Distribution theory and transform analysis: an introduction to generalized functions, with applications
An introduction to wavelets
Multirate systems and filter banks
Multirate systems and filter banks
Wavelets and subband coding
Approximation from shift-invariant spaces by integral operators
SIAM Journal on Mathematical Analysis
Fourier analysis and applications: filtering, numerical computation, wavelets
Fourier analysis and applications: filtering, numerical computation, wavelets
Image interpolation and resampling
Handbook of medical imaging
Oversampling in shift-invariant spaces with a rational sampling period
IEEE Transactions on Signal Processing
Quantitative Fourier analysis of approximation techniques. I.Interpolators and projectors
IEEE Transactions on Signal Processing
On the approximation power of convolution-based least squaresversus interpolation
IEEE Transactions on Signal Processing
MOMS: maximal-order interpolation of minimal support
IEEE Transactions on Image Processing
Quasi-Interpolating Spline Models for Hexagonally-Sampled Data
IEEE Transactions on Image Processing
| Hi-index | 35.68 |
We consider the problem of approximating a regular function f(t) from its samples, f(nT), taken in a uniform grid. Quasi-interpolation schemes approximate f(t) with a dilated version of a linear combination of shifted versions of a kernel ϕ(t), specifically fapproxT(t) = Σaf[n]ϕ(t/T - n), in a way that the polynomials of degree at most L - 1 are recovered exactly. These approximation schemes give order L, i.e., the error is O(TL) where T is the sampling period. Recently, quasi-interpolation schemes using a discrete prefiltering of the samples f(nT) to obtain the coefficients af[n], have been proposed. They provide tight approximation with a low computational cost. In this work, we generalize considering rational filter banks to prefilter the samples, instead of a simple filter. This generalization provides a greater flexibility in the design of the approximation scheme. The upsampling and downsampling ratio r of the rational filter bank plays a significant role. When r = 1, the scheme has similar characteristics to those related to a simple filter. Approximation schemes corresponding to smaller ratios give less approximation quality, but, in return, they have less computational cost and involve less storage load in the system.