem that reduces the problem to an equivalent one, where the unknowns are the positions of the sign changes subject to feasibility restrictions at the sign changes. Furthermore, we present counterexamples on two conjectures that investigate whether the search for optimal sign changes may be restricted to certain subranges of the data. [Copyright &y& Elsevier]

For many years the Butterworth lowpass filter has been used to smooth many kinds of biomechanical data, despite the fact that it is underdamped and therefore overshoots and/or undershoots data during rapid transitions. A comparison of the conventional Butterworth filter with a critically damped filter shows that the critically damped filter not only removes the undershooting and overshooting, but has a superior rise time during rapid transitions. While analog filters always create phase distortion, both the critically damped and Butterworth filters can be modified to become zero-lag filters when the data are processed in both the forward and reverse directions. In such cases little improvement is realized by applying multiple passes. The Butterworth filter has superior ‘roll-off’ (attenuation of noise above the cutoff frequency) than the critically damped filter, but by increasing the number of passes of the critically damped filter the same ‘roll-off’ can be achieved. In summary, the critically damped filter was shown to have superior performance in the time domain than the Butterworth filter, but for data that need to be double differentiated (e.g. displacement data) the Butterworth filter may still be the better choice. [Copyright &y& Elsevier]

In this paper, we solve the motion smoothing problem using genetic algorithms. Smooth motion generation is essential in the computer animation and virtual reality area. The motion of a rigid body in general consists of translation and orientation. The former is described by a space curve in three-dimensional Euclidean space while the latter is represented by a curve in the unit quaternion space. By adopting the geometric approach, the smoothness of both translation data and orientation data is measured from the strain energy perspective and a nonlinear optimization problem is formulated that aims to minimize the weighted sum of the strain–energy and the sum of the squared errors. A hybrid algorithm that combines genetic algorithms and local search schemes is deployed to solve this optimization problem and the experiments show that both smoothness and shape preservation of the resulting motion can be achieved by the proposed algorithm. [Copyright &y& Elsevier]

First, we briefly introduce the basic idea of data smoothing regularization, which was firstly proposed by Xu [Brain-like computing and intelligent information systems (1997) 241] for parameter learning in a way similar to Tikhonov regularization but with an easy solution to the difficulty of determining an appropriate hyper-parameter. Also, the roles of this regularization are demonstrated on Gaussian-mixture via smoothed versions of the EM algorithm, the BYY model selection criterion, adaptive harmony algorithm as well as its related Rival penalized competitive learning. Second, these studies are extended to a mixture of reconstruction errors of Gaussian types, which provides a new probabilistic formulation for the multi-sets learning approach [Proc. IEEE ICNN94 I (1994) 315] that learns multiple objects in typical geometrical structures such as points, lines, hyperplanes, circles, ellipses, and templates of given shapes. Finally, insights are provided on three problem solving strategies, namely the competition-penalty adaptation based learning, the global evidence accumulation based selection, and the guess-test based decision, with a general problem solving paradigm suggested. [Copyright &y& Elsevier]

The well-developed theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. These models are powerful tools for many forms of parametric data smoothing and are particularly well-suited to problems in which there is little or no theory to guide a choice of probability models, e.g., smoothing a distribution to eliminate roughness and zero frequencies in order to equate scores from different tests. Attention is given to efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and to computationally efficient methods for obtaining the asymptotic standard errors of the fitted frequencies and proportions. We discuss tools that can be used to diagnose the quality of the fitted frequencies for both the univariate and the bivariate cases. Five examples, using real data, are used to illustrate the methods of this paper. [ABSTRACT FROM PUBLISHER]

This paper reviews estimation problems with missing, or hidden data. We formulate this problem in the context of Markov models and consider two interrelated issues, namely, the estimation of a state given measured data and model parameters, and the estimation of model parameters given the measured data alone. We also consider situations where the measured data is, itself, incomplete in some sense. We deal with various combinations of discrete and continuous states and observations. [ABSTRACT FROM AUTHOR]

