Abstract: A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.

Abstract: We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell center in a dimensionally unsplit fashion using the Corner Transport Upwind method. Time stepping relies on a characteristic tracing step where piecewise parabolic method, weighted essentially non-oscillatory, or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes, such as viscosity, resistivity, and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.

Abstract: In this paper, we present a new publicly available high-resolution daily precipitation gridded dataset developed for peninsular Spain and the Balearic islands using 2756 quality-controlled stations (this dataset is referred to as Spain02). The grid has a regular 0.2° (approx. 20 km) horizontal resolution and spans the period from 1950 to 2003. Different interpolation methods were tested using a cross-validation approach to compare the resulting interpolated values against station data: kriging, angular distance weighting, and thin plane splines. Finally, the grid was produced applying the kriging method in a two-step process. First, the occurrence was interpolated using a binary kriging and, in a second step, the amounts were interpolated by applying ordinary kriging to the occurrence outcomes. This procedure is similar to the interpolation method used to generate the E-OBS gridded data—the state-of-the-art publicly available high-resolution daily dataset for Europe—which was used in this study for comparison purposes. Climatological statistics and extreme value indicators from the resulting grid were compared to those from the 25 km E-OBS dataset using the observed station records as a reference. Spain02 faithfully reproduces climatological features such as annual precipitation occurrence, accumulated amounts and variability, whereas E-OBS has some deficiencies in the southern region. When focusing on upper percentiles and other indicators of extreme precipitation regimes, Spain02 accurately reproduces the amount and spatial distribution of the observed extreme indicators, whereas E-OBS data present serious limitations over Spain due to the sparse data used in this region. As extreme values are more sensitive to interpolation, the dense station coverage of this new data set was crucial to get an accurate reproduction of the extremes. Copyright © 2010 Royal Meteorological Society

Abstract: Local and global approaches to digital image correlation are compared when the displacement interpolation is based upon bilinear shape functions (i.e., with four-node quadrilaterals). The resolution in terms of displacements and strains associated with both techniques are evaluated a priori and validated a posteriori by using series of images of real experiments. It is shown that global approaches generally out-perform a local approach.

Abstract: This paper presents a 3-D near-field imaging algorithm that is formulated for 2-D wideband multiple-input-multiple-output (MIMO) imaging array topology. The proposed MIMO range migration technique performs the image reconstruction procedure in the frequency-wavenumber domain. The algorithm is able to completely compensate the curvature of the wavefront in the near-field through a specifically defined interpolation process and provides extremely high computational efficiency by the application of the fast Fourier transform. The implementation aspects of the algorithm and the sampling criteria of a MIMO aperture are discussed. The image reconstruction performance and computational efficiency of the algorithm are demonstrated both with numerical simulations and measurements using 2-D MIMO arrays. Real-time 3-D near-field imaging can be achieved with a real-aperture array by applying the proposed MIMO range migration techniques.

Abstract: 4 Interpolation & Constraints 12 4.1 Interpolation Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.1.1 Defaults in ROOT 5.32 . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Constraint Terms (+ global observables and nuisance parameter priors) . . . 16 4.2.1 Consistent Bayesian and Frequentist modeling . . . . . . . . . . . . . 16 4.2.2 Options for Constraint Terms . . . . . . . . . . . . . . . . . . . . . . . 17

Abstract: This paper compares two algorithms for three-dimensional target localization from passive radar measurements. The algorithms use bistatic range measurements from multiple transmitter-receiver pairs to calculate the target position. The algorithms derived are based on the methods known for time-difference-of-arrival (TDOA) systems, namely spherical interpolation (SI) and spherical intersection (SX). Both algorithms rely on closed-form equations. A theoretical accuracy analysis of the algorithms is provided. This analysis is verified with Monte-Carlo simulations and a real-life example is presented.

Abstract: This paper presents the nearest neighbor value (NNV) algorithm for high resolution (H.R.) image interpolation. The difference between the proposed algorithm and conventional nearest neighbor algorithm is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. In other words, the proposed concept selects one pixel, among four directly surrounding the empty location, whose value is almost equal to the value generated by the conventional bilinear interpolation algorithm. The proposed method demonstrated higher performances in terms of H.R. when compared to the conventional interpolation algorithms mentioned.

Abstract: A patch of prestack data depends on four spatial dimensions ( x , y midpoints and x , y offsets) and frequency. The spatial data at one temporal frequency can be represented by a fourth-order tensor. In ideal conditions of high signal-to-noise ratio and complete sampling, one can assume that the seismic data can be approximated via a low-rank fourth-order tensor. Missing samples were recovered by reinserting data obtained by approximating the original noisy and incomplete data volume with new observations obtained via the rank-reduction process. The higher-order singular value decompostion was used to reduce the rank of the prestack seismic tensor. Synthetic data demonstrated the ability of the proposed seismic data completion algorithm to reconstruct events with curvature. The synthetic example allowed to quantify the quality of the reconstruction for different levels of noise and survey sparsity. We also provided a real data example from the Western Canadian sedimentary basin.

