In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of nding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p (Lp), p 1, the optim...

In order to release the limitations on the computational complexity and the detail missing of the traditional interpolation algorithm, this paper proposes a double channel hybrid interpolation algorithm for superresolution reconstruction that can not only reduce the complexity effectively but also keep the details of the image sufficiently. The improved algorithm involves following methods: fir...

Based on analysis of cubic spline interpolation, the differentiation formulas of the cubic spline interpolation on the three boundary conditions are put up forward in this paper. At last, this calculation method is illustrated through an example. The numerical results show that the spline numerical differentiations are quite effective for estimating first and higher derivatives of equally and u...

Given a finite subset Ξ ⊂ R and data |Ξ , the surface spline interpolant to the data |Ξ is a function s which minimizes a certain seminorm subject to the interpolation conditions |Ξ = |Ξ . It is known that surface spline interpolation is stable on the Sobolev space W in the sense that ‖s‖L∞(Ω) ≤ const ‖f‖Wm , where m is an integer parameter which specifies the surface spline. In this note we sh...

In this paper the one-dimensional two-phase Stefan problem is studied analytically leading to a system of non-linear Volterra-integral-equations describing heat distribution in each phase. For unified transform method has been employed which provides via global relation, by these problems can be solved using integral representations. To do this, underlying partial differential equation rewritte...

This paper deals with fast image and video segmentation using active contours. Region based active contours using level-sets are powerful techniques for video segmentation but they suffer from large computational cost. A parametric active contour method based on B-Spline interpolation has been proposed in [1] to highly reduce the computational cost but this method is sensitive to noise. Here, w...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while second DQM. resulting system of ODEs solved by SSP RK43 method after aforementioned spatially discretized. To assess success chosen tactics, a comparison errors shown. graphs can...