{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T01:40:01Z","timestamp":1781574001095,"version":"3.54.5"},"reference-count":38,"publisher":"Society of Exploration Geophysicists","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an l2-regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct l1-regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular recording locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined nonequispaced curvelet reconstruction with sparsity-promoting inversion (NCRSI) for the regularization and interpolation of irregularly sampled data. We demonstrate that for a pure regularization problem the reconstruction is very accurate. The signal-to-reconstruction error ratio in our example is above 40dB. We also conduct combined interpolation and regularization experiments. The reconstructions for synthetic data are accurate, particularly when the recording locations are optimally jittered. The reconstruction in our real data example shows amplitudes along the main wavefronts smoothly varying with limited acquisition imprint.<\/jats:p>","DOI":"10.1190\/1.3494032","type":"journal-article","created":{"date-parts":[[2010,12,22]],"date-time":"2010-12-22T19:24:35Z","timestamp":1293045875000},"page":"WB203-WB210","source":"Crossref","is-referenced-by-count":134,"title":["Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach"],"prefix":"10.1190","volume":"75","author":[{"given":"Gilles","family":"Hennenfent","sequence":"first","affiliation":[{"name":"1Formerly Seismic Laboratory for Imaging and Modeling, Department of Earth and Ocean Sciences, The University of British Columbia, Vancouver, British Columbia, Canada; presently Chevron Energy Technology Company, San Ramon, California, U.S.A. E-mail: ghennenfent@chevron.com."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lloyd","family":"Fenelon","sequence":"additional","affiliation":[{"name":"2Formerly \u00c9cole Nationale Sup\u00e9rieure de Physique de Strasbourg, Illkirch-Graffenstaden, France; presently British Columbia Cancer Research Centre, Vancouver, British Columbia, Canada. E-mail: lfenelon@bccrc.ca."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felix J.","family":"Herrmann","sequence":"additional","affiliation":[{"name":"3Seismic Laboratory for Imaging and Modeling, Department of Earth and Ocean Sciences, University of British Columbia, Vancouver, British Columbia, Canada. E-mail: fherrmann@eos.ubc.ca."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"186","published-online":{"date-parts":[[2010,12,22]]},"reference":[{"key":"2025121111483227800_R1","doi-asserted-by":"crossref","first-page":"1586","DOI":"10.1190\/1.1444261","article-title":"Estimation of multiple scattering by iterative inversion, part I: Theoretical considerations","volume":"62","author":"Berkhout","year":"1997","journal-title":"Geophysics"},{"key":"2025121111483227800_R2","unstructured":"Cand\u00e8s\n              E. 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