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external.bib
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% This file was created with JabRef 2.6.
% Encoding: MacRoman
@CONFERENCE{erlangga08SINBADimf,
author = {Yogi A. Erlangga and K. Vuik and K. Oosterlee and D. Riyanti and R. Nabben},
title = {Iterative methods for 2{D}/3{D} {Helmholtz} operator},
booktitle = {SINBAD 2008},
year = {2008},
abstract = {We present an iterative method for solving the 2D/3D
Helmholtz equation. The method is mainly based on a
Krylov method, preconditioned by a special operator
which represents a damped Helmholtz operator. The
discretization of the preconditioning operator is
then solved by one multigrid sweep. It can be shown
that while the spectrum is bounded above by one, the
smallest eigenvalue of the preconditioned system is
of order $k^{-1}$. In this situation, the
convergence of a Krylov method will be proportional
to the frequency of the problem. Further convergence
acceleration can be achieved if eigenvalues of order
$k^{-1}$ are projected from the spectrum. This can
be done by a projection operator, similar to but
more stable than deflation. This projection operator
has been the core of a new multilevel method, called
multilevel Krylov method, proposed by Erlangga and
Nabben only recently. Putting the preconditioned
Helmholtz operator in this setting, a convergence
which is independent of frequency can be obtained.},
keywords = {Presentation, SINBAD, SLIM},
url = {http://slim.gatech.edu/SINBAD2008/Program_files/SINBAD2008_Erlangga_Ite.pdf}
}
@ARTICLE{berkhout97eom,
author = {A. J. Berkhout and D. J. Verschuur},
title = {Estimation of multiple scattering by iterative inversion, {Part} {I}: {Theoretical} considerations},
journal = {Geophysics},
year = {1997},
volume = {62},
pages = {1586-1595},
number = {5},
abstract = {A review has been given of the surface-related multiple
problem by making use of the so-called feedback
model. From the resulting equations it has been
concluded that the proposed solution does not
require any properties of the subsurface. However,
source-detector and reflectivity properties of the
surface need be specified. Those properties have
been quantified in a surface operator and this
operator is estimated as part of the multiple
removal problem. The surface-related multiple
removal algorithm has been formulated in terms of a
Neumann series and in terms of an iterative
equation. The Neumann formulation requires a
nonlinear optimization process for the surface
operator; while the iterative formulation needs a
number of linear optimizations. The iterative
formulation also has the advantage that it can be
integrated easily with another multiple removal
method. An algorithm for the removal of internal
multiples has been proposed as well. This algorithm
is an extension of the surface-related
method. Removal of internal multiples requires
knowledge of the macro velocity model between the
surface and the upper boundary of the multiple
generating layer. In part II (also published in this
issue) the success of the proposed algorithms has
been demonstrated on numerical experiments and field
data examples. {\copyright}1997 Society of
Exploration Geophysicists},
bdsk-url-1 = {http://library.seg.org/doi/abs/10.1190/1.1444261},
bdsk-url-2 = {http://dx.doi.org/10.1190/1.1444261},
date-added = {2008-05-07 18:38:50 -0700},
date-modified = {2008-08-14 14:46:15 -0700},
doi = {10.1190/1.1444261},
issue = {5},
keywords = {SRME},
publisher = {SEG},
url = {http://library.seg.org/doi/abs/10.1190/1.1444261}
}
@BOOK{biondo063ds,
author = {B. L. Biondi},
title = {3-{D} seismic imaging},
publisher = {SEG},
year = {2006},
number = {14},
series = {Investigations in Geophysics},
date-added = {2008-05-08 15:25:18 -0700},
date-modified = {2008-05-20 19:45:00 -0700},
issue = {14},
keywords = {imaging}
}
@ARTICLE{cordoba78wpa,
author = {A. C\'ordoba and C. Fefferman},
title = {Wave packets and {Fourier} integral operators},
journal = {Communications in Partial Differential Equations},
year = {1978},
volume = {3},
pages = {979-1005},
number = {11},
bdsk-url-1 = {http://dx.doi.org/10.1080/03605307808820083},
date-added = {2008-05-07 11:53:23 -0700},
date-modified = {2008-05-20 11:48:08 -0700},
doi = {10.1080/03605307808820083},
issue = {11},
keywords = {wave packets, FIO},
publisher = {Taylor \& Francis}
}
@PHDTHESIS{candes98rta,
author = {E. J. Cand\`es},
title = {Ridgelets: theory and applications},
school = {Stanford University},
year = {1998},
address = {Stanford, CA},
bdsk-url-1 = {http://www-stat.stanford.edu/%7Ecandes/papers/Thesis.ps.gz},
date-added = {2008-05-27 18:24:11 -0700},
date-modified = {2008-05-27 18:26:14 -0700},
keywords = {ridgelet transform}
}
@ARTICLE{candes05tcr,
author = {E. J. Cand\`es and L. Demanet},
title = {The curvelet representation of wave propagators is optimally sparse},
journal = {Communications on Pure and Applied Mathematics},
year = {2005},
volume = {58},
pages = {1472-1528},
number = {11},
abstract = {This paper argues that curvelets provide a powerful tool
for representing very general linear symmetric
systems of hyperbolic differential
equations. Curvelets are a recently developed
multiscale system [10, 7] in which the elements are
highly anisotropic at fine scales, with effective
support shaped according to the parabolic scaling
principle width ≈ length^2 at fine scales. We prove
that for a wide class of linear hyperbolic
differential equations, the curvelet representation
of the solution operator is both optimally sparse
and well organized. * It is sparse in the sense that
the matrix entries decay nearly exponentially fast
(i.e. faster than any negative polynomial), * and
well-organized in the sense that the very few
nonnegligible entries occur near a few shifted
diagonals. Indeed, we show that the wave group maps
each curvelet onto a sum of curvelet-like waveforms
whose locations and orientations are obtained by
following the different Hamiltonian flows---hence
the diagonal shifts in the curvelet representation.
