Gibbs phenomenon ≈ Gibbs phenomenon
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Nodal Sampling: A New Image Reconstruction Algorithm for SMOS Open
Soil moisture and ocean salinity (SMOS) brightness temperature (TB) images and calibrated visibilities are related by the so-called G -matrix. Due to the incomplete sampling at some spatial frequencies, sharp transitions in the TB scenes g…
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Deringing and denoising in extremely under-sampled Fourier single pixel imaging Open
Undersampling in Fourier single pixel imaging (FSI) is often employed to reduce imaging time for real-time applications. However, the undersampled reconstruction contains ringing artifacts (Gibbs phenomenon) that occur because the high-fre…
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Removal of partial Fourier‐induced Gibbs (RPG) ringing artifacts in MRI Open
Purpose To investigate and remove Gibbs‐ringing artifacts caused by partial Fourier (PF) acquisition and zero filling interpolation in MRI data. Theory and Methods Gibbs ringing of fully sampled data, leading to oscillations around tissue …
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Gibbs‐ringing artifact removal based on local subvoxel‐shifts Open
Purpose To develop a fast and stable method for correcting the gibbs‐ringing artifact. Methods Gibbs‐ringing is a well‐known artifact which manifests itself as spurious oscillations in the vicinity of sharp image gradients at tissue bounda…
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Jumping with variably scaled discontinuous kernels (VSDKs) Open
In this paper we address the problem of approximating functions with discontinuities via kernel-based methods. The main result is the construction of discontinuous kernel-based basis functions. The linear spaces spanned by these discontinu…
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A New Image Denoising Method Based on Adaptive Multiscale Morphological Edge Detection Open
Wavelet transform is an effective method for removal of noise from image. But traditional wavelet transform cannot improve the smooth effect and reserve image’s precise details simultaneously; even false Gibbs phenomenon can be produced. T…
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An Infrared and Visible Image Fusion Algorithm Based on LSWT-NSST Open
Regarding the problems of image distortion, edge blurring, Gibbs phenomena in the traditional wavelet transform algorithm and the loss of subtle features in the Non-Subsampled Shearlet Transform (NSST), and considering the physical charact…
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Approximation of signals by general matrix summability with effects of Gibbs Phenomenon Open
In the proposed paper the degree of approximation of signals (functions) belonging to $Lip(\alpha,p_{n})$ class has been obtained using general sub-matrix summability and a new theorem is established that generalizes the results of Mittal …
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The importance of the photosynthetic Gibbs effect in the elucidation of the Calvin–Benson–Bassham cycle Open
The photosynthetic carbon reduction cycle, or Calvin–Benson–Bassham (CBB) cycle, is now contained in every standard biochemistry textbook. Although the cycle was already proposed in 1954, it is still the subject of intense research, and ev…
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The Gibbs Phenomenon and its Resolution Open
It is well known that given an arbitrary continuous and periodic function f(x), it is possible to represent it as a Fourier series. However, attempting to approximate a discontinuous or non periodic function, using a Fourier series, yields…
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Steady-state linear harmonic vibrations of multiple-stepped Euler-Bernoulli beams under arbitrarily distributed loads carrying any number of concentrated elements Open
In this paper, general beam vibration problems with several attachments under arbitrarily distributed harmonic loading are solved. A multiple-stepped beam is modelled by the Euler-Bernoulli beam theory and an extension of an efficient nume…
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On a class of splines free of Gibbs phenomenon Open
When interpolating data with certain regularity, spline functions are useful. They are defined as piecewise polynomials that satisfy certain regularity conditions at the joints. In the literature about splines it is possible to find severa…
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Stable discontinuous mapped bases: the Gibbs-Runge-Avoiding Stable\n Polynomial Approximation (GRASPA) method Open
The mapped bases or Fake Nodes Approach (FNA), introduced in [10], allows to\nchange the set of nodes without the need of resampling the function. Such\nscheme has been successfully applied in preventing the appearance of the Gibbs\nphenom…
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Gibbs phenomena for L<i><sup>q</sup></i>-best approximation in finite element spaces Open
Recent developments in the context of minimum residual finite element methods are paving the way for designing quasi-optimal discretization methods in non-standard function spaces, such as q -type Sobolev spaces. For q → 1, these methods h…
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Accuracy of High Order and Spectral Methods for Hyperbolic Conservation Laws with Discontinuous Solutions Open
Higher order and spectral methods have been used with success for elliptic and parabolic initial and boundary value problems with smooth solutions. On the other hand, higher order methods have been applied to hyperbolic problems with less …