Abstract: In this paper, we propose a new interpolation-based method of image super-resolution reconstruction. The idea is using multisurface fitting to take full advantage of spatial structure information. Each site of low-resolution pixels is fitted with one surface, and the final estimation is made by fusing the multisampling values on these surfaces in the maximum a posteriori fashion. With this method, the reconstructed high-resolution images preserve image details effectively without any hypothesis on image prior. Furthermore, we extend our method to a more general noise model. Experimental results on the simulated and real-world data show the superiority of the proposed method in both quantitative and visual comparisons.

Abstract: Image interpolation is a very important branch in image processing. It is widely used in imaging world, for example, image interpolation is often used in 3-D medical image to compensate for information insufficiency during image reconstruction by simulating additional images between two-dimensional images. Reversible data hiding has become significant branch in information hiding field. Reversibility allows the original media to be completely restored without any degradation after the embedded messages have been extracted. This study proposes a high-capacity image hiding scheme by exploiting an interpolating method called Interpolation by Neighboring Pixels (INP) on Maximum Difference Values to improve the performance of data hiding scheme proposed by Jung and Yoo. The proposed scheme offers the benefits of high embedding capacity with low computational complexity and good image quality. The experimental results showed that the proposed scheme has good performance for payload up to 2.28 bpp. Moreover, the INP yields higher PSNRs than other interpolating methods such as NMI, NNI and BI.

Abstract: The reconstruction of acoustical sources from discrete field measurements is a difficult inverse problem that has been approached in different ways Classical methods (beamforming, near-field acoustical holography, inverse boundary elements, wave superposition, equivalent sources, etc) all consist—implicitly or explicitly—in interpolating the measurements onto some spatial functions whose propagation are known and in reconstructing the source field by retropropagation This raises the fundamental question as whether, for a given source topology and array geometry, there exists an optimal interpolation basis which minimizes the reconstruction error This paper provides a general answer to this question, by proceeding from a Bayesian formulation that is ideally suited to combining information of physical and probabilistic natures The main findings are the followings: (1) The optimal basis functions are the M eigen-functions of a specific continuous-discrete propagation operator, with M being the number of microphones in the array (2) The a priori inclusion of spatial information on the source field causes super-resolution according to a phenomenon coined “Bayesian focusing” (3) The approach is naturally endowed with an internal regularization mechanism and results in a robust regularization criterion with no more than one minimum (4) It admits classical methods as particular cases

Abstract: Hardy’s multiquadric and its related interpolators have been found to be highly efficient for interpolating continuous, multivariate functions, as well as for the solution of partial differential equations. Particularly, the interpolation error can be dramatically reduced by varying the shape parameter to make the interpolator optimally flat. This improvement of accuracy is accomplished without reducing the fill distance of collocation points, that is, without the increase of computational cost. There exist a number of mathematical theories investigating the multiquadric family of radial basis functions. These theories are often not fully tested due to the computation difficulty associated with the ill-conditioning of the interpolation matrix. This paper overcomes this difficulty by utilizing arbitrary precision arithmetic in the computation. The issues investigated include conditional positive definiteness, error estimate, optimal shape parameter, traditional and effective condition numbers, round-off error, derivatives of interpolator, and the edge effect of interpolation.

Abstract: In this paper, we will discuss the problem of optimal model order reduction of bilinear control systems with respect to the generalization of the well-known ${\cal H}_2$-norm for linear systems. We...

Abstract: The main objective of this paper is to develop an efficient method for learning and reproduction of complex trajectories for robot programming by demonstration. Encoding of the demonstrated trajectories is performed with hidden Markov model, and generation of a generalized trajectory is achieved by using the concept of key points. Identification of the key points is based on significant changes in position and velocity in the demonstrated trajectories. The resulting sequences of trajectory key points are temporally aligned using the multidimensional dynamic time warping algorithm, and a generalized trajectory is obtained by smoothing spline interpolation of the clustered key points. The principal advantage of our proposed approach is utilization of the trajectory key points from all demonstrations for generation of a generalized trajectory. In addition, variability of the key points' clusters across the demonstrated set is employed for assigning weighting coefficients, resulting in a generalization procedure which accounts for the relevance of reproduction of different parts of the trajectories. The approach is verified experimentally for trajectories with two different levels of complexity.

Abstract: A key role of the CNC is to perform the feedrate interpolation which consists in generating the setpoints sent to each axis of a machine tool based on a NC program In high speed machining, the feedrate is limited by the velocity, acceleration and jerk of each axis of the machine tool The algorithm presented in this paper aims to obtain an optimized feedrate profile which makes best use of the kinematical characteristics of the machine This minimum time feedrate profile is computed by intersecting all the constraints due to the drives in an iterative algorithm It is worth noting that both tangential jerk and axis jerk are taken into consideration The proposed VPOp (Velocity Profile Optimization) method is universal and can be applied to any articulated mechanical structure as it is demonstrated in the examples Moreover the algorithm has been implemented for various formats: linear interpolation (G1) and NURBS interpolation in 3- and 5-axes The effectiveness of the algorithm is demonstrated thanks to a comparison with an industrial CNC and can be freely tested using the VPOp software which is available on the Internet http://webservlurpaens-cachanfr/geo3d/premium/vpop

Abstract: I introduce a unified approach for denoising and interpolation of seismic data in the frequency-wavenumber (f-k) domain. First, an angular search in the f-k domain is carried out to identify a sparse number of dominant dips, not only using low frequencies but over the whole frequency range. Then, an angular mask function is designed based on the identified dominant dips. The mask function is utilized with the least-squares fitting principle for optimal denoising or interpolation of data. The least-squares fit is directly applied in the time-space domain. The proposed method can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid. Synthetic and real data examples are provided to examine the performance of the proposed method.