A physical interpretation of this result is that
curvelets may be viewed as coherent waveforms with
enough frequency localization so that they behave
like waves but at the same time, with enough spatial
localization so that they simultaneously behave like
particles.},
bdsk-url-1 = {http://www-stat.stanford.edu/%7Ecandes/papers/CurveletsWaves.pdf},
date-added = {2008-05-07 11:10:43 -0700},
date-modified = {2008-08-14 14:57:23 -0700},
doi = {10.1002/cpa.20078},
issue = {11},
keywords = {curvelet transform, FIO},
pdf = {http://www-stat.stanford.edu/%7Ecandes/papers/CurveletsWaves.pdf}
}
@ARTICLE{candes06fdc,
author = {E. J. Cand\`es and L. Demanet and D. L. Donoho and L. Ying},
title = {Fast discrete curvelet transforms},
journal = {Multiscale Modeling and Simulation},
year = {2006},
volume = {5},
pages = {861-899},
number = {3},
abstract = {This paper describes two digital implementations of a
new mathematical transform, namely, the second
generation curvelet transform [12, 10] in two and
three dimensions. The first digital transformation
is based on unequally-spaced fast Fourier transforms
(USFFT) while the second is based on the wrapping of
specially selected Fourier samples. The two
implementations essentially differ by the choice of
spatial grid used to translate curvelets at each
scale and angle. Both digital transformations return
a table of digital curvelet coefficients indexed by
a scale parameter, an orientation parameter, and a
spatial location parameter. And both implementations
are fast in the sense that they run in O(n^2 log n)
flops for n by n Cartesian arrays; in addition, they
are also invertible, with rapid inversion algorithms
of about the same complexity. Our digital
transformations improve upon earlier
implementations---based upon the first generation of
curvelets---in the sense that they are conceptually
simpler, faster and far less redundant. The software
CurveLab, which implements both transforms presented
in this paper, is available at
http://www.curvelet.org.},
bdsk-url-1 = {http://dx.doi.org/10.1137/05064182X},
bdsk-url-2 = {http://www-stat.stanford.edu/%7Ecandes/papers/FDCT.pdf},
date-added = {2008-05-06 19:34:41 -0700},
date-modified = {2008-08-14 14:58:30 -0700},
doi = {10.1137/05064182X},
issue = {3},
keywords = {curvelet transform},
pdf = {http://www-stat.stanford.edu/%7Ecandes/papers/FDCT.pdf},
publisher = {SIAM}
}
@INCOLLECTION{candes00cas,
author = {E. J. Cand\`es and D. L. Donoho},
title = {Curvelets: a surprisingly effective nonadaptive representation of objects with edges},
booktitle = {Curve and surface fitting},
publisher = {Vanderbilt University Press},
year = {2000},
editor = {A. Cohen, C. Rahut, and L. L. Schumaker},
pages = {105-120},
address = {Nashville, TN},
abstract = {It is widely believed that to efficiently represent an
otherwise smooth ob ject with discontinuities along
edges, one must use an adaptive representation that
in some sense `tracks' the shape of the
discontinuity set. This folk-belief --- some would
say folk-theorem --- is incorrect. At the very
least, the possible quantitative advantage of such
adaptation is vastly smaller than commonly
believed. We have recently constructed a tight frame
of curvelets which provides stable, efficient, and
near-optimal representation of otherwise smooth ob
jects having discontinuities along smooth curves. By
applying naive thresholding to the curvelet
transform of such an ob ject, one can form m-term
approximations with rate of L2 approximation
rivaling the rate obtainable by complex adaptive
schemes which attempt to `track' the discontinuity
set. In this article we explain the basic issues of
efficient m-term approximation, the construction of
efficient adaptive representation, the construction
of the curvelet frame, and a crude analysis of the
performance of curvelet schemes.},
bdsk-url-1 = {http://www-stat.stanford.edu/%7Ecandes/papers/Curvelet-SMStyle.pdf},
date-added = {2008-05-26 17:48:55 -0700},
date-modified = {2008-08-14 15:26:58 -0700},
keywords = {curvelet transform}
}
@ARTICLE{candes05cct,
author = {E. J. Cand\`es and D. L. Donoho},
title = {Continuous curvelet transform: {I.} {Resolution} of the wavefront set},
journal = {Applied and Computational Harmonic Analysis},
year = {2005},
volume = {19},
pages = {162-197},
number = {2},
month = {09},
bdsk-url-1 = {http://dx.doi.org/10.1016/j.acha.2005.02.003},
date-added = {2008-05-26 18:21:22 -0700},
date-modified = {2008-05-26 18:23:57 -0700},
issue = {2},
keywords = {curvelet transform}