A class of new fundamental functions with compact support called many-knot spline is introduced. The two-scale relation for the fundamental functions is investigated, and the higher order accuracy spline approximation scheme is constructed by using the available degrees of freedom which come from additional knots. The technique has been efficiently applied to the problems such as time-frequency analysis, computer aided geometric design, and digital signal processing. [ABSTRACT FROM AUTHOR]

Data-smoothing can be particularly useful in predicting human behavior, detecting behavioral patterns, and monitoring treatment effectiveness in highly variable single-subject behavioral experiments that cannot be determined by only visual inspection of their graphs. Using an example from the applied behavior analytic literature, the use of moving-average and exponential data-smoothing aided the detection of the unique behavioral patterns of a child with autism across different treatments. Furthermore, the utility of the data-smoothing procedures to monitor and control the effectiveness of an intervention is discussed. The ease of their calculations suggest use of data-smoothing by behavior analysts whenever the effects of particular interventions are questionable. [ABSTRACT FROM AUTHOR]

When analysing and evaluating human motion, two strictly interconnected problems arise: the data smoothing and the determination of velocities and accelerations from displacement data. Differentiating procedures magnify the noise superimposed on the useful kinematic data. A smoothing procedure is thus required to reduce the measurement noise before the differentiation can be carried out. In the paper two techniques for derivative assessment are presented, tested and compared. One of these is the procedure known as one of the best automatic smoothing and differentiating techniques: generalised cross validatory spline smoothing and differentiation (GCVC). The other, which has recently been presented, features an automatic model-based bandwidth-selection procedure (LAMBDA). The procedures have been tested with signals presented by other authors and available in the literature, by test signals acquired using the ELITE motion analyser and by synthetic data. The results show better or similar performance of LAMBDA compared with GCVC. In the cases in which the natural conditions at the signal boundaries are not met GCVC gives bad results (especially on the third derivative) whereas LAMBDA is not affected at all. Moreover, analysis time is dramatically lower for LAMBDA. [ABSTRACT FROM AUTHOR]

A common problem in underwater side-scan sonar images is the acoustic shadow generated by the beam. Apart from that, there are a number of reasons impairing image quality. In this paper, an innovative algorithm with two alternative histogram approximation methods is presented. Histogram approximation is based on automatically estimating the optimal threshold for converting the original gray scale images into binary images. The proposed algorithm clears the shadows and masks most of the impairments in side-scan sonar images. The idea is to select a proper threshold towards the rightmost local minimum of the histogram, i.e., closest to the white values. For this purpose, the histogram envelope is approximated by two alternative contour extraction methods: polynomial curve fitting and data smoothing. Experimental results indicate that the proposed algorithm produces superior results than popular thresholding methods and common edge detection filters, even after corrosion expansion. The algorithm is simple, robust and adaptive and can be used in automatic target recognition, classification and storage in large-scale multimedia databases. [ABSTRACT FROM AUTHOR]

The low-distortion processing of well-testing geological parameters is a key way to provide decision-making support for oil and gas field development. However, the classical processing methods face many problems, such as the stochastic nature of the data, the randomness of initial parameters, poor denoising ability, and the lack of data compression and prediction mechanisms. These problems result in poor real-time predictability of oil operation status and difficulty in offline interpreting the played back data. Given these, we propose a wavelet-based Kalman smoothing method for processing uncertain oil well-testing data. First, we use correlation and reconstruction errors as analysis indicators and determine the optimal combination of decomposition scale and vanishing moments suitable for wavelet analysis of oil data. Second, we build a ground pressure measuring platform and use the pressure gauge equipped with the optimal combination parameters to complete the downhole online wavelet decomposition, filtering, Kalman prediction, and data storage. After the storage data are played back, the optimal Kalman parameters obtained by particle swarm optimization are used to complete the data smoothing for each sample. The experiments compare the signal-to-noise ratio and the root mean square error before and after using different classical processing models. In addition, robustness analysis is added. The proposed method, on the one hand, has the features of decorrelation and compressing data, which provide technical support for real-time uploading of downhole data; on the other hand, it can perform minimal variance unbiased estimates of the data, filter out the interference and noise, reduce the reconstruction error, and make the data have a high resolution and strong robustness. [ABSTRACT FROM AUTHOR]

