Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#287104] of Ingrid Daubechies

Papers Published

  1. Charléty, J; Voronin, S; Nolet, G; Loris, I; Simons, FJ; Sigloch, K; Daubechies, IC, Global seismic tomography with sparsity constraints: Comparison with smoothing and damping regularization, Journal of Geophysical Research, vol. 118 no. 9 (October, 2013), pp. 4887-4899, ISSN 0148-0227 [doi]
    (last updated on 2018/07/23)

    We present a realistic application of an inversion scheme for global seismic tomography that uses as prior information the sparsity of a solution, defined as having few nonzero coefficients under the action of a linear transformation. In this paper, the sparsifying transform is a wavelet transform. We use an accelerated iterative soft-thresholding algorithm for a regularization strategy, which produces sparse models in the wavelet domain. The approach and scheme we present may be of use for preserving sharp edges in a tomographic reconstruction and minimizing the number of features in the solution warranted by the data. The method is tested on a data set of time delays for finite-frequency tomography using the USArray network, the first application in global seismic tomography to real data. The approach presented should also be suitable for other imaging problems. From a comparison with a more traditional inversion using damping and smoothing constraints, we show that (1) we generally retrieve similar features, (2) fewer nonzero coefficients under a properly chosen representation (such as wavelets) are needed to explain the data at the same level of root-mean-square misfit, (3) the model is sparse or compressible in the wavelet domain, and (4) we do not need to construct a heterogeneous mesh to capture the available resolution. Key Points Global tomography with solution sparsity in a certain basis as prior informationOne-norm of model wavelet coefficients as constraint regularizes the inversionFirst realistic application on actual data for global seismic tomography. © 2013 American Geophysical Union. All Rights Reserved.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320