In this paper, we propose an image reconstruction method utilizing an optimized adaptive interpolation kernel along with a 2D M-channel perfect reconstruction filter bank(M-ch PR-FB) structure. In particular, the proposed approach leads to sharper reconstructed images than a direct conversion, still preserving high frequency components of the original image by employing the subband processing o...

In this paper we perform a numerical study of Newton polynomial interpolation. We explore the Leja ordering of Chebyshev knots and the Fast Leja knots introduced by Reichel. In all previous publications we are aware of, the degree of interpolation polynomials in use is in the order of a few hundreds. We show that it is possible to employ degrees of up to one million or higher without a numerica...

The problems of polynomial interpolation with several variables present more difficulties than those one-dimensional interpolation. first problem is to study the regularity schemes. In fact, it well-known that, in contrast univariate case, there no universal space polynomials which admits unique Lagrange for all point sets a given cardinality, and so will depend on set <math xmlns="http://www.w...

A function and its first two derivatives are estimated by convolutions with well-chosen non-differentiable kernels. The convolutions are in turn approximated by Newton–Cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points. Precise numerical results are obtained with far fewer points than that in classic SPH, and error bounds are deriv...