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Concept: Linear interpolation


Electroencephalography (EEG), magnetoencephalography (MEG) and related techniques are prone to glitches, slow drift, steps, etc., that contaminate the data and interfere with the analysis and interpretation. These artifacts are usually addressed in a preprocessing phase that attempts to remove them or minimize their impact. This paper offers a set of useful techniques for this purpose: robust detrending, robust rereferencing, outlier detection, data interpolation (inpainting), step removal, and filter ringing artifact removal. These techniques provide a less wasteful alternative to discarding corrupted trials or channels, and they are relatively immune to artifacts that disrupt alternative approaches such as filtering. Robust detrending allows slow drifts and common mode signals to be factored out while avoiding the deleterious effects of glitches. Robust rereferencing reduces the impact of artifacts on the reference. Inpainting allows corrupt data to be interpolated from intact parts based on the correlation structure estimated over the intact parts. Outlier detection allows the corrupt parts to be identified. Step removal fixes the high-amplitude flux jump artifacts that are common with some MEG systems. Ringing removal allows the ringing response of the antialiasing filter to glitches (steps, pulses) to be suppressed. The performance of the methods is illustrated and evaluated using synthetic data and data from real EEG and MEG systems. These methods, which are mainly automatic and require little tuning, can greatly improve the quality of the data.

Concepts: Linear interpolation, Electroencephalography, Interpolation, Magnetoencephalography, Low-pass filter, Bicubic interpolation, Corruption, Ringing artifacts


The performance of functionals based on the idea of interpolating between the weak- and the strong-interaction limits the global adiabatic-connection integrand is carefully studied for the challenging case of noble-metal clusters. Different interpolation formulas are considered and various features of this approach are analyzed. It is found that these functionals, when used as a correlation correction to Hartree-Fock, are quite robust for the description of atomization energies, while performing less well for ionization potentials. Future directions that can be envisaged from this study and a previous one on main group chemistry are discussed.

Concepts: Chemical element, Linear interpolation, Quantum chemistry, Performance, Cultural studies, Music, Interpolation


Aerosol is an important component of the atmosphere that affects the environment, climate, and human health. Remote sensing is an efficient observation method for monitoring global aerosol distribution and changes over time. The daily Moderate Resolution Imaging Spectroradiometer (MODIS) level-2 aerosol optical depth (AOD) (Collection 6) product (10 km resolution) is often used to study climate change and air pollution. However, the product is prone to yielding large amounts of data gaps due to the unfeasibility of retrieving reliable estimates under cloudy conditions, and these data gaps inevitably affect the results and analysis of the product’s application. In this study, a geostatistical data interpolation framework based on the spatiotemporal kriging method was implemented to interpolate satellite AOD products in Beijing, China. Compared to the ordinary kriging method for filling data gaps, the spatiotemporal interpolation not only utilizes spatial autocorrelation but also considers the temporal and spatiotemporal autocorrelations between different locations. In the study region, the completeness of the spatiotemporal-interpolated AOD product reaches 67.73%, which is significantly superior to the completeness of the original MODIS product (14.27%) and that of the spatial kriging-interpolated AOD product (33.3%). The cross-validation results show that the mean absolute error of the spatiotemporal kriging results (0.07) is lower than that of the ordinary kriging (0.09).

Concepts: Regression analysis, Climate, Linear interpolation, Atmosphere, Numerical analysis, Interpolation, Kriging, Multivariate interpolation


In elastography, conventional linear array (CLA)-based RF data acquisition provides more accurate displacement measurements in the direction of beam propagation (axial direction) when compared to the perpendicular direction (lateral). Obtaining good quality lateral displacement estimates in ultrasound (US) elastography will lead to several benefits such as obtaining accurate inverse solutions, improving shear strain elastogram quality, getting good quality poroelastograms, and obtaining reliable rotation elastograms. For accomplishing high-precision lateral displacement estimation (LDE), one of the popular methods is by interpolating additional A-lines in between neighboring RF A-lines. We describe a method wherein true RF A-lines (not interpolated) are acquired and augmented at subpitch locations using CLA transducer, instead of interpolating the data, and using this new frame data for further image formation and/or processing to yield better lateral resolution and LDE. We demonstrate the proposed method by translating the US beam of CLA transducer in subpitch range by the following two approaches: 1) actuator-assisted beam translation and 2) electronic translation of subaperture of a CLA by activating odd and even number of consecutive elements sequentially, referred to as electronic beam translation. The performances of the different methods were studied through simulations and experiments on phantoms. The results demonstrate that these methods yield better quality LDE compared to those obtained from interpolation of RF A-lines. These methods may provide affordable ways to obtain subpitch precision LDE using CLA.

