Projection onto the Cosparse Set is NP-Hard

Abstract : The computational complexity of a problem arising in the context of sparse optimization is considered, namely, the projection onto the set of $k$-cosparse vectors w.r.t. some given matrix $\Omeg$. It is shown that this projection problem is (strongly) \NP-hard, even in the special cases in which the matrix $\Omeg$ contains only ternary or bipolar coefficients. Interestingly, this is in contrast to the projection onto the set of $k$-sparse vectors, which is trivially solved by keeping only the $k$ largest coefficients.
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Submitted on : Tuesday, March 11, 2014 - 8:50:04 AM
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Andreas M. Tillmann, Rémi Gribonval, Marc E. Pfetsch. Projection onto the Cosparse Set is NP-Hard. ICASSP14 - International Conference on Acoustics, Speech, and Signal Processing, May 2014, Florence, Italy. ⟨10.1109/ICASSP.2014.6854987⟩. ⟨hal-00802359v2⟩

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