Exact support recovery for linear inverse problems with sparsity constraints

Dennis Trede
2011 Methods and Applications of Analysis  
There are a couple of methods with sparsity enhancing properties for regularization of inverse problems. This paper deals with the Tikhonov regularization with an ℓ 1 penalty and with the orthogonal matching pursuit. Conditions are derived, which ensure that the regularized solution has the exact support. These conditions are especially applicable in the case of ill-posed problems, where other conditions based on coherence or the restricted isometry property are usually not applicable.
more » ... gly, the conditions coincide for both, for the ℓ 1 -penalized Tikhonov regularization and for the orthogonal matching pursuit.
doi:10.4310/maa.2011.v18.n1.a7 fatcat:zcimt7b6mfg4nbmya3dg3ub4ci