0000000001262817
AUTHOR
Valery Zheludev
Analytic and directional wavelet packets in the space of periodic signals
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based orthonormal WPs designed in [2]. The imaginary parts are the so-called complementary orthonormal WPs, which, unlike the symmetric regular WPs, they are antisymmetric. Tensor products of 1D quasi-analytic WPs provide a diversity of 2D WPs oriented in multiple directions. For example, a set of the fourth-level WPs comprises 62 different directions. The designed computational scheme in the paper enables us to get fast and easy implementation of the WP transforms…
Fast Computation by Subdivision of Multidimensional Splines and Their Applications
We present theory and algorithms for fast explicit computations of uni- and multi-dimensional periodic splines of arbitrary order at triadic rational points and of splines of even order at diadic rational points. The algorithms use the forward and the inverse Fast Fourier transform (FFT). The implementation is as fast as FFT computation. The algorithms are based on binary and ternary subdivision of splines. Interpolating and smoothing splines are used for a sample rate convertor such as resolution upsampling of discrete-time signals and digital images and restoration of decimated images that were contaminated by noise. The performance of the rate conversion based spline is compared with the…
Local cubic splines on non-uniform grids and real-time computation of wavelet transform
In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are designed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, the splines use either clean or noised arbitrarily-spaced samples. Formulas for the spline’s extrapolation beyond the sampling interval are established. Sharp estimations of the approximation errors are presented. The capability to adapt the grid to the structure of an object and to have minimal requirements to the operating memory are of great advantages for offline processing of s…