Tomographic inversion using L1-norm regularization of wavelet coefficients
By Ignace Loris, Guust Nolet, Ingrid Daubechies, Francis Anthony Dahlen. 2006
182 citations recorded by the source corpus.
We propose the use of $ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=data$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $data$ to within its assigned errors.
Subfields: Computer Vision and Pattern Recognition, Geophysics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/85f2660e3a30e77a3af134d32e00fa5756074b6f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Vision and Pattern Recognition
- Ignace Loris
- Ingrid Daubechies
- Peter Gerstoft
- Massimo Fornasier
- Michael J. Bianco
- Zachary E. Ross
- Zuowei Shen
- Jian-Feng Cai
In Geophysics
- Peter Gerstoft
- Ingrid Daubechies
- Massimo Fornasier
- Ignace Loris
- Zachary E. Ross
- Gregory C. Beroza
- S. M. Mousavi
- Holger Rauhut
In Mathematical Physics
- Ignace Loris
- Ingrid Daubechies
- Massimo Fornasier
- Yin Zhang
- Ewout van den Berg
- Michael P. Friedlander
- David L. Donoho
- Julien Mairal
Citations in the corpus
- Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints (2007, background): “Because the complexity of LARS is cubic in the number of nonzero components of the solution, such 3D problems are expected to lie beyond its useful range.”
- Discretization-invariant Bayesian inversion and Besov space priors (2009, unknown): “There is an interesting parallel to algorithms computing map estimates with penalty on the l(1) norm of Fourier or wavelet coefficients [21, 61, 17, 42].”
- Machine Learning in Seismology: Turning Data into Insights (2018, background): “Sparse representations are appealing because they can model both discontinuous and smooth geophysical features (Loris et al. , 2007).”