Matching pursuits and basis pursuits are nonoptimal sparse approximation algorithms in a redundant dictionary D, but are computationally efficient. However, pursuit approximations can be nearly as precise as optimal M-term approximations, depending on the properties of the approximation supports in D.

Beyond approximation, this section studies the ability of pursuit algorithms to recover a specific set Λ of vectors providing a sparse signal approximation in a redundant dictionary. The stability of this recovery is important for pattern recognition when selected dictionary vectors are used to analyze the signal information. It is also at the core of the sparse super-resolution algorithms introduced in Section 13.3.

The stability ...

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