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This paper presents an interpolation method based on shifted versions of two piecewise linear generators, which provides approximation order 2 like usual piecewise-linear interpolation; i.e., this method is able to represent the constant and the ramp exact ...
We consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomials. We demonstrate that by using an adequate sampling kernel and a sampli ...
We review the current state of Fourier and Chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations. Throughout the discussion we emphasize recent develop ...
We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation ...
Due to magnetic field inhomogeneities, EPI images are geometrically distorted, predominantly along the phase-encoding direction. Currently, the distortion is either ignored or compensated manually using a warping function defined through a set of landmarks ...
We extended Gross's method of volume wavelet rendering by computing splats via an orthogonal projection operator. The method decomposes the volume data into a wavelet pyramid representation in the spline domain. The splats of the basis functions are approx ...
The most essential ingredient of interpolation is its basis function. We have shown in previous papers that this basis need not be necessarily interpolating to achieve good results. On the contrary, several recent studies have confirmed that non-interpolat ...
Wavelet or sub–band coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate–distortion (RD) bounds for the wavelet approximati ...
The standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate. However, one can obtain more accurate results if one applies a filter prior to sampling, a fact well ...
We present a simple, original method to improve piecewise linear interpolation with uniform knots: We shift the sampling knots by a fixed amount, while enforcing the interpolation property. Thanks to a theoretical analysis, we determine the optimal shift t ...