Fast algorithms for nonconvex compression sensing: MRI reconstruction from very few data

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Compressive sensing is the reconstruction of sparse images or signals from very few samples, by means of solving a tractable optimization problem. In the context of MRI, this can allow reconstruction from many fewer k-space samples, thereby reducing scanning time. Previous work has shown that nonconvex optimization reduces still further the number of samples required for reconstruction, while still being tractable. In this work, we extend recent Fourier-based algorithms for convex optimization to the nonconvex setting, and obtain methods that combine the reconstruction abilities of previous nonconvex approaches with the computational speed of state-of-the-art convex methods.

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Chartrand, Rick January 1, 2009.

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Compressive sensing is the reconstruction of sparse images or signals from very few samples, by means of solving a tractable optimization problem. In the context of MRI, this can allow reconstruction from many fewer k-space samples, thereby reducing scanning time. Previous work has shown that nonconvex optimization reduces still further the number of samples required for reconstruction, while still being tractable. In this work, we extend recent Fourier-based algorithms for convex optimization to the nonconvex setting, and obtain methods that combine the reconstruction abilities of previous nonconvex approaches with the computational speed of state-of-the-art convex methods.

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  • International Symposium on Biomedical Imaging ; June 28, 2009 ; Boston, MA

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  • Report No.: LA-UR-09-00316
  • Report No.: LA-UR-09-316
  • Grant Number: AC52-06NA25396
  • Office of Scientific & Technical Information Report Number: 956525
  • Archival Resource Key: ark:/67531/metadc931523

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  • January 1, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 3:50 p.m.

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Chartrand, Rick. Fast algorithms for nonconvex compression sensing: MRI reconstruction from very few data, article, January 1, 2009; [New Mexico]. (digital.library.unt.edu/ark:/67531/metadc931523/: accessed June 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.