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: A new method is presented that is capable of extracting the full 2D phase distribution from a single fringe pattern and is compared with the Fourier transform and the integration methods, and an important conclusion that the phase of the optical fringe pattern is equal to thephase of its wavelet transform on the ridge of the wave let transform is theoretically clarified.
Abstract: A new method for phase retrieval of optical fringe patterns is presented This method is based on a wavelet transform and is capable of extracting the full 2D phase distribution from a single fringe pattern An important conclusion that the phase of the optical fringe pattern is equal to the phase of its wavelet transform on the ridge of the wavelet transform is theoretically clarified The method is compared with the Fourier transform and the integration methods A numerical simulation and an experimental example of phase retrieval are shown
153 citations
12 May 1998
TL;DR: This paper develops two new adaptive wavelet transforms based on the lifting scheme, which 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.
152 citations
TL;DR: In this paper, an image analysis technique using the Fourier transform of the image to evaluate orientation in a fibrous assembly is presented. And the results are compared with those for the tracking method presented in Part II.
Abstract: This paper addresses the development of an image analysis technique using the Fourier transform of the image to evaluate orientation in a fibrous assembly. The algorithms are evaluated using simulated images presented in Part I of the series. The results are compared with those for the tracking method presented in Part II.
151 citations
TL;DR: The fractional Fourier transform (FFT) as discussed by the authors is a generalization of the ordinary FFT with an order parameter a, and it is used to interpolate between a function f(u) and its FFT F(μ).
Abstract: Publisher Summary This chapter is an introduction to the fractional Fourier transform and its applications. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a . Mathematically, the a th order fractional Fourier transform is the a th power of the Fourier transform operator. The a = 1st order fractional transform is the ordinary Fourier transform. In essence, the a th order fractional Fourier transform interpolates between a function f(u) and its Fourier transform F(μ) . The 0th order transform is simply the function itself, whereas the 1st order transform is its Fourier transform. The 0.5th transform is something in between, such that the same operation that takes us from the original function to its 0.5 th transform will take us from its 0.5th transform to its ordinary Fourier transform. More generally, index additivity is satisfied: The a 2 th transform of the a 1 th transform is equal to the ( a 2 + a 1 )th transform. The –1th transform is the inverse Fourier transform, and the – a th transform is the inverse of the a th transform.
151 citations
TL;DR: Two-stage mapping-based complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping to create a directional, non-redundant, complexWavelet transform with potential benefits for image coding systems.
Abstract: Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce two-stage mapping-based complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, non-redundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and non-redundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we can exploit this flexibility to create the complex double-density DWT (CDDWT): a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3/sup m/-1/2/sup m/-1) in m dimensions. To the best of our knowledge, no other transform achieves all these properties at a lower redundancy.
150 citations