Hierarchical parallel matching pursuit

Hans Georg Feichtinger; Andreas Turk; Thomas Strohmer

doi:10.1117/12.188061

30 September 1994 Hierarchical parallel matching pursuit

Hans Georg Feichtinger, Andreas Turk, Thomas Strohmer

Proceedings Volume 2302, Image Reconstruction and Restoration; (1994) https://doi.org/10.1117/12.188061
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

The by now well-known matching pursuit method of S. Mallat as well as the recently proposed orthogonal matching pursuit work purely sequential and are based on the idea of choosing only one single atom at a given time. Pursuing ideas which are related to modifications of the POCS method, we suggest a new type of orthogonalization procedure which allows to operate in parallel at different 'levels'. More precisely, we assume that we have a dictionary which consists of similar 'pages', i.e. those pages are collection of functions, generated from a single function by translations along a subgroup which is the same for all such pages. Based on a certain hierarchical structure (preference of pages) we apply an appropriate Gram-Schmidt type orthogonalization procedure which allows to deal with the matching pursuit problem in parallel at different levels. After carrying out appropriate approximations at the different, now orthogonal levels, one comes back to a representation based on the given family of atoms, in a straight-forward way.

Citation Download Citation

Hans Georg Feichtinger, Andreas Turk, and Thomas Strohmer "Hierarchical parallel matching pursuit", Proc. SPIE 2302, Image Reconstruction and Restoration, (30 September 1994); https://doi.org/10.1117/12.188061

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