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SIAM Review
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Computational Methods for Inverse Problems
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Atomic Decomposition by Basis Pursuit
SIAM Review
The fractional spline wavelet transform: definition end implementation
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 01
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
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IEEE Transactions on Image Processing
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IEEE Transactions on Signal Processing
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In this paper an alternative approach to the blind seismic deconvolution problem is presented that aims for two goals namely recovering the location and relative strength of seismic reflectors, possibly with super-localization, as well as obtaining detailed parametric characterizations for the reflectors. We hope to accomplish these goals by decomposing seismic data into a redundant dictionary of parameterized waveforms designed to closely match the properties of reflection events associated with sedimentary records. In particular, our method allows for highly intermittent non-Gaussian records yielding a reflectivity that can no longer be described by a stationary random process or by a spike train. Instead, we propose a reflector parameterization that not only recovers the reflector's location and relative strength but which also captures reflector attributes such as its local scaling, sharpness and instantaneous phase-delay. The first set of parameters delineates the stratigraphy whereas the second provides information on the lithology. As a consequence of the redundant parameterization, finding the matching waveforms from the dictionary involves the solution of an ill-posed problem. Two complementary sparseness-imposing methods Matching and Basis Pursuit are compared for our dictionary and applied to seismic data.