dorsal/arxiv
View SchemaTomographic inversion using $\ell_1$-norm regularization of wavelet coefficients
| Authors | Ignace Loris, Guust Nolet, Ingrid Daubechies, F. A. Dahlen |
|---|---|
| Categories | |
| ArXiv ID | physics/0608094 |
| URL | https://arxiv.org/abs/physics/0608094 |
| DOI | 10.1111/j.1365-246X.2007.03409.x |
| Journal | Geophysical Journal International 170 (2007) 359-370 |
Abstract
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, 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 $d$ to within its assigned errors.
{
"annotation_id": "fbd6cfef-8027-4113-b7a4-4f369fa697d3",
"date_created": "2026-03-02T18:01:10.315000Z",
"date_modified": "2026-03-02T18:01:10.315000Z",
"file_hash": "e1ddef889f69e55636bcae59235143928673567550d4d336b7d18f637ab57ad3",
"private": false,
"record": {
"abstract": "We propose the use of $\\ell_1$ regularization in a wavelet basis for the\nsolution of linearized seismic tomography problems $Am=d$, allowing for the\npossibility of sharp discontinuities superimposed on a smoothly varying\nbackground. An iterative method is used to find a sparse solution $m$ that\ncontains no more fine-scale structure than is necessary to fit the data $d$ to\nwithin its assigned errors.",
"arxiv_id": "physics/0608094",
"authors": [
"Ignace Loris",
"Guust Nolet",
"Ingrid Daubechies",
"F. A. Dahlen"
],
"categories": [
"physics.geo-ph"
],
"doi": "10.1111/j.1365-246X.2007.03409.x",
"journal_ref": "Geophysical Journal International 170 (2007) 359-370",
"title": "Tomographic inversion using $\\ell_1$-norm regularization of wavelet coefficients",
"url": "https://arxiv.org/abs/physics/0608094"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "0a003300-4051-42dc-919e-8850e3643107",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}