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A class of C2 quasi-interpolating splines free of Gibbs phenomenon Open
In many applications, it is useful to use piecewise polynomials that satisfy certain regularity conditions at the joint points. Cubic spline functions emerge as good candidates having C 2 regularity. On the other hand, if the data points p…
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Bi-orthogonal wavelets for investigating Gibbs effects via oblique extension principle Open
Gibbs effect is generally known for Fourier and Wavelets expansions of a function in the neighborhood of its discontinuities points which deals with the nonuniform convergence of its truncated sums of these expansions. We study this phenom…
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A Piecewise Polynomial Harmonic Nonlinear Interpolatory Reconstruction Operator on Non Uniform Grids—Adaptation around Jump Discontinuities and Elimination of Gibbs Phenomenon Open
In this paper, we analyze the behavior of a nonlinear reconstruction operator called PPH around discontinuities. The acronym PPH stands for Piecewise Polynomial Harmonic, since it uses piecewise polynomials defined by means of an adaption …
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Gibbs-like phenomenon inherent in a lumped element model of a rod Open
The underlying assumption of a lumped element model is that a spatially distributed physical system can be approximated by a topology of discrete entities. The impact of this assumption is illustrated by a model of a finitely long elastic …
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Efficient function approximation on general bounded domains using wavelets on a cartesian grid Open
Fourier extension is an approximation method that alleviates the periodicity requirements of Fourier series and avoids the Gibbs phenomenon when approximating functions. We describe a similar extension approach using regular wavelet bases …
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Gibbs–Wilbraham phenomenon on Lagrange interpolation based on analytic weights on the unit circle Open
This paper is devoted to study Lagrange interpolation based on nodal systems constituted by the roots of para-orthogonal polynomials with respect to analytic weights on the unit circle. The presented results address, in addition to algorit…
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Image Quality Assessment for Gibbs Ringing Reduction Open
Gibbs ringing is an artefact that is inevitable in any imaging modality where the measurement is Fourier band-limited. It impacts the quality of the image by creating a ringing appearance around discontinuities. Many novel ways of suppress…
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A Novel Shape Representation Method for Complex Trademark Image Open
Trademark orthogonal representation is an important research field in artificial intelligence technology and has extensive applications in trademark retrieval and recognition. However, the Gibbs phenomenon arises when complex trademark sha…
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On solving some Cauchy singular integral equations by de la Vallée Poussin filtered approximation Open
The paper deals with the numerical solution of Cauchy Singular Integral Equations based on some non standard polynomial quasi–projection of de la Vallée Poussin type. Such kind of approximation presents several advantages over classical La…
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FECAM: Frequency Enhanced Channel Attention Mechanism for Time Series Forecasting Open
Time series forecasting is a long-standing challenge due to the real-world information is in various scenario (e.g., energy, weather, traffic, economics, earthquake warning). However some mainstream forecasting model forecasting result is …
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Attention-based Convolutional Neural Network for MRI Gibbs-ringing Artifact Suppression Open
Gibbs-ringing artifact is a common artifact in MRI image processing. As MRI raw data is taken in a frequency domain, 2D in- verse discrete Fourier transform is applied to visualize data. Inability to take inverse Fourier transform of full …
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A Family of 5-Point Nonlinear Ternary Interpolating Subdivision Schemes with C2 Smoothness Open
The occurrence of the Gibbs phenomenon near irregular initial data points is a widely known fact in curve generation by interpolating subdivision schemes. In this article, we propose a family of 5-point nonlinear ternary interpolating subd…
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Nonlinear 2D C1 Quadratic Spline Quasi-Interpolants on Triangulations for the Approximation of Piecewise Smooth Functions Open
The aim of this paper is to present and study nonlinear bivariate C1 quadratic spline quasi-interpolants on uniform criss-cross triangulations for the approximation of piecewise smooth functions. Indeed, by using classical spline quasi-int…
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An Adaptive Approach to Gibbs’ Phenomenon Open
Gibbs’ Phenomenon, an unusual behavior of functions with sharp jumps, is encountered while applying the Fourier Transform on them. The resulting reconstructions have high frequency oscillations near the jumps making the reconstructions far…
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Fast algorithms for band-limited extrapolation by over sampling and Fourier series Open
In this paper, fast algorithms for the extrapolation of band-limited signals are presented by the sampling theorem and Fourier series in the case of over sampling. Assume the band-limited signal is known in a finite interval. We update the…