19 October 1998 Decomposition and compression of Kirchhoff migration operator by adapted wavelet packet transform
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Abstract
Kirchhoff migration operator is a highly oscillatory integral operator. In our previous work (see `Seismic Imaging in Wavelet Domain', Wu and Yang, 1997), we have shown that the matrix representation of Kirchhoff migration operator for homogeneous background in space-frequency domain is a dense matrix, while the compressed beamlet- operator, which is the wavelet decomposition of the Kirchhoff migration operator in beamlet-frequency (space- scale-frequency) domain, is a highly sparse matrix. Using the compressed matrix for imaging, we can obtain high quality images with high efficiency. We found that the compression ratio of the migration operator is very different for different wavelet basis. In the present work, we study the decomposition and compression of Kirchhoff migration operator by adapted wavelet packet transform, and compare with the standard discrete wavelet transform (DWT). We propose a new maximum sparsity adapted wavelet packet transform (MSAWPT), which differs from the well-known Coifman-Wickerhauser's best basis algorithm, to implement the decomposition of Kirchhoff operator to achieve the maximum possible sparsity. From the numerical tests, it is found that the MSAWPT can generate a more efficient matrix representation of Kirchhoff migration operator than DWT and the compression capability of MSAWPT is much greater than that of DWT.
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Yongzhong Wang, Ru-Shan Wu, "Decomposition and compression of Kirchhoff migration operator by adapted wavelet packet transform", Proc. SPIE 3458, Wavelet Applications in Signal and Imaging Processing VI, (19 October 1998); doi: 10.1117/12.328142; https://doi.org/10.1117/12.328142
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KEYWORDS
Wavelets

Discrete wavelet transforms

Wavelet transforms

Wave propagation

Image compression

Data compression

3D image processing

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