{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T02:52:44Z","timestamp":1789527164201,"version":"build-2803163510"},"reference-count":18,"publisher":"Society of Exploration Geophysicists","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Geophysical inverse problems typically involve a trade-off between data misfit and some prior model. Pareto curves trace the optimal trade-off between these two competing aims. These curves are used commonly in problems with two-norm priors in which they are plotted on a log-log scale and are known as L-curves. For other priors, such as the sparsity-promoting one-norm prior, Pareto curves remain relatively unexplored. We show how these curves lead to new insights into one-norm regularization. First, we confirm theoretical properties of smoothness and convexity of these curves from a stylized and a geophysical example. Second, we exploit these crucial properties to approximate the Pareto curve for a large-scale problem. Third, we show how Pareto curves provide an objective criterion to gauge how different one-norm solvers advance toward the solution.<\/jats:p>","DOI":"10.1190\/1.2944169","type":"journal-article","created":{"date-parts":[[2008,6,24]],"date-time":"2008-06-24T18:00:45Z","timestamp":1214330445000},"page":"A23-A26","source":"Crossref","is-referenced-by-count":59,"title":["New insights into one-norm solvers from the Pareto curve"],"prefix":"10.1190","volume":"73","author":[{"given":"Gilles","family":"Hennenfent","sequence":"first","affiliation":[{"name":"1University of British Columbia, Department of Earth and Ocean Science, Seismic Laboratory for Imaging and Modeling, Vancouver, British Columbia, Canada. E-mail: ghennenfent@eos.ubc.ca; mpf@cs.ubc.ca; fherrmann@eos.ubc.ca."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ewout","family":"van den Berg","sequence":"additional","affiliation":[{"name":"2University of British Columbia, Department of Computer Science, Scientific Computing Laboratory, Vancouver, British Columbia, Canada. E-mail: ewout78@cs.ubc.ca; mpf@cs.ubc.ca."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael P.","family":"Friedlander","sequence":"additional","affiliation":[{"name":"2University of British Columbia, Department of Computer Science, Scientific Computing Laboratory, Vancouver, British Columbia, Canada. E-mail: ewout78@cs.ubc.ca; mpf@cs.ubc.ca."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felix J.","family":"Herrmann","sequence":"additional","affiliation":[{"name":"1University of British Columbia, Department of Earth and Ocean Science, Seismic Laboratory for Imaging and Modeling, Vancouver, British Columbia, Canada. E-mail: ghennenfent@eos.ubc.ca; mpf@cs.ubc.ca; fherrmann@eos.ubc.ca."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"186","published-online":{"date-parts":[[2008,6,24]]},"reference":[{"key":"2025121113090070000_R1","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","article-title":"Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information","volume":"52","author":"Cand\u00e8s","year":"2006","journal-title":"IEEE Transactions on Information Theory"},{"key":"2025121113090070000_R2","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1137\/S1064827596304010","article-title":"Atomic decomposition by basis pursuit","volume":"20","author":"Chen","year":"1998","journal-title":"SIAM Journal on Scientific Computing"},{"key":"2025121113090070000_R3","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1002\/cpa.20042","article-title":"An iterative thresholding algorithm for linear inverse problems with a sparsity constraint","volume":"57","author":"Daubechies","year":"2004","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"2025121113090070000_R4","article-title":"Accelerated projected gradient method for linear inverse problems with sparsity constraints","author":"Daubechies","year":"2007"},{"key":"2025121113090070000_R5","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Transactions on Information Theory"},{"key":"2025121113090070000_R6","article-title":"Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit","author":"Donoho","year":"2006"},{"key":"2025121113090070000_R7","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1109\/TIP.2003.814255","article-title":"An EM algorithm for wavelet-based image restoration","volume":"12","author":"Figueiredo","year":"2003","journal-title":"IEEE Transactions on Image Processing"},{"key":"2025121113090070000_R8","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1190\/1.1442095","article-title":"Robust iterative inversion for the one-dimensional acoustic wave equation","volume":"51","author":"Gersztenkorn","year":"1986","journal-title":"Geophysics"},{"issue":"3","key":"2025121113090070000_R9","doi-asserted-by":"crossref","first-page":"V19","DOI":"10.1190\/1.2841038","article-title":"Simply denoise: Wavefield reconstruction via jittered undersampling","volume":"73","author":"Hennenfent","year":"2008","journal-title":"Geophysics"},{"issue":"1","key":"2025121113090070000_R10","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1111\/j.1365-246X.2007.03698.x","article-title":"Non-parametric seismic data recovery with curvelet frames","volume":"173","author":"Herrmann","year":"2008","journal-title":"Geophysical Journal International"},{"key":"2025121113090070000_R11","volume-title":"Solving least squares problems","author":"Lawson","year":"1974"},{"key":"2025121113090070000_R12","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1190\/1.1441413","article-title":"Recovery of the acoustic impedance from reflection seismograms","volume":"48","author":"Oldenburg","year":"1983","journal-title":"Geophysics"},{"key":"2025121113090070000_R13","doi-asserted-by":"crossref","DOI":"10.1515\/9780691206837","volume-title":"Geophysical inverse theory","author":"Parker","year":"1994"},{"key":"2025121113090070000_R14","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1145\/321105.321114","article-title":"A technique for the numerical solution of certain integral equations of the first kind","volume":"9","author":"Phillips","year":"1962","journal-title":"Journal of the Association for Computing Machinery"},{"key":"2025121113090070000_R15","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.acha.2006.05.002","article-title":"Random sampling of sparse trigonometric polynomials","volume":"22","author":"Rauhut","year":"2007","journal-title":"Applied and Computational Harmonic Analysis"},{"key":"2025121113090070000_R16","first-page":"1035","article-title":"Solution of incorrectly formulated problems and regularization method","volume":"4","author":"Tikhonov","year":"1963","journal-title":"Soviet mathematics - 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