caa a22 4500 463246772 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s00041-006-6908-x doi (NATIONALLICENCE)springer-10.1007/s00041-006-6908-x Morphological Component Analysis and Inpainting on the Sphere: Application in Physics and Astrophysics [Elektronische Daten] [P. Abrial, Y. Moudden, J.-L. Starck, B. Afeyan, J. Bobin, J. Fadili, M.K. Nguyen] Morphological Component Analysis (MCA) is a new method which takes advantage of the sparse representation of structured data in large overcomplete dictionaries to separate features in the data based on the diversity of their morphology. It is an efficient technique in such problems as separating an image into texture and piecewise smooth parts or for inpainting applications. The MCA algorithm consists of an iterative alternating projection and thresholding scheme, using a successively decreasing threshold towards zero with each iteration. In this article, the MCA algorithm is extended to the analysis of spherical data maps as may occur in a number of areas such as geophysics, astrophysics or medical imaging. Practically, this extension is made possible thanks to the variety of recently developed transforms on the sphere including several multiscale transforms such as the undecimated isotropic wavelet transform on the sphere, the ridgelet and curvelet transforms on the sphere. An MCA-inpainting method is then directly extended to the case of spherical maps allowing us to treat problems where parts of the data are missing or corrupted. We demonstrate the usefulness of these new tools of spherical data analysis by focusing on a selection of challenging applications in physics and astrophysics. Birkhauser Boston, 2007 Abrial P. DAPNIA/SEDI-Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France aut Moudden Y. DAPNIA/SEDI-Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France aut Starck J.-L DAPNIA/SEDI-Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France aut Afeyan B. Polymath Research Inc., Pleasanton, CA, 94566, USA aut Bobin J. DAPNIA/SEDI-Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France aut Fadili J. GREYC - CNRS UMR 6072 / ENSICAEN, 14050 Caen, France aut Nguyen M.K. ETIS - CNRS UMR 8051 / ENSEA / Universit de Cergy-Pontoise, 95014 Cergy-Pontoise, France aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/6(2007-12-01), 729-748 1069-5869 13:6<729 2007 13 41 https://doi.org/10.1007/s00041-006-6908-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6908-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abrial P. DAPNIA/SEDI-Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France aut NATIONALLICENCE 700 1- Moudden Y. DAPNIA/SEDI-Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France aut NATIONALLICENCE 700 1- Starck J.-L DAPNIA/SEDI-Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France aut NATIONALLICENCE 700 1- Afeyan B. Polymath Research Inc., Pleasanton, CA, 94566, USA aut NATIONALLICENCE 700 1- Bobin J. DAPNIA/SEDI-Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France aut NATIONALLICENCE 700 1- Fadili J. GREYC - CNRS UMR 6072 / ENSICAEN, 14050 Caen, France aut NATIONALLICENCE 700 1- Nguyen M.K. ETIS - CNRS UMR 8051 / ENSEA / Universit de Cergy-Pontoise, 95014 Cergy-Pontoise, France aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/6(2007-12-01), 729-748 1069-5869 13:6<729 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer