This paper addresses the problem of estimating, analyzing and tracking objects moving with spatio-temporal rotational motion (spin or orbit). It is assumed that the digital signals of interest are acquired from a camera and structured as digital image sequences. The trajectories in the signal are two-dimensional spatial projections in time of motion taking place in a three-dimensional space. Th...

Fourier transform has been shown to be a powerful tool in many area of science. However, there is another class of unitary transforms, the wavelet transforms, which are as useful as the Fourier transform. Wavelet transforms are used to expose the multi-scale structure of a signal and very useful for image processing and data compression. In this paper, we construct quantum algorithms for Haar w...

Much work has been done to optimize wavelet transforms for SIMD extensions of modern CPUs. However, these approaches are mostly restricted to the vertical part of 2-D transforms with line-wise organized memory layouts because this leads to a rather straight forward SIMD-implementation. This work shows for an example of a common wavelet filter new approaches to use SIMD operations on 1-D transfo...

This papers gives an overview of wavelet transforms application to signal denoising problem. Wavelets perform well for this application and have been used before with great success. To further improve the transform efficiency adaptivity is introduced to traditional wavelet transforms. The lifting framework as a method to construct wavelets facilitates the effort to develop efficient adaptation ...

Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequ...

We present new multiwavelet transforms for discrete signals. The transforms are implemented in two phases: 1. Pre (post)processing which transform the scalar signal into the vector one (and back). 2.Wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting aggregate in the vector wavelet transform. We p...

Investigation of the dynamics of internal gravity waves often includes the interrelationship between wave amplitudes, wave speeds, and wavelengths. These relationships are commonly thought of as dispersion relations. Because internal gravity waves are the result of nonlinear dynamics dispersion relations are a challenge to obtain in a quantitative sense. Model data for internal gravity waves in...

JPEG-2000 is the latest image coding standard and is based on wavelet transforms and dyadic spectral decompositions. We have adapted the JPEG-2000 image coder for use with uniform transforms, by replacing the wavelet stage by lapped transforms. We set code-blocks that do not cross subband boundaries and encode the lapped transform coefficients directly as if they were wavelet ones. Results indi...

This thesis deals with applied mathematics with wavelets as a joint subject. There is an introduction and two extensive papers, of which one is already published in an international journal. The introduction presents wavelet theory including both the discrete and continuous wavelet transforms, the corresponding Fourier transforms, wavelet packets and the uncertainty principle. Moreover, it is a...

Invertible wavelet transforms that map integers to integers have important applications in lossless coding. In this paper we present two approaches to build integer to integer wavelet transforms. The first approach is to adapt the precoder of Laroia et al., which is used in information transmission; we combine it with expansion factors for the high and low pass band in subband filtering. The se...