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Weighted sparse signal decomposition

Babaie Zadeh, M ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1109/ICASSP.2012.6288652
  3. Publisher: IEEE , 2012
  4. Abstract:
  5. Standard sparse decomposition (with applications in many different areas including compressive sampling) amounts to finding the minimum ℓ 0-norm solution of an underdetermined system of linear equations. In this decomposition, all atoms are treated 'uniformly' for being included or not in the decomposition. However, one may wish to weigh more or less certain atoms, or, assign higher costs to some other atoms to be included in the decomposition. This can happen for example when there is prior information available on each atom. This motivates generalizing the notion of minimal ℓ 0-norm solution to that of minimal weighted ℓ 0-norm solution. On the other hand, relaxing weighted ℓ 0-norm via the weighted ℓ 1-norm is challenging. This paper deals with minimal weighted ℓ 0-norm solutions of underdetermined linear systems, provides conditions for their uniqueness, and develops an algorithm for their estimation
  6. Keywords:
  7. Compressive sampling ; Weighted compressive sampling ; Weighted sparse decomposition ; Prior information ; Sparse decomposition ; Sparse signals ; System of linear equations ; Linear systems ; Signal processing ; Atoms
  8. Source: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings ; 2012 , Pages 3425-3428 ; 15206149 (ISSN) ; 9781467300469 (ISBN)
  9. URL: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6288652&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6288652