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Uniqueness and Uncertainty

  • Michael Elad
Chapter

Abstract

We return to the basic problem (P 0), which is at the core of our discussion,
$${\left(P_o\right):\quad \min\limits_X \parallel \mathbf{X}\parallel_0 \,{\rm subject\,\, to} \mathbf \quad \mathbf{b}=\mathbf{A\mathbf{x}}}.$$
While we shall refer hereafter to this problem as our main goal, we stress that we are quite aware of its two major shortcomings in leading to any practical tool. 1. The equality requirement b = A X is too strict, as there are small chances for any vector b to be represented by a few columns from A. A better requirement would be one that allows for small deviation. 2. The sparsity measure is too sensitive to very small entries in X, and a better measure would adopt a more forgiving approach towards such small entries.

Keywords

Uncertainty Principle Diagonal Entry Generalize Uncertainty Principle Sparse Solution Small Entry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Computer Science DepartmentThe Technion – Israel Institute of TechnologyHaifaIsrael

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