Topic
Harmonic wavelet transform
About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.
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TL;DR: In this paper, the wavelet transform is used as a time-frequency representation for the determination of modal parameters such as natural frequencies, damping ratios and mode shapes of a vibrating system.
174 citations
15 Jan 1999
TL;DR: In this article, two adaptive wavelet transforms based on the lifting scheme were developed. But the lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms.
Abstract: This paper develops two new adaptive wavelet transforms based on the lifting scheme. The lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We use the lifting construction to adaptively tune a wavelet transform to a desired signal by optimizing data-based prediction error criteria. The performances of the new transforms are compared to existing wavelet transforms, and applications to signal denoising are investigated.
173 citations
13 Nov 2003
TL;DR: In this paper, a non-separable oriented 3-D dual-tree wavelet transform is proposed for video denoising, which gives a motion-based multi-scale decomposition for video.
Abstract: The denoising of video data should take into account both temporal and spatial dimensions, however, true 3D transforms are rarely used for video denoising. Separable 3-D transforms have artifacts that degrade their performance in applications. This paper describes the design and application of the non-separable oriented 3-D dual-tree wavelet transform for video denoising. This transform gives a motion-based multi-scale decomposition for video - it isolates in its subbands motion along different directions. In addition, we investigate the denoising of video using the 2-D and 3-D dual-tree oriented wavelet transforms, where the 2-D transform is applied to each frame individually.
171 citations
TL;DR: The theory of various established and novel techniques are reviewed, pointing out their assumptions, adaptability, and expected time-frequency localization, and their performances on a provided collection of benchmark signals are illustrated.
Abstract: Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.
171 citations
TL;DR: A new algorithm to recognize a two-dimensional object of arbitrary shape is presented and shows that, compared with the use of Fourier descriptors, this algorithm gives more stable and accurate results.
Abstract: A new algorithm to recognize a two-dimensional object of arbitrary shape is presented. The object boundary is first represented by a one-dimensional signal. This signal is then used to build the wavelet transform zero-crossing representation of the object. The algorithm is invariant to translation, rotation and scaling. Experimental results show that, compared with the use of Fourier descriptors, our algorithm gives more stable and accurate results.
171 citations