SOME FURTHER RESULTS ON THE RECOVERY ALGORITHMS

When seeking a representation of a signal on a redundant basis one generally replaces the quest for the sparsest model by an`1 minimization and solves thus a linear program. In the presence of noise one has in addition to replace the exact reconstruction constraint by an approximate one. We consider simultaneously several ways to allow for reconstruction errors and detail the optimality conditions of each of the criterion. We then analyze if these conditions are helpful in the implementation of optimization algorithms.

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