Compressed wavefield extrapolation

Lin, Tim; Herrmann, Felix J.

doi:10.1190/1.2750716

Cited by 82 publications

(50 citation statements)

References 42 publications

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“…In this approach, sub-sampling interferences are removed by exploiting transform-domain sparsity, properties of certain sub-sampling schemes, and the existence of sparsity promoting solvers. Following earlier work by Lin and Herrmann (2007) (with a formal proof recently established by Demanet and Peyré, 2008), we adapt the ideas from CS towards the problem of seismic waveform simulation. Instead of compressively sampling along the source/receiver coordinates in the modal domain (spanned by the eigenfunctions of the Helmholtz operator), we propose to compressively sample the source wavefields.…”

Section: Introductionmentioning

confidence: 99%

Compressive simultaneous full-waveform simulation

2009

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The fact that the computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem-where simulated data is recovered from a relatively small number of independent simultaneous sources-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program.Depending on the wavefield's sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.

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Section: Introductionmentioning

confidence: 99%

Compressive simultaneous full-waveform simulation

2009

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“…The noiselet method takes random noiselet measurements and then reconstructs by 1 minimization whereas our chirp and ReedMuller algorithms use deterministic measurements and the reconstruction is by a least squares method. Error dB 10 .…”

Section: Stability Of the Deterministic Compressed Sensing Algorithmsmentioning

confidence: 99%

“…By now, many authors have proposed different sensing matrices and reconstruction algorithms, establishing the feasibility of such reconstruction in practice. Applications have been shown for medical images [7], communications [8], analog-to-information conversion [9], geophysical data analysis [10], etc. The standard compressed sensing technique guarantees exact recovery of the original signal with overwhelmingly high probability if the sensing matrix satisfies the Restricted Isometry Property (RIP).…”

Section: Introductionmentioning

confidence: 99%

Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences

Datta¹,

Ni²,

Mahanti³

et al. 2013

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We explore the stability of image reconstruction algorithms under deterministic compressed sensing. Recently, we have proposed [1-3] deterministic compressed sensing algorithms for 2D images. These algorithms are suitable when Daubechies wavelets are used as the sparsifying basis. In the initial work, we have shown that the algorithms perform well for images with sparse wavelets coefficients. In this work, we address the question of robustness and stability of the algorithms, specifically, if the image is not sparse and/or if noise is present. We show that our algorithms perform very well in the presence of a certain degree of noise. This is especially important for MRI and other real world applications where some level of noise is always present.

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“…See [16] for an example of Helmholtz operator with a quadratic profile, and [28] for a spectral approach that leverages sparsity, also for the Helmholtz operator.…”

Section: Related Workmentioning

confidence: 99%

Discrete Symbol Calculus

Demanet¹,

Ying²

2011

SIAM Rev.

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This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space x and frequency ξ. The symbol smoothness conditions obeyed by many operators in connection to smooth linear partial differential equations allow to write fast-converging, non-asymptotic expansions in adequate systems of rational Chebyshev functions or hierarchical splines. The classical results of closedness of such symbol classes under multiplication, inversion and taking the square root translate into practical iterative algorithms for realizing these operations directly in the proposed expansions. Because symbol-based numerical methods handle operators and not functions, their complexity depends on the desired resolution N very weakly, typically only through log N factors. We present three applications to computational problems related to wave propagation: 1) preconditioning the Helmholtz equation, 2) decomposing wavefields into one-way components and 3) depth-stepping in reflection seismology.

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Compressed wavefield extrapolation

Cited by 82 publications

References 42 publications

Compressive simultaneous full-waveform simulation

Compressive simultaneous full-waveform simulation

Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences

Discrete Symbol Calculus

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