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Multidimensional Seismic Compression by Hybrid Transform with Multiscale-Based Coding

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Handbook of Geomathematics

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Abstract

We present algorithms that compress two- and three-dimensional seismic data arrays. These arrays are piecewise smooth in the horizontal directions and have oscillating events in the vertical direction. The transform part of the compression process is an algorithm that combines wavelet and the local cosine transform (LCT). The quantization and the entropy coding parts of the compression were taken from wavelet-based coding such as set partitioning in hierarchical trees (SPIHT) and embedded zerotree wavelet (EZW) encoding/decoding schemes that efficiently use the multiscale (multiresolution) structure of the wavelet coefficients. To efficiently apply these codecs (SPIHT or EZW) to a mixed coefficient array, reordering of the LCT coefficients takes place. This algorithm outperforms other algorithms that are based only on the 2D wavelet transforms such as JPEG 2000 standard. The algorithms retain fine oscillatory events including texture even at low bit rate. The wavelet part in the mixed transform of the hybrid algorithm utilizes the library of Butterworth wavelet transforms that outperforms the commonly used 9/7 biorthogonal wavelets. In the 3D case, the 2D wavelet transform is applied to horizontal planes while the LCT is applied to its vertical direction. After reordering the LCT coefficients, the 3D coding (SPIHT or EZW) is applied. In addition, a 3D compression method for visualization is described. For this, the data cube is decomposed into relatively small cubes, which are processed separately.

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Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Amir Z. Averbuch, Valery A. Zheludev & Dan D. Kosloff

Authors
  1. Amir Z. Averbuch
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  2. Valery A. Zheludev
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  3. Dan D. Kosloff
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Correspondence to Amir Z. Averbuch .

Editor information

Editors and Affiliations

  1. Geomathematische Gruppe, TU Kaiserslautern FB Mathematik, Kaiserslautern, Germany

    Willi Freeden

  2. University of Central Florida Dept. Mathematics, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Inst. Analysis, TU Braunschweig FB 1 Mathematik und Informatik, Braunschweig, Germany

    Thomas Sonar

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Averbuch, A.Z., Zheludev, V.A., Kosloff, D.D. (2013). Multidimensional Seismic Compression by Hybrid Transform with Multiscale-Based Coding. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27793-1_43-2

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  • DOI: https://doi.org/10.1007/978-3-642-27793-1_43-2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Online ISBN: 978-3-642-27793-1

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