Convergence Rates And Exact Recovery With Tikhonov Regularization With Sparsity Constraints

This thesis studied the Tikhonov regularization of ill-posed problems and exact recovery with Tikhonov regularization with sparsity constraints.We address the regularization by sparsity constraints by means of weighted lp penalties As main results it is proven that one gets a convergence rate of (?)δ in the2-norm for1<q≤2by the source condition, while q=1, a convergence rate δ in the stronger1-norm can be achieved.The Tikhonov regularization has been popularized.The Tikhonov regularization of nonlinear ill-posed problems with an l1penalty is considered. Moreover, we derive conditions for exact support recovery which are especially applicable in the case of ill-posed problems. Additionally, the relations between different conditions for exact support recovery are investigated.The Tikhonov regularization of nonlinear ill-posed problems with an l1penalty has been popularize.