}
@ARTICLE{candes05cct1,
author = {E. J. Cand\`es and D. L. Donoho},
title = {Continuous curvelet transform: {II.} {Discretization} and frames},
journal = {Applied and Computational Harmonic Analysis},
year = {2005},
volume = {19},
pages = {198-222},
number = {2},
month = {09},
bdsk-url-1 = {http://dx.doi.org/10.1016/j.acha.2005.02.004},
date-added = {2008-05-26 18:23:17 -0700},
date-modified = {2008-05-26 18:24:36 -0700},
issue = {2},
keywords = {curvelet transform}
}
@ARTICLE{candes04ntf,
author = {E. J. Cand\`es and D. L. Donoho},
title = {New tight frames of curvelets and optimal representations of objects with piecewise-{C}$^2$ singularities},
journal = {Communications on Pure and Applied Mathematics},
year = {2004},
volume = {57},
pages = {219-266},
number = {2},
bdsk-url-1 = {http://dx.doi.org/10.1002/cpa.10116},
bdsk-url-2 = {http://www-stat.stanford.edu/%7Ecandes/papers/CurveEdges.pdf},
date-added = {2008-05-07 11:47:59 -0700},
date-modified = {2008-08-14 14:46:59 -0700},
doi = {10.1002/cpa.10116},
issue = {2},
keywords = {curvelet transform},
pdf = {http://www-stat.stanford.edu/%7Ecandes/papers/CurveEdges.pdf}
}
@ARTICLE{chauris08sdm,
author = {H. Chauris and T. Nguyen},
title = {Seismic demigration/migration in the curvelet domain},
journal = {Geophysics},
year = {2008},
volume = {73},
pages = {S35-S46},
number = {2},
abstract = {Curvelets can represent local plane waves. They
efficiently decompose seismic images and possibly
imaging operators. We study how curvelets are
distorted after demigration followed by migration in
a different velocity model. We show that for small
local velocity perturbations, the
demigration/migration is reduced to a simple
morphing of the initial curvelet. The derivation of
the expected curvature of the curvelets shows that
it is easier to sparsify the demigration/migration
operator than the migration operator. An application
on a 2D synthetic data set, generated in a smooth
heterogeneous velocity model and with a complex
reflectivity, demonstrates the usefulness of
curvelets to predict what a migrated image would
become in a locally different velocity model without
the need for remigrating the full input data
set. Curvelets are thus well suited to study the
sensitivity of a prestack depth-migrated image with
respect to the heterogeneous velocity model used for
migration. {\copyright}2008 Society of Exploration
Geophysicists},
bdsk-url-1 = {http://library.seg.org/doi/abs/10.1190/1.2831933},
bdsk-url-2 = {http://dx.doi.org/10.1190/1.2831933},
date-added = {2008-05-07 14:48:33 -0700},
date-modified = {2008-08-14 14:59:04 -0700},
doi = {10.1190/1.2831933},
issue = {2},
keywords = {curvelet transform, imaging},
pdf = {http://library.seg.org/doi/abs/10.1190/1.2831933},
publisher = {SEG}
}
@BOOK{claerbout92esa,
author = {J. F. Claerbout},
title = {Earth soundings analysis: processing versus inversion},
publisher = {Blackwell Scientific Publications},
year = {1992},
address = {Boston},
bdsk-url-1 = {http://sepwww.stanford.edu/sep/prof/pvi.pdf},
date-added = {2008-05-06 19:27:28 -0700},
date-modified = {2008-05-07 11:44:19 -0700},
keywords = {PEF},
pdf = {http://sepwww.stanford.edu/sep/prof/pvi.pdf}
}
@ARTICLE{claerbout71tau,
author = {J. F. Claerbout},
title = {Toward a unified theory of reflector mapping},
journal = {Geophysics},
year = {1971},
volume = {36},
pages = {467-481},
number = {3},
abstract = {Schemes for seismic mapping of reflectors in the
presence of an arbitrary velocity model, dipping and
curved reflectors, diffractions, ghosts, surface
elevation variations, and multiple reflections are
reviewed and reduced to a single formula involving
up and downgoing waves. The mapping formula may be
implemented without undue complexity by means of
difference approximations to the relativistic
Schroedinger equation. {\copyright}1971 Society of
Exploration Geophysicists},
bdsk-url-1 = {http://library.seg.org/doi/abs/10.1190/1.1440185},
bdsk-url-2 = {http://dx.doi.org/10.1190/1.1440185},
date-added = {2008-05-08 14:59:36 -0700},
date-modified = {2008-08-14 14:59:35 -0700},
doi = {10.1190/1.1440185},
issue = {3},
keywords = {WEM, imaging},
pdf = {http://library.seg.org/doi/abs/10.1190/1.1440185},
publisher = {SEG}
}
@ARTICLE{daubechies04ait,
author = {I. Daubechies and M. Defrise and C. {De Mol}},
title = {An iterative thresholding algorithm for linear inverse problems with a sparsity constraint},
journal = {Communications on Pure and Applied Mathematics},
year = {2004},
volume = {57},
pages = {1413-1457},
