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.

A fast method for the numerical evaluation of continuous Fourier and Laplace transforms

Abstract: The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems often requires a large FFT to be performed, even though most of the input data to this FFT may be zero and only a small fraction of the output data may be of interest. In this note, the “fractional Fourier transform,” previously developed by the authors, is applied to this problem with a substantial savings in computation.

Wavelet-based contourlet transform and its application to image coding

Abstract: In this paper, we first propose a new family of geometrical image transforms that decompose images both radially and angularly. Our construction comprises two stages of filter banks that are non-redundant and perfect reconstruction and therefore lead to an overall non-redundant and perfect reconstruction transform. Using the wavelet transform as the first stage, we apply directional filter banks to the wavelet coefficients in such a way to maintain the anisotropy scaling law. Furthermore, we propose a new image coding scheme based on the proposed transform, the wavelet-based contourlet transform (WBCT), using a new contourlet-based set partitioning in hierarchical trees (CSPIHT) algorithm that provides an embedded code. Due to differences in parent-child relationships between the WBCT coefficients and wavelet coefficients, under CSPIHT, we developed an elaborated repositioning algorithm for the WBCT coefficients in such a way that we could scan spatial orientation trees that are similar to the original SPIHT algorithm. Our experiments demonstrate that the proposed approach is efficient in coding images that possess mostly textures and contours. Our simulation results also show that this new coding approach is competitive to the wavelet coder in terms of the PSNR-rate curves, and is visually superior to the wavelet coder for the mentioned images.

Applications of Discrete and Continuous Fourier Analysis

Abstract: An applications oriented, introductory text covering the concepts and properties of Fourier Analysis. Emphasizes applications to real scientific and engineering problems. Defines the Fourier series, Fourier transform, and discrete Fourier transform. Includes over 200 illustrations.