• Densely clustered tracer breakthrough curve datasets • Descimating densely clustered breakthrough curve datasets • Smoothing densely clustered breakthrough curve datasets • Tracer breakthrough curve probability distribution type A tracer breakthrough curve (BTC) for each sampling station is the ultimate goal of every quantitative hydrologic tracing study, and dataset size can critically affect the BTC. Groundwater-tracing data obtained using in situ automatic sampling or detection devices may result in very high-density data sets. Data-dense tracer BTCs obtained using in situ devices and stored in dataloggers can result in visually cluttered overlapping data points. The relatively large amounts of data detected by high-frequency settings available on in situ devices and stored in dataloggers ensure that important tracer BTC features, such as data peaks, are not missed. Alternatively, such dense datasets can also be difficult to interpret. Even more difficult, is the application of such dense data sets in solute-transport models that may not be able to adequately reproduce tracer BTC shapes due to the overwhelming mass of data. One solution to the difficulties associated with analyzing, interpreting, and modeling dense data sets is the selective removal of blocks of the data from the total dataset. Although it is possible to arrange to skip blocks of tracer BTC data in a periodic sense (data decimation) so as to lessen the size and density of the dataset, skipping or deleting blocks of data also may result in missing the important features that the high-frequency detection setting efforts were intended to detect. Rather than removing, reducing, or reformulating data overlap, signal filtering and smoothing may be utilized but smoothing errors (e.g., averaging errors, outliers, and potential time shifts) need to be considered. Appropriate probability distributions to tracer BTCs may be used to describe typical tracer BTC shapes, which usually include long tails. Recognizing appropriate probability distributions applicable to tracer BTCs can help in understanding some aspects of the tracer migration. [ABSTRACT FROM AUTHOR]

Vegetation dynamics and phenology play an important role in inter-annual vegetation changes in terrestrial ecosystems and are key indicators of climate-vegetation interactions, land use/land cover changes and variation in year-to-year vegetation productivity. Satellite remote sensing data have been widely used for vegetation phenology monitoring over large geographic domains using various types of observations and methods over the past several decades. The goal of this paper is to present a detailed review of existing methods for phenology detection and emerging new techniques based on the analysis of time-series, multispectral remote sensing imagery. This paper summarizes the objective and applications of detecting general vegetation phenology stages (e.g., green onset, time or peak greenness and growing season length) often termed 'land surface phenology', as well as more advanced methods that estimate species-specific phenological stages (e.g., silking stage of maize). Common data processing methods, such as data smoothing, applied to prepare the time-series remote sensing observations to be applied to phenological detection methods are presented. Specific land surface phenology detection methods as well as species-specific phenology detection methods based on multispectral satellite data are then discussed. The impact of different error sources in the data on remote-sensing based phenology detection are also discussed in detail, as well as ways to reduce these uncertainties and errors. Joint analysis of multi-scale observations ranging from satellite to more recent ground-based sensors is helpful for us to understand satellite-based phenology detection mechanism and extent phenology detection to regional scale in the future. Finally, emerging opportunities to further advance remote sensing of phenology is presented that includes observations from Cubesats, near-surface observations such as PhenoCams and image data fusion techniques to improve the spatial resolution of time-series image data sets needed for phenological characterization. • Review of satellite remote sensing-based land surface phenology detection methods. • Discussion of advantages and drawbacks of phenological metrics extraction methods. • Review of error sources and methods to reduce their effects on phenology detection. • Opportunities and challenges related to improve phonological metrics extraction. [ABSTRACT FROM AUTHOR]

