Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints

Details Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints

2010-01-19

arxiv.org/abs/1001.3276v4

Mathematics

Functional Analysis

Scientific paper

The Tikhonov regularization of linear ill-posed problems with an $\ell^1$ penalty is considered. We recall results for linear convergence rates and results on exact recovery of the support. Moreover, we derive conditions for exact support recovery which are especially applicable in the case of ill-posed problems, where other conditions, e.g. based on the so-called coherence or the restricted isometry property are usually not applicable. The obtained results also show that the regularized solutions do not only converge in the $\ell^1$-norm but also in the vector space $\ell^0$ (when considered as the strict inductive limit of the spaces $\R^n$ as $n$ tends to infinity). Additionally, the relations between different conditions for exact support recovery and linear convergence rates are investigated. With an imaging example from digital holography the applicability of the obtained results is illustrated, i.e. that one may check a priori if the experimental setup guarantees exact recovery with Tikhonov regularization with sparsity constraints.

Affiliated with

Also associated with

No associations

Rating

Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-636169