Concepts: Medical imaging, Linear interpolation, Continuum mechanics, Ultrasound, Interpolation, Elastography


In view of the relatively low computational load, look-up tables (or maps) are usually used to approximate nonlinear function or characterize operating-point-dependent system variables in typical embedded applications. Aiming at the problem of off-line identifying the look-up tables, a method based on the gradient algorithm is presented to estimate the look-up table parameters in this paper. The nonlinear function is approximated in terms of the piecewise linear interpolation model with the look-up table parameters, which can be rewritten as a dot product between the regression vector and unknown parameter vector using membership function. With the approximation error of the nonlinear function, a method for updating look-up tables using the gradient algorithm is given, and the relationship between the parameter estimation error and model approximation error is explicitly derived. To guarantee the convergence of the look-up table parameters estimation, a condition for the persistent excitation of the look-up table input is derived, which also provides a theoretical basis for the data characteristics of the look-up table input required to identify look-up table parameters offline using dynamic data. The validity of the proposed method is verified respectively by updating a one-dimensional (1D) look-up table, and the identification of the two-dimensional (2D) look-up table for the throttle discharge coefficient of a spark ignition gasoline engine form engine simulation tool enDYNA.

Concepts: Linear interpolation, Vector space, Approximation, Estimation, Numerical analysis, Interpolation, Array data structure, Lookup table


Frame rate up conversion (FRUC) can improve the visual quality by interpolating new intermediate frames. However, high frame rate videos by FRUC are confronted with more bitrate consumption or annoying artifacts of interpolated frames. In this paper, a novel integration framework of FRUC and high efficiency video coding (HEVC) is proposed based on rate-distortion optimization, and the interpolated frames can be reconstructed at encoder side with low bitrate cost and high visual quality. First, joint motion estimation (JME) algorithm is proposed to obtain robust motion vectors, which are shared between FRUC and video coding. What’s more, JME is embedded into the coding loop and employs the original motion search strategy in HEVC coding. Then, the frame interpolation is formulated as a rate-distortion optimization problem, where both the coding bitrate consumption and visual quality are taken into account. Due to the absence of original frames, the distortion model for interpolated frames is established according to the motion vector reliability and coding quantization error. Experimental results demonstrate that the proposed framework can achieve 21% ~ 42% reduction in BDBR, when compared with the traditional methods of FRUC cascaded with coding.

Concepts: Linear interpolation, Numerical analysis, Interpolation, Video, Frame rate


The physical model test of landslides is important for studying landslide structural damage, and parameter measurement is key in this process. To meet the measurement requirements for deep displacement in landslide physical models, an automatic flexible inclinometer probe with good coupling and large deformation capacity was designed. The flexible inclinometer probe consists of several gravity acceleration sensing units that are protected and positioned by silicon encapsulation, all the units are connected to a 485-comunication bus. By sensing the two-axis tilt angle, the direction and magnitude of the displacement for a measurement unit can be calculated, then the overall displacement is accumulated according to all units, integrated from bottom to top in turn. In the conversion from angle to displacement, two spline interpolation methods are introduced to correct and resample the data; one is to interpolate the displacement after conversion, and the other is to interpolate the angle before conversion; compared with the result read from checkered paper, the latter is proved to have a better effect, with an additional condition that the displacement curve move up half the length of the unit. The flexible inclinometer is verified with respect to its principle and arrangement by a laboratory physical model test, and the test results are highly consistent with the actual deformation of the landslide model.

