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 transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the Fast Fourier Transform (FFT) algorithm as discussed by the authors.
Abstract: A transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the 'fast Fourier transform' algorithm. The transform may be applied to the problem of calculating convolutions of long integer sequences by means of integer arithmetic.
431 citations
TL;DR: This report compares the three classical spectral analysis approaches: Fourier, Hilbert and wavelet transform and demonstrates that the three techniques are in fact formally (i.e. mathematically) equivalent when using the class of wavelets that is typically applied in spectral analyses.
430 citations
13 Nov 1994
TL;DR: In the image fusion scheme presented in this paper, the wavelet transforms of the input images are appropriately combined, and the new image is obtained by taking the inverse wavelet transform of the fused wavelet coefficients.
Abstract: In the image fusion scheme presented in this paper, the wavelet transforms of the input images are appropriately combined, and the new image is obtained by taking the inverse wavelet transform of the fused wavelet coefficients. An area-based maximum selection rule and a consistency verification step are used for feature selection. A performance measure using specially generated test images is also suggested. >
422 citations
26 Oct 1997
TL;DR: A novel approach to the fusion of spatially registered images and image sequences is proposed that incorporates a shift invariant extension of the discrete wavelet transform, which yields an overcomplete signal representation.
Abstract: In this paper, we propose a novel approach to the fusion of spatially registered images and image sequences. The fusion method incorporates a shift invariant extension of the discrete wavelet transform, which yields an overcomplete signal representation. The advantage of the proposed method is the improved temporal stability and consistency of the fused sequence compared to other existing fusion methods. We further introduce an information theoretic quality measure based on mutual information to quantify the stability and consistency of the fused image sequence.
403 citations
TL;DR: In this paper, the authors proposed a matching pursuit algorithm to map a seismogram into the frequency-time (FT) space of seismic data, and showed that the matching pursuit provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable.
Abstract: Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency-time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time-frequency resolution limitation. Recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition. The continuous wavelet transform with its scale-translation plane is conceptually best understood when contrasted to a short time Fourier transform. The discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into FT space. Decomposition into FT space of synthetic and calibrated explosive-source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable. Wavelet-based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods.
387 citations