number = {11},
abstract = {We consider linear inverse problems where the solution
is assumed to have a sparse expansion on an
arbitrary preassigned orthonormal basis. We prove
that replacing the usual quadratic regularizing
penalties by weighted p-penalties on the
coefficients of such expansions, with 1 p 2, still
regularizes the problem. Use of such p-penalized
problems with p < 2 is often advocated when one
expects the underlying ideal noiseless solution to
have a sparse expansion with respect to the basis
under consideration. To compute the corresponding
regularized solutions, we analyze an iterative
algorithm that amounts to a Landweber iteration with
thresholding (or nonlinear shrinkage) applied at
each iteration step. We prove that this algorithm
converges in norm. {\copyright} 2004 Wiley
Periodicals, Inc.},
bdsk-url-1 = {http://dx.doi.org/10.1002/cpa.20042},
date-added = {2008-05-20 13:58:17 -0700},
date-modified = {2008-08-14 15:01:17 -0700},
issue = {11},
pdf = {http://dx.doi.org/10.1002/cpa.20042},
refer1 = {10.1002/cpa.20042}
}
@ARTICLE{do2002can,
author = {M. N. Do and M. Vetterli},
title = {Contourlets: a new directional multiresolution image representation},
journal = {Proceedings. 2002 International Conference on Image Processing.},
year = {2002},
volume = {1},
abstract = {We propose a new scheme, named contourlet, that provides
a flexible multiresolution, local and directional
image expansion. The contourlet transform is
realized efficiently via a double iterated filter
bank structure. Furthermore, it can be designed to
satisfy the anisotropy scaling relation for curves,
and thus offers a fast and structured curvelet-like
decomposition. As a result, the contourlet transform
provides a sparse representation for two-dimensional
piecewise smooth signals resembling images. Finally,
we show some numerical experiments demonstrating the
potential of contourlets in several image processing
tasks.},
bdsk-url-1 = {http://dx.doi.org/10.1109/ICIP.2002.1038034},
date-added = {2008-05-07 11:58:00 -0700},
date-modified = {2008-08-14 15:01:55 -0700},
doi = {10.1109/ICIP.2002.1038034},
keywords = {contourlet transform}
}
@TECHREPORT{donoho99dct,
author = {D. L. Donoho and M. R. Duncan},
title = {Digital curvelet transform: strategy, implementation, and experiments},
institution = {Stanford Statistics Department},
year = {1999},
month = {11},
bdsk-url-1 = {http://citeseer.ist.psu.edu/rd/44392127,300178,1,0.25,Download/http://citeseer.ist.psu.edu/cache/papers/cs/15527/http:zSzzSzwww-stat.stanford.eduzSz~donohozSzReportszSz1999zSzDCvT.pdf/donoho99digital.pdf},
date-added = {2008-05-26 17:33:51 -0700},
date-modified = {2008-05-26 17:35:32 -0700},
keywords = {curvelet transform}
}
@ARTICLE{douma07los,
author = {H. Douma and M. V. de Hoop},
title = {Leading-order seismic imaging using curvelets},
journal = {Geophysics},
year = {2007},
volume = {72},
pages = {S231-S248},
number = {6},
abstract = {Curvelets are plausible candidates for simultaneous
compression of seismic data, their images, and the
imaging operator itself. We show that with
curvelets, the leading-order approximation (in
angular frequency, horizontal wavenumber, and
migrated location) to common-offset (CO) Kirchhoff
depth migration becomes a simple transformation of
coordinates of curvelets in the data, combined with
amplitude scaling. This transformation is calculated
using map migration, which employs the local slopes
from the curvelet decomposition of the data. Because
the data can be compressed using curvelets, the
transformation needs to be calculated for relatively
few curvelets only. Numerical examples for
homogeneous media show that using the leading-order
approximation only provides a good approximation to
CO migration for moderate propagation times. As the
traveltime increases and rays diverge beyond the
spatial support of a curvelet; however, the
leading-order approximation is no longer accurate
enough. This shows the need for correction beyond
leading order, even for homogeneous
media. {\copyright}2007 Society of Exploration
Geophysicists},
bdsk-url-1 = {http://library.seg.org/doi/abs/10.1190/1.2785047},
bdsk-url-2 = {http://dx.doi.org/10.1190/1.2785047},
date-added = {2008-05-07 14:35:47 -0700},
date-modified = {2008-08-14 15:02:25 -0700},
doi = {10.1190/1.2785047},
issue = {6},
keywords = {curvelet transform, imaging},
pdf = {http://library.seg.org/doi/abs/10.1190/1.2785047},
publisher = {SEG}
}
@INCOLLECTION{feichtinger94tap,
author = {H. G. Feichtinger and K. Grochenig},
