We present a general framework for the design and efficient implementation of various types of running (or over-sampled) wavelet transforms (RWT) using polynomial splines. Unlike previous techniques, the proposed algorithms are not necessarily restricted to scales that are powers of two; yet they all achieve the lowest possible complexity : 0(N) per scale, where N is signal length. In particula...

We study p-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating MRAs (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions. We also suggest a method for the construction of wavelet functions and prove that any wavelet function generates a p-adic wavelet frame.

Every m th order cardinal spline wavelet is a linear combination of the functions fN (l) m+l (2x?j); j 2 Zg. Here the function N m is the m th order cardinal B-spline. In this paper we prove that the single function N (l) m+l (2x), or N (l) m+l (2x ? 1) is a wavelet when m and l satisfy some mild conditions. As l decreases, so does the support of the wavelet. When l increases, the smoothness of...

This paper concerns the issue of wavelet analysis of signals by continuous and discrete wavelet transforms (CWT – Continous Wavelet Transform, DWT – Discrete Wavelet Transform). The main goal of our work was to develop a program which, through the CWT and the DWT analyses, would obtain graph of time-scale changes and would transform it into the spectrum, that is a graph of frequency changes. In...

In this paper we propose an image super-resolution algorithm using wavelet-domain Hidden Markov Tree (HMT) model. Wavelet-domain HMT models the dependencies of multiscale wavelet Coefficients through the state probabilities of wavelet coefficients, whose distribution densities can be approximated by the Gaussian mixture. Because wavelet-domain HMT accurately characterizes the statistics of real...

Wavelet analyses of tunable diode laser absorption spectroscopy signals were performed. The absorption spectroscopy data were obtained by repeatedly scanning the beams from a tunable diode laser operating in the near infrared across absorption lines of gaseous NH(3) contained within a windowed glass tube. The laser was modulated and wavelet analyses of the absorption data were performed. It was...

New methods for lossy image compression based on wavelet theory are introduced. Unlike the classical wavelet decomposition scheme it is possible to have diierent scaling and wavelet lters at every scale by using non-stationary multiresolution analyses. For the bidimensional case inhomogeneous multires-olution analyses using diierent wavelet lters for the two variables are introduced. Beyond it,...