Crop phenology is an important parameter for crop growth monitoring, yield prediction, and growth simulation. The dynamic threshold method is widely used to retrieve vegetation phenology from remotely sensed vegetation index time series. However, crop growth is not only driven by natural conditions, but also modified through field management activities. Complicated planting patterns, such as multiple cropping, makes the vegetation index dynamics less symmetrical. These impacts are not considered in current approaches for crop phenology retrieval based on the dynamic threshold method. Thus, this paper aimed to (1) investigate the optimal thresholds for retrieving the start of the season (SOS) and the end of the season (EOS) of different crops, and (2) compare the performances of the Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) in retrieving crop phenology with a modified version of the dynamic threshold method. The reference data included SOS and EOS ground observations of three major crop types in 2015 and 2016, which includes rice, wheat, and maize. Results show that (1) the modification of the original method ensures a 100% retrieval rate, which was not guaranteed using the original method. The modified dynamic threshold method is more suitable to retrieve crop SOS/EOS because it considers the asymmetry of crop vegetation index time series. (2) It is inappropriate to retrieve SOS and EOS with the same threshold for all crops, and the commonly used 20% or 50% thresholds are not the optimal thresholds for all crops. (3) For single and late rice, the accuracies of the SOS estimations based on EVI are generally higher compared to those based on NDVI. However, for spring maize and summer maize, results based on NDVI give higher accuracies. In terms of EOS, for early rice and summer maize, estimates based on EVI result in higher accuracies, but, for late rice and winter wheat, results based on NDVI are closer to the ground records. [ABSTRACT FROM AUTHOR]

Fine-resolution Light Detection and Ranging (LiDAR) data often exhibit excessive surface roughness that can hinder the characterization of topographic shape and the modeling of near-surface flow processes. Digital elevation model (DEM) smoothing methods, commonly low-pass filters, are sometimes applied to LiDAR data to subdue the roughness. These techniques can negatively impact the representation of topographic features, most notably drainage features, such as headwater streams. This paper presents the feature-preserving DEM smoothing (FPDEMS) method, which modifies surface normals to smooth the topographic surface in a similar manner to approaches that were originally designed for de-noising three-dimensional (3D) meshes. The FPDEMS method has been optimized for application with raster DEM data. The method was compared with several low-pass filters while using a 0.5-m resolution LiDAR DEM of an agricultural area in southwestern Ontario, Canada. The findings demonstrated that the technique was better at removing roughness, when compared with mean, median, and Gaussian filters, while also preserving sharp breaks-in-slope and retaining the topographic complexity at broader scales. Optimal smoothing occurred with kernel sizes of 11–21 grid cells, threshold angles of 10°–20°, and 3–15 elevation-update iterations. These parameter settings allowed for the effective reduction in roughness and DEM noise and the retention of terrace scarps, channel banks, gullies, and headwater streams. [ABSTRACT FROM AUTHOR]

Water level data sets acquired by ultrasonic sensors in stream-scale channels exhibit relatively large numbers of outliers that are off the measurement range between the ultrasonic sensor and water surface, as well as data dispersion of approximately 2 cm due to random errors such as water waves. Therefore, this study develops a data processing algorithm for outlier removal and smoothing for water level data measured by ultrasonic sensors to consider these characteristics. The outlier removal process includes an initial cutoff process to remove outliers out of the measurement range and an outlier detection process using modified Z-scores based on the median absolute deviation (MAD) of a robust estimator. In addition, an exponentially weighted moving average (EWMA) method is applied to smooth the processed data. Sensitivity analyses are performed for factors that are subjectively set by the user, including the window size for the MAD outlier detection stage, the rejection criterion for the modified Z-score outlier removal stage, and the smoothing constant for the EWMA smoothing stage, based on four different water level data sets acquired by ultrasonic sensors in stream-scale experiments. [ABSTRACT FROM AUTHOR]