title = {Theory and practice of irregular sampling},
booktitle = {Wavelets: mathematics and applications},
publisher = {CRC Press},
year = {1994},
editor = {J. J. Benedetto and M. Frazier},
series = {Studies in Advanced Mathematics},
chapter = {8},
pages = {305-363},
address = {Boca Raton, FL},
bdsk-url-1 = {http://www.univie.ac.at/nuhag-php/bibtex/open_files/fegr94_fgthpra.pdf},
date-added = {2008-05-20 17:10:18 -0700},
date-modified = {2008-05-20 17:24:38 -0700},
keywords = {sampling},
pdf = {http://www.univie.ac.at/nuhag-php/bibtex/open_files/fegr94_fgthpra.pdf}
}
@MISC{fomel07mos,
author = {S. Fomel and P. Sava},
title = {{MADAGASCAR}: open-source software package for geophysical data processing and reproducible numerical experiments},
year = {2007},
abstract = {Madagascar is an open-source software package for
geophysical data analysis and reproducible numerical
experiments. Its mission is to provide -a convenient
and powerful environment -a convenient technology
transfer tool for researchers working with digital
image and data processing. The technology developed
using the Madagascar project management system is
transferred in the form of recorded processing
histories, which become "computational recipes" to
be verified, exchanged, and modified by users of the
system.},
bdsk-url-1 = {http://rsf.sf.net},
date-added = {2008-06-26 15:31:10 -0700},
date-modified = {2008-08-14 15:31:44 -0700},
keywords = {software},
url = {http://rsf.sf.net}
}
@ARTICLE{guo07osm,
author = {K. Guo and D. Labate},
title = {Optimally sparse multidimensional representation using shearlets},
journal = {Journal of Mathematical Analysis},
year = {2007},
volume = {39},
pages = {298-318},
number = {1},
bdsk-url-1 = {http://www4.ncsu.edu/~dlabate/shear_GL.pdf},
bdsk-url-2 = {http://dx.doi.org/10.1137/060649781},
date-added = {2008-05-07 12:03:03 -0700},
date-modified = {2008-05-08 10:28:30 -0700},
doi = {10.1137/060649781},
issue = {1},
keywords = {shearlet transform},
pdf = {http://www4.ncsu.edu/~dlabate/shear_GL.pdf},
publisher = {SIAM}
}
@ARTICLE{hampson86ivs,
author = {D. Hampson},
title = {Inverse velocity stacking for multiple elimination},
journal = {Journal of the Canadian Society of Exploration Geophysicists},
year = {1986},
volume = {22},
pages = {44-45},
number = {1},
bdsk-url-1 = {http://209.91.124.56/publications/journal/1986_12/1986_Hampson_D_inverse_velocity_stacking.pdf},
date-added = {2008-05-06 19:09:45 -0700},
date-modified = {2008-05-07 11:44:52 -0700},
issue = {1},
keywords = {Radon transform},
pdf = {http://209.91.124.56/publications/journal/1986_12/1986_Hampson_D_inverse_velocity_stacking.pdf},
publisher = {CSEG}
}
@ARTICLE{hindriks00ro3,
author = {K. Hindriks and A. J. W. Duijndam},
title = {Reconstruction of {3-D} seismic signals irregularly sampled along two spatial coordinates},
journal = {Geophysics},
year = {2000},
volume = {65},
pages = {253-263},
number = {1},
abstract = {Seismic signals are often irregularly sampled along
spatial coordinates, leading to suboptimal
processing and imaging results. Least-squares
estimation of Fourier components is used for the
reconstruction of band-limited seismic signals that
are irregularly sampled along two spatial
coordinates. A simple and efficient diagonal
weighting scheme, based on the areas surrounding the
spatial samples, takes the properties of the noise
(signal outside the bandwidth) into account in an
approximate sense. Diagonal stabilization based on
the energies of the signal and the noise ensures
robust estimation. Reconstruction by temporal
frequency component allows the specification of
varying bandwidth in two dimensions, depending on
the minimum apparent velocity. This parameterization
improves the reconstruction capability for lower
temporal frequencies. The shape of the spatial
aperture affects the method of sampling the Fourier
domain. Taking into account this property, a larger
bandwidth can be recovered. The properties of the
least-squares estimator allow a very efficient
implementation which, when using a conjugate
gradient algorithm, requires a modest number of 2-D
fast Fourier transforms per temporal frequency. The
method shows signicant improvement over the
conventionally used binning and stacking method on
both synthetic and real data. The method can be
applied to any subset of seismic data with two
varying spatial coordinates. {\copyright}2000
Society of Exploration Geophysicists},
bdsk-url-1 = {http://link.aip.org/link/?GPY/65/253/1},
