The Experts below are selected from a list of 79113 Experts worldwide ranked by ideXlab platform

Maarten V. De Hoop - One of the best experts on this subject based on the ideXlab platform.

  • Discrete Almost-Symmetric Wave Packets and Multiscale Geometrical Representation of (Seismic) Waves
    IEEE Transactions on Geoscience and Remote Sensing, 2010
    Co-Authors: Anton A. Duchkov, Fredrik Andersson, Maarten V. De Hoop
    Abstract:

    We discuss a multiscale geometrical representation of (seismic) waves through a decomposition into wave packets. Wave packets can be thought of as certain localized “fat” plane waves. Here, we construct Discrete almost-symmetric 3-D wave packets by using the unequally spaced fast Fourier Transform. The resulting Discrete Transform is unitary, implying that the reconstruction operator is simply the adjoint of the decomposition operator. Another relevant aspect of the discretization scheme is the appearance of parameters that control the tiling of the phase space that corresponds with the dyadic parabolic decomposition, preserving the relative parabolic scaling while adapting to the physical problem at hand. We consider applications in exploration and global seismology, in particular for higher dimensional data regularization, seismic map migration, denoising, directional regularity analysis, and feature extraction.

M J Shensa - One of the best experts on this subject based on the ideXlab platform.

  • the Discrete wavelet Transform wedding the a trous and mallat algorithms
    IEEE Transactions on Signal Processing, 1992
    Co-Authors: M J Shensa
    Abstract:

    Two separately motivated implementations of the wavelet Transform are brought together. It is observed that these algorithms are both special cases of a single filter bank structure, the Discrete wavelet Transform, the behavior of which is governed by the choice of filters. In fact, the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the Discrete wavelet Transform is exact. Moreover, it is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the Discrete wavelet Transform is provided, and conditions are derived under which it computes the continuous wavelet Transform exactly. Suitable filter constraints for finite energy and boundedness of the Discrete Transform are also derived. Relevant signal processing parameters are examined, and it is observed that orthonormality is balanced by restrictions on resolution. >

  • The Discrete Wavelet Transform
    1991
    Co-Authors: M J Shensa
    Abstract:

    Abstract : In a general sense, this report represents an effort to clarify the relationship of Discrete and continuous wavelet Transforms. More narrowly, it focuses on bringing together two separately motivated implementations of the wavelet Transform, the algorithm a trous and Mallat's multiresolution decomposition. These algorithms are special cases of a single filter bank structure, the Discrete wavelet Transform, the behavior of which is governed by one's choice of filters. In fact, the a trous algorithm, originally devised as a computationally efficient implementation, is more properly viewed as a nonorthogonal multiresolution algorithm for which the Discrete wavelet Transform is exact. Moreover, we show that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the Discrete wavelet Transform is provided, and conditions are derived under which it computer the continuous wavelet Transform exactly. Suitable filter constraints for finite energy and boundedness of the Discrete Transform are also derived. Finally, relevant signal-processing parameters are examined, and it is remarked that orthonormality is balanced by restrictions on resolution.

Anton A. Duchkov - One of the best experts on this subject based on the ideXlab platform.

  • Discrete Almost-Symmetric Wave Packets and Multiscale Geometrical Representation of (Seismic) Waves
    IEEE Transactions on Geoscience and Remote Sensing, 2010
    Co-Authors: Anton A. Duchkov, Fredrik Andersson, Maarten V. De Hoop
    Abstract:

    We discuss a multiscale geometrical representation of (seismic) waves through a decomposition into wave packets. Wave packets can be thought of as certain localized “fat” plane waves. Here, we construct Discrete almost-symmetric 3-D wave packets by using the unequally spaced fast Fourier Transform. The resulting Discrete Transform is unitary, implying that the reconstruction operator is simply the adjoint of the decomposition operator. Another relevant aspect of the discretization scheme is the appearance of parameters that control the tiling of the phase space that corresponds with the dyadic parabolic decomposition, preserving the relative parabolic scaling while adapting to the physical problem at hand. We consider applications in exploration and global seismology, in particular for higher dimensional data regularization, seismic map migration, denoising, directional regularity analysis, and feature extraction.

Kurt Kubik - One of the best experts on this subject based on the ideXlab platform.

  • Shift, scaling and derivative properties for the Discrete cosine Transform
    Signal Processing, 2006
    Co-Authors: Robert Reeves, Kurt Kubik
    Abstract:

    A set of DCT domain properties for shifting and scaling by real amounts, and taking linear operations such as differentiation is described. The DCT coefficients of a sampled signal are subjected to a linear Transform, which returns the DCT coefficients of the shifted, scaled and/or differentiated signal. The properties are derived by considering the inverse Discrete Transform as a cosine series expansion of the original continuous signal, assuming sampling in accordance with the Nyquist criterion. This approach can be applied in the signal domain, to give, for example, DCT based interpolation or derivatives. The same approach can be taken in decoding from the DCT to give, for example, derivatives in the signal domain. The techniques may prove useful in compressed domain processing applications, and are interesting because they allow operations from the continuous domain such as differentiation to be implemented in the Discrete domain. An image matching algorithm illustrates the use of the properties, with improvements in computation time and matching quality.

M.r. Petraglia - One of the best experts on this subject based on the ideXlab platform.

  • ICASSP - A method for fast approximate computation of Discrete time Transforms
    International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: Sanjit K. Mitra, O.v. Shentov, M.r. Petraglia
    Abstract:

    The fast approximated Discrete Transform is proposed as a method for reducing the time necessary to compute the Discrete Transform of a finite-length sequence. It is based on a subband decomposition and can be viewed as a link between the fast Transform methods (like the fast Fourier Transform), which compute all points in the Transform domain, and the variety of methods to evaluate the Discrete Transforms at a given set of points. The method uses knowledge about the input signal to obtain an approximation to its Transform by discarding the computations in bands that have little or no energy contribution. In a number of practical cases the proposed fast approximation is reasonably accurate, and in all cases the method can be iterated to yield the exact Transform, if necessary. >