The discrete harmonic wavelet transform was developed by Newland in 1993 1, 2 . Similar to the ordinary discrete wavelet transform, the classical harmonic wavelet transform can also perform multiresolution analysis of a function. In addition, it has a fast algorithm based on fast Fourier transform for numerical implementation. A distinct advantage of harmonic wavelets is that they are disjoint ...

New methods for compact image coding based on generalized wavelet decompositions have been introduced recently. Unlike in the classical wavelet decomposition scheme it is possible to use diier-ent scaling and wavelet functions at every scale by using non-stationary multiresolution analyses. In this work we introduce parallel algorithms (suitable for MIMD architectures) that excel the execution ...

Abstract. In order to get an efficient representation of images which contain orientated edges we construct a directional wavelet basis for L(R). The wavelets basis consists of Haar wavelets with compact support on triangles. In comparison with the classical wavelet transform our functions offer two more directions (diagonal directions). Applying our simple wavelet system to image denoising and...

This communication aims to combine several previously proposed wavelet denoising algorithms into a novel heuristic block method. The proposed “hysteresis” thresholding uses two thresholds simultaneously in order to combine detection and minimal alteration of informative features of the processed signal. This approach exploits the graph structure of the wavelet decomposition to detect clusters o...

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for ...

Recent advances in applied mathematics and signal processing have shown that, in order to obtain sparse representations of multi-dimensional functions and signals, one has to use representation elements distributed not only at various scales and locations – as in classical wavelet theory – but also at various directions. In this paper, we show that we obtain a construction having exactly these ...

New methods for lossy image compression based on generalized wavelet decompositions have been introduced recently. Unlike in the classical wavelet decomposition scheme it is possible to use diierent scaling and wavelet functions at every scale by using non-stationary multiresolution analyses. This freedom in using diierent functions can be exploited for adaptive compression techniques. In this ...

In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of nding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p (Lp), p 1, the optim...