bdsk-url-2 = {http://dx.doi.org/10.1190/1.1444716},
date-added = {2008-05-20 16:12:37 -0700},
date-modified = {2008-08-14 15:05:01 -0700},
doi = {10.1190/1.1444716},
issue = {1},
keywords = {reconstruction},
pdf = {http://link.aip.org/link/?GPY/65/253/1},
publisher = {SEG}
}
@PHDTHESIS{kunis06nff,
author = {S. Kunis},
title = {Nonequispaced {FFT}: generalisation and inversion},
school = {L\"ubeck university},
year = {2006},
bdsk-url-1 = {http://www.analysis.uni-osnabrueck.de/kunis/paper/KunisDiss.pdf},
date-added = {2008-05-07 18:51:16 -0700},
date-modified = {2008-05-20 11:49:04 -0700},
keywords = {NFFT},
pdf = {http://www.analysis.uni-osnabrueck.de/kunis/paper/KunisDiss.pdf}
}
@ARTICLE{lu07mdf,
author = {Y. M. Lu and M. N. Do},
title = {Multidimensional directional filter banks and surfacelets},
journal = {IEEE Transactions on Image Processing},
year = {2007},
volume = {16},
pages = {918-931},
number = {4},
month = {04},
abstract = {In 1992, Bamberger and Smith proposed the directional
filter bank (DFB) for an efficient directional
decomposition of 2-D signals. Due to the
nonseparable nature of the system, extending the DFB
to higher dimensions while still retaining its
attractive features is a challenging and previously
unsolved problem. We propose a new family of filter
banks, named NDFB, that can achieve the directional
decomposition of arbitrary N-dimensional (Nges2)
signals with a simple and efficient tree-structured
construction. In 3-D, the ideal passbands of the
proposed NDFB are rectangular-based pyramids
radiating out from the origin at different
orientations and tiling the entire frequency
space. The proposed NDFB achieves perfect
reconstruction via an iterated filter bank with a
redundancy factor of N in N-D. The angular
resolution of the proposed NDFB can be iteratively
refined by invoking more levels of decomposition
through a simple expansion rule. By combining the
NDFB with a new multiscale pyramid, we propose the
surfacelet transform, which can be used to
efficiently capture and represent surface-like
singularities in multidimensional data},
bdsk-url-1 = {http://dx.doi.org/10.1109/TIP.2007.891785},
date-added = {2008-05-07 12:19:48 -0700},
date-modified = {2008-08-14 15:05:31 -0700},
doi = {10.1109/TIP.2007.891785},
issn = {1057-7149},
issue = {4},
keywords = {surfacelet transform},
publisher = {IEEE}
}
@BOOK{mallat99awt,
title = {A wavelet tour of signal processing, second edition},
publisher = {Academic Press},
year = {1999},
author = {S. Mallat},
month = {09},
date-added = {2008-05-22 16:32:31 -0700},
date-modified = {2008-05-22 16:33:57 -0700},
howpublished = {Hardcover},
isbn = {012466606X},
keywords = {wavelet transform}
}
@CONFERENCE{morton98fsr,
author = {S. A. Morton and C. C. Ober},
title = {Faster shot-record depth migrations using phase encoding},
booktitle = {SEG Technical Program Expanded Abstracts},
year = {1998},
volume = {17},
number = {1},
pages = {1131-1134},
publisher = {SEG},
bdsk-url-1 = {http://link.aip.org/link/?SGA/17/1131/1},
bdsk-url-2 = {http://dx.doi.org/10.1190/1.1820088},
date-added = {2008-05-27 16:44:01 -0700},
date-modified = {2008-05-27 16:45:21 -0700},
doi = {10.1190/1.1820088},
issue = {1},
pdf = {http://link.aip.org/link/?SGA/17/1131/1}
}
@ARTICLE{paige82lsq,
author = {C. C. Paige and M. A. Saunders},
title = {{LSQR}: an algorithm for sparse linear equations and sparse least squares},
journal = {Transactions on Mathematical Software},
year = {1982},
volume = {8},
pages = {43-71},
number = {1},
address = {New York, NY, USA},
bdsk-url-1 = {http://doi.acm.org/10.1145/355984.355989},
date-added = {2008-05-20 14:00:44 -0700},
date-modified = {2008-05-20 19:47:37 -0700},
doi = {http://doi.acm.org/10.1145/355984.355989},
issn = {0098-3500},
issue = {1},
keywords = {LSQR},
publisher = {ACM}
}
@INCOLLECTION{potts01mst,
author = {D. Potts and G. Steidl and M. Tasche},
title = {Fast {Fourier} transforms for nonequispaced data: a tutorial},
booktitle = {Modern sampling theory: mathematics and applications},
publisher = {Birkhauser},
year = {2001},
editor = {J. J. Benedetto and P. Ferreira},
chapter = {12},
pages = {249-274},
abstract = {In this section, we consider approximate methods for the
fast computiation of multivariate discrete Fourier
transforms for nonequispaced data (NDFT) in the time
domain and in the frequency domain. In particular,
we are interested in the approximation error as
function of arithmetic complexity of the
algorithm. We discuss the robustness of
NDFT-algorithms with respect to roundoff errors and
