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.

Characterization of Dirac-structure edges with wavelet transform

Abstract: This paper aims at studying the characterization of Dirac-structure edges with wavelet transform, and selecting the suitable wavelet functions to detect them. Three significant characteristics of the local maximum modulus of the wavelet transform with respect to the Dirac-structure edges are presented: (1) slope invariant: the local maximum modulus of the wavelet transform of a Dirac-structure edge is independent on the slope of the edge; (2) grey-level invariant: the local maximum modulus of the wavelet transform with respect to a Dirac-structure edge takes place at the same points when the images with different grey-levels are processed; and (3) width light-dependent: for various widths of the Dirac-structure edge images, the location of maximum modulus of the wavelet transform varies lightly under the certain circumscription that the scale of the wavelet transform is larger than the width of the Dirac-structure edges. It is important, in practice, to select the suitable wavelet functions, according to the structures of edges. For example, Haar wavelet is better to represent brick-like images than other wavelets. A mapping technique is applied in this paper to construct such a wavelet function. In this way, a low-pass function is mapped onto a wavelet function by a derivation operation. In this paper, the quadratic spline wavelet is utilized to characterize the Dirac-structure edges and a novel algorithm to extract the Dirac-structure edges by wavelet transform is also developed.

Image watermarking scheme using nonnegative matrix factorization and wavelet transform

Abstract: We introduce a robust image watermarking scheme for copyright protection using discrete wavelet transform (DWT) and nonnegative matrix factorization (NMF). The core idea of the proposed approach is to decompose an image into four wavelet sub-bands and then apply NMF to the blocks of each sub-band, followed by an eigendecomposition distortion step. The experimental results clearly show a better visual imperceptibility and an excellent resiliency of the proposed watermarking scheme against intentional and geometric attacks.

The history and current status of fourier transform spectroscopy.

Abstract: This paper is concerned with the development of Fourier transform spectroscopy from its beginnings in Michelson's visibility technique through the present day application using modern digital computers. Methods used in maximizing the efficiency of the computation, as well as the interferometer, are discussed. Means of finding the Fourier transform other than by digital computer are mentioned, and currently available commercial instruments are named.

Continuous and discrete Fourier transforms of steplike waveforms

Abstract: A steplike waveform which has attained its final value is converted into a duration-limited one which preserves the spectrum of the original waveform and is suitable for discrete Fourier transform (DFT) computations. The method, which is based upon the response of a time-invariant linear system excited by a rectangular pulse of suitable duration, is first applied to continuous waveforms and then to discrete (sampled) waveforms. The difference (errors) between the spectra of a continuous waveform and a discrete representation of it are reviewed.

Rapid computation of the discrete Fourier transform

Abstract: Algorithms for the rapid computation of the forward and inverse discrete Fourier transform for points which are nonequispaced or whose number is unrestricted are presented. The computational procedure is based on approximation using a local Taylor series expansion and the fast Fourier transform (FFT). The forward transform for nonequispaced points is computed as the solution of a linear system involving the inverse Fourier transform. This latter system is solved using the iterative method GMRES with preconditioning. Numerical results are given to confirm the efficiency of the algorithms.