Abstract: Image-zooming is a technique of producing a high-resolution image from its low-resolution counterpart. It is also called image interpolation because it is usually implemented by interpolation. Keys' cubic convolution (CC) interpolation method has become a standard in the image interpolation field, but CC interpolates indiscriminately the missing pixels in the horizontal or vertical direction and typically incurs blurring, blocking, ringing or other artefacts. In this study, the authors propose a novel edge-directed CC interpolation scheme which can adapt to the varying edge structures of images. The authors also give an estimation method of the strong edge for a missing pixel location, which guides the interpolation for the missing pixel. The authors' method can preserve the sharp edges and details of images with notable suppression of the artefacts that usually occur with CC interpolation. The experiment results demonstrate that the authors'method outperforms significantly CC interpolation in terms of both subjective and objective measures.

Abstract: This paper describes a three-dimensional immersed boundary method (IBM) that facilitates the explicit resolution of complex terrain within the Weather Research and Forecasting (WRF) model. Two interpolation methods—trilinear and inverse distance weighting (IDW)—are used at the core of the IBM algorithm. This work expands on the previous two-dimensional IBM algorithm of Lundquist et al., which uses bilinear interpolation. Simulations of flow over a three-dimensional hill are performed with WRF’s native terrain-following coordinate and with both IB methods. Comparisons of flow fields from the three simulations show excellent agreement, indicating that both IB methods produce accurate results. IDW proves more adept at handling highly complex urban terrain, where the trilinear interpolation algorithm fails. This capability is demonstrated by using the IDW core to model flow in Oklahoma City, Oklahoma, from intensive observation period 3 (IOP3) of the Joint Urban 2003 field campaign. Flow in Oklahoma C...

Abstract: In this paper, we present Ufo, a framework and a tool for verifying (and finding bugs in) sequential C programs. The framework is built on top of the LLVM compiler infrastructure and is targeted at researchers designing and experimenting with verification algorithms. It allows definition of different abstract post operators, refinement strategies and exploration strategies. We have built three instantiations of the framework: a predicate abstraction-based version, an interpolation-based version, and a combined version which uses a novel and powerful combination of interpolation-based and predicate abstraction-based algorithms.

Abstract: In this paper we present error estimates for kernel interpolation at scattered sites on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\math...

Abstract: Based on third-order Newton's Interpolation theory, this paper proposed one method to compute milling stability. The machining is first considered as a dynamic process expressed by a mathematical equation, and this equation integrates the regenerative effect utilizing a time delay item. The time period is discretized as a series of small elements. Then, in each time element, the third-order Newton's interpolation algorithm is used to approximate the state item of the equation. The time-period and time-delay items are expressed by liner-interpolation. After equation items are expressed using the interpolation method on the time period, a matrix denoting the machining system is built. Taking advantage of the matrix, the stability of milling process is investigated, and the convergence feature of the proposed method is also analyzed. Finally, examples of 1-dof and 2-dof dynamic systems are conducted and the comparison results show that the method is effective.

Abstract: The fingerprint-based approach for positioning in WLAN has been drawing great attention these days. However, the approach usually requires tremendous time and efforts to collect location fingerprints for the target area. In this paper, we propose an interpolation method based on Voronoi tessellation to significantly reduce such calibration efforts and to improve accuracy. Unlike other interpolation methods, our method refines the propagation model for each cell of the target area tessellated by a higher-order Voronoi diagram. Consequently, our method can take into account the signal fading caused by walls and obstacles more accurately. The proposed method significantly outperformed other interpolation methods in accuracy.

Abstract: Recent advances in radio environmental mapping enable novel, practical and efficient cognitive radio and dynamic spectrum access solutions. A crucial aspect of such solutions is to ensure the reliability of the constructed Radio Environmental Maps (REMs). Especially important is the accurate and up-to-date Radio Interference Field (RIF) estimation based on distributed spectrum use measurements. This paper analyzes the use of spatial interpolation techniques that allow robust, yet sufficiently reliable, RIF estimation from a limited number of field measurements. Several spatial interpolation techniques based on Inverse Distance Weighting (IDW) are analyzed and compared in terms of reliability bounds of the interpolation errors for an indoor environment. Performance evaluation using REM prototype implementation and a wireless testbed shows that the spatial interpolation techniques can provide a robust and reliable RIF estimation within the entire REM concept.