apply NDFT-algorithms for the fast computation of
Bessel transforms.},
bdsk-url-1 = {http://www.tu-chemnitz.de/~potts/paper/ndft.pdf},
date-added = {2008-05-07 18:44:29 -0700},
date-modified = {2008-08-14 15:28:37 -0700},
keywords = {NFFT},
pdf = {http://www.tu-chemnitz.de/~potts/paper/ndft.pdf}
}
@ARTICLE{romero00peo,
author = {L. A. Romero and D. C. Ghiglia and C. C. Ober and S. A. Morton},
title = {Phase encoding of shot records in prestack migration},
journal = {Geophysics},
year = {2000},
volume = {65},
pages = {426-436},
number = {2},
abstract = {Frequency-domain shot-record migration can produce
higher quality images than Kirchhoff migration but
typically at a greater cost. The computing cost of
shot-record migration is the product of the number
of shots in the survey and the expense of each
individual migration. Many attempts to reduce this
cost have focused on the speed of the individual
migrations, trying to achieve a better trade-off
between accuracy and speed. Another approach is to
reduce the number of migrations. We investigate the
simultaneous migration of shot records using
frequency-domain shot-record migration algorithms.
The difficulty with this approach is the production
of so-called crossterms between unrelated shot and
receiver wavefields, which generate unwanted
artifacts or noise in the final image. To reduce
these artifacts and obtain an image comparable in
quality to the single-shot-per-migration result, we
have introduced a process called phase encoding,
which shifts or disperses these crossterms. The
process of phase encoding thus allows one to trade
S/N ratio for the speed of migrating the entire
survey. Several encoding functions and two
application strategies have been tested. The first
strategy, combining multiple shots per migration and
using each shot only once, reduces computation in
direct relation to the number of shots combined. The
second strategy, performing multiple migrations of
all the shots in the survey, provides a means to
reduce the crossterm noise by stacking the resulting
images. The additional noise in both strategies may
be tolerated if it is no stronger than the inherent
seismic noise in the migrated image and if the final
image is achieved with less cost. {\copyright}2000
Society of Exploration Geophysicists},
bdsk-url-1 = {http://library.seg.org/doi/abs/10.1190/1.1444737},
bdsk-url-2 = {http://dx.doi.org/10.1190/1.1444737},
date-added = {2008-05-27 16:42:50 -0700},
date-modified = {2008-08-14 15:07:08 -0700},
doi = {10.1190/1.1444737},
issue = {2},
pdf = {http://library.seg.org/doi/abs/10.1190/1.1444737},
publisher = {SEG}
}
@ARTICLE{sacchi98iae,
author = {M. D. Sacchi and T. J. Ulrych and C. J. Walker},
title = {Interpolation and extrapolation using a high-resolution discrete {Fourier} transform},
journal = {IEEE Transactions on Signal Processing},
year = {1998},
volume = {46},
pages = {31-38},
number = {1},
abstract = {We present an iterative nonparametric approach to
spectral estimation that is particularly suitable
for estimation of line spectra. This approach
minimizes a cost function derived from Bayes'
theorem. The method is suitable for line spectra
since a ``long tailed'' distribution is used to
model the prior distribution of spectral
amplitudes. An important aspect of this method is
that since the data themselves are used as
constraints, phase information can also be recovered
and used to extend the data outside the original
window. The objective function is formulated in
terms of hyperpa- rameters that control the degree
of fit and spectral resolution. Noise rejection can
also be achieved by truncating the number of
iterations. Spectral resolution and extrapolation
length are controlled by a single parameter. When
this parameter is large compared with the spectral
powers, the algorithm leads to zero extrapolation of
the data, and the estimated Fourier transform yields
the periodogram. When the data are sampled at a
constant rate, the algorithm uses one Levinson
recursion per iteration. For irregular sampling
(unevenly sampled and/or gapped data), the algorithm
uses one Cholesky decomposition per iteration. The
performance of the algorithm is illustrated with
three different problems that frequently arise in
geophysical data processing: 1) harmonic retrieval
from a time series contaminated with noise; 2)
linear event detection from a finite aperture array
of receivers [which, in fact, is an extension of
1)], 3) interpolation/extrapolation of gapped data.
