Theis, Fabian J. and Tanaka, T. (2006) Sparseness by Iterative Projections Onto Spheres. In: 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, 2006, ICASSP 2006 : 14 - 19 May 2006, Toulouse, France; proceedings. IEEE Operations Center, Piscataway, NJ, V-V. ISBN 1-424-40469-X.
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Many interesting signals share the property of being sparsely active. The search for such sparse components within a data set commonly involves a linear or nonlinear projection step in order to fulfil the sparseness constraints. In addition to the proximity measure used for the projection, the result of course is also intimately connected with the actual definition of the sparseness criterion. In this work, we introduce a novel sparseness measure and apply it to the problem of finding a sparse projection of a given signal. Here, sparseness is defined as the fixed ratio of p- over 2-norm, and existence and uniqueness of the projection holds. This framework extends previous work by Hoyer in the case of p = 1, where it is easy to give a deterministic, more or less closed-form solution. This is not possible for p ne 1, so we introduce an algorithm based on alternating projections onto spheres (POSH), which is similar to the projection onto convex sets (POCS). Although the assumption of convexity does not hold in our setting, we observe not only convergence of the algorithm, but also convergence to the correct minimal distance solution. Indications for a proof of this surprising property are given. Simulations confirm these results.
|Item Type:||Book Section|
|Institutions:||Biology, Preclinical Medicine > Institut für Biophysik und physikalische Biochemie > Prof. Dr. Elmar Lang|
|Subjects:||500 Science > 570 Life sciences|
|Created at the University of Regensburg:||Unknown|
|Deposited On:||13 Oct 2010 07:57|
|Last Modified:||13 Oct 2010 07:57|
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