Concepts: Measurement, Metrology, Linear interpolation, Test method, Units of measurement, Interpolation, Conversion of units, Spline


Heart rate variability (HRV) analysis is widely used to investigate the autonomic regulation of the cardiovascular system. HRV is often analyzed using RR time series, which can be affected by different types of artifacts. Although there are several artifact correction methods, there is no study that compares their performances in actual experimental contexts. This work aimed to evaluate the impact of different artifact correction methods on several HRV parameters. Initially, 36 ECG recordings of control rats or rats with heart failure or hypertension were analyzed to characterize artifacts occurrence rates and distributions, in order to be mimicked in simulations. After a rigorous analysis, only sixteen recordings (N=16) with artifact-free segments of at least 10.000 beats were selected. Then, RR interval losses were simulated in the artifact-free (reference) time series according to real observations. Correction methods applied to simulated series were deletion (DEL), linear interpolation (LI), cubic spline interpolation (CI), modified moving average window (mMAW) and nonlinear predictive interpolation (NPI). Linear (time- and frequency-domain) and nonlinear HRV parameters were calculated from corrupted-corrected time series, as well as for reference series to evaluate the accuracy of each correction method. Results show that NPI provides the overall best performance. However, several correction approaches, for example, the simple deletion procedure, can provide good performance in some situations, depending on the HRV parameters under consideration.

Concepts: Cardiology, Circulatory system, Linear interpolation, Time series analysis, Spline interpolation, Interpolation, Polynomial interpolation, Spline


Our overarching goal is to be able to describe both weak and strong correlation with a single, computationally affordable method without sacrificing important qualities of the wavefunction, e.g. symmetries of the Hamiltonian. We know that coupled cluster theory with low-order excitations is excellent at describing weakly-correlated systems near equilibrium, but breaks down as systems become more strongly correlated. Projected Hartree-Fock on the other hand is inherently capable of describing multireference character, but misses weak correlation. We are thus exploring how best to combine coupled cluster and projected Hartree-Fock in our search for a computationally feasible method that is applicable across a wide range of correlation strengths. In this manuscript, we adapt our earlier work on the pairing Hamiltonian to repulsive Hamiltonians, resulting in the spin polynomial similarity transformation (SpinPoST) interpolation. SpinPoST parameterizes the wavefunction in order to interpolate between the coupled cluster and spin-projected unrestricted Hartree-Fock ansätze self consistently, and is a spin-symmetry adapted model which involves only single and double excitations. We employ a unique approach of optimizing the wavefunction by minimizing the effect of connected quadruple excitations, resulting in a method which is spin-symmetry adapted and is comparable energetically to coupled cluster with singles and doubles for weak correlation and spin-projected Hartree-Fock for strong correlation.

Concepts: Linear interpolation, Numerical analysis, Coupled cluster, Interpolation


This paper investigates the task assignment and path planning problem for multiple AUVs in three dimensional (3D) underwater wireless sensor networks where nonholonomic motion constraints of underwater AUVs in 3D space are considered. The multi-target task assignment and path planning problem is modeled by the Multiple Traveling Sales Person (MTSP) problem and the Genetic Algorithm (GA) is used to solve the MTSP problem with Euclidean distance as the cost function and the Tour Hop Balance (THB) or Tour Length Balance (TLB) constraints as the stop criterion. The resulting tour sequences are mapped to 2D Dubins curves in the X - Y plane, and then interpolated linearly to obtain the Z coordinates. We demonstrate that the linear interpolation fails to achieve G 1 continuity in the 3D Dubins path for multiple targets. Therefore, the interpolated 3D Dubins curves are checked against the AUV dynamics constraint and the ones satisfying the constraint are accepted to finalize the 3D Dubins curve selection. Simulation results demonstrate that the integration of the 3D Dubins curve with the MTSP model is successful and effective for solving the 3D target assignment and path planning problem.

Concepts: Euclidean space, Linear interpolation, Problem solving, Numerical analysis, Distance, Metric space, Linear programming, Autonomous underwater vehicle