The performance of the algorithm as a spectral
estimator is tested with the Kay and Marple data
set. It is shown that the achieved resolution is
comparable with parametric methods but with more
accurate representation of the relative power in the
spectral lines.},
bdsk-url-1 = {http://saig.physics.ualberta.ca/s/sites/default/files/upload/articles/Sacchi_Ulrych_Walker_IEEE_98.pdf},
date-added = {2008-05-06 19:18:50 -0700},
date-modified = {2008-08-14 15:08:37 -0700},
doi = {10.1109/78.651165},
issue = {1},
keywords = {Fourier transform, reconstruction},
pdf = {http://saig.physics.ualberta.ca/s/sites/default/files/upload/articles/Sacchi_Ulrych_Walker_IEEE_98.pdf},
publisher = {IEEE}
}
@PHDTHESIS{schonewille00phd,
author = {M. A. Schonewille},
title = {Fourier reconstruction of irregularly sampled seismic data},
school = {Delft University of Technology},
year = {2000},
address = {Delft, The Netherlands},
month = {11},
date-added = {2008-05-06 19:03:35 -0700},
date-modified = {2008-05-09 14:43:57 -0700},
keywords = {Fourier transform, reconstruction},
rating = {0},
read = {Yes}
}
@ARTICLE{smith98ahs,
author = {H. Smith},
title = {A {Hardy} space for {Fourier} integral operators},
journal = {Journal of Geometric Analysis},
year = {1998},
volume = {8},
pages = {629-653},
number = {4},
date-added = {2008-05-07 12:25:03 -0700},
date-modified = {2008-08-14 15:09:47 -0700},
issue = {4},
keywords = {FIO}
}
@BOOK{snieder93giu,
author = {R. Snieder},
title = {Global inversions using normal mode and long-period surface waves},
publisher = {Chapman and Hall},
year = {1993},
date-added = {2008-05-20 17:16:42 -0700},
date-modified = {2008-05-20 17:19:44 -0700},
keywords = {sampling}
}
@ARTICLE{spitz91sti,
author = {S. Spitz},
title = {Seismic trace interpolation in the {FX} domain},
journal = {Geophysics},
year = {1991},
volume = {56},
pages = {785-794},
number = {6},
abstract = {Interpolation of seismic traces is an effective means of
improving migration when the data set exhibits
spatial aliasing. A major difficulty of standard
interpolation methods is that they depend on the
degree of reliability with which the various
geological events can be separated. In this respect,
a multichannel interpolation method is described
which requires neither a priori knowledge of the
directions of lateral coherence of the events, nor
estimation of these directions. The method is based
on the fact that linear events present in a section
made of equally spaced traces may be interpolated
exactly, regardless of the original spatial
interval, without any attempt to determine their
true dips. The predictability of linear events in
the f-x domain allows the missing traces to be
expressed as the output of a linear system, the
input of which consists of the recorded traces. The
interpolation operator is obtained by solving a set
of linear equations whose coefficients depend only
on the spectrum of the spatial prediction filter
defined by the recorded traces. Synthetic examples
show that this method is insensitive to random noise
and that it correctly handles curvatures and lateral
amplitude variations. Assessment of the method with
a real data set shows that the interpolation yields
an improved migrated section. {\copyright}1991
Society of Exploration Geophysicists},
bdsk-url-1 = {http://dx.doi.org/10.1190/1.1443096},
date-added = {2008-05-06 19:29:12 -0700},
date-modified = {2008-08-14 15:18:16 -0700},
doi = {10.1190/1.1443096},
issue = {6},
keywords = {PEF},
publisher = {SEG}
}
@ARTICLE{starck02tct,
author = {J.-L. Starck and E. J. Cand\`es and D. L. Donoho},
title = {The curvelet transform for image denoising},
journal = {IEEE Transactions on Image Processing},
year = {2002},
volume = {11},
pages = {670-684},
number = {6},
month = {06},
abstract = {We describe approximate digital implementations of two
new mathematical transforms, namely, the ridgelet
transform and the curvelet transform. Our
implementations offer exact reconstruction,
stability against perturbations, ease of
implementation, and low computational complexity. A
central tool is Fourier-domain computation of an
approximate digital Radon transform. We introduce a
very simple interpolation in the Fourier space which
takes Cartesian samples and yields samples on a
rectopolar grid, which is a pseudo-polar sampling
set based on a concentric squares geometry. Despite
the crudeness of our interpolation, the visual
performance is surprisingly good. Our ridgelet