Add to ORKGWe study the regularising properties of Tikhonov regularisation on the sequence space ℓ2 with weighted, non-quadratic penalty term acting separately on the coefficients of a given sequence. We derive sufficient conditions for the penalty term that guarantee the well-posedness of the method, and investigate to which extent the same conditions are also necessary. A particular interest of this paper is the application to the so-lution of operator equations with sparsity constraints. Assuming a linear growth of the penalty term at zero, we prove the sparsity of all regu-larised solutions. Moreover, we derive a linear convergence rate under the assumptions of even faster growth at zero and a certain injectivity of the operator to be inverted. Th...
We study compact operator equations with noisy data in Hilbert space. Instead of assuming that the e...
In the area of sparse recovery, numerous researches hint that non-convex penalties might induce bett...
There exists a vast literature on convergence rates results for Tikhonov regularized minimizers. We ...
AbstractWe study the regularising properties of Tikhonov regularisation on the sequence space ℓ2 wit...
Tikhonov-type regularization of linear and nonlinear ill-posed problems in abstract spaces under spa...
Non-convex sparsity-inducing penalties outperform their convex counterparts, but generally sacrifice...
For Tikhonov regularization of ill-posed nonlinear operator equations, convergence is studied in a H...
In this paper, we study linear inverse problems on a closed convex set and the constrained sparsity ...
In this work, we consider ill-posed linear problems, where instead of exact data we are given noisy ...
Abstract. The Tikhonov regularization of linear ill-posed problems with an `1 penalty is considered....
Sparse representation and low-rank approximation are fundamental tools in fields of signal processin...
In the last decade l1-regularization became a powerful and popular tool for the regularization of In...
We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the it...
This paper considers the problem of recovering either a low rank matrix or a sparse vector from obse...
Non-convex regularizers are more and more applied to high-dimensional inference with s-parsity prior...
We study compact operator equations with noisy data in Hilbert space. Instead of assuming that the e...
In the area of sparse recovery, numerous researches hint that non-convex penalties might induce bett...
There exists a vast literature on convergence rates results for Tikhonov regularized minimizers. We ...
AbstractWe study the regularising properties of Tikhonov regularisation on the sequence space ℓ2 wit...
Tikhonov-type regularization of linear and nonlinear ill-posed problems in abstract spaces under spa...
Non-convex sparsity-inducing penalties outperform their convex counterparts, but generally sacrifice...
For Tikhonov regularization of ill-posed nonlinear operator equations, convergence is studied in a H...
In this paper, we study linear inverse problems on a closed convex set and the constrained sparsity ...
In this work, we consider ill-posed linear problems, where instead of exact data we are given noisy ...
Abstract. The Tikhonov regularization of linear ill-posed problems with an `1 penalty is considered....
Sparse representation and low-rank approximation are fundamental tools in fields of signal processin...
In the last decade l1-regularization became a powerful and popular tool for the regularization of In...
We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the it...
This paper considers the problem of recovering either a low rank matrix or a sparse vector from obse...
Non-convex regularizers are more and more applied to high-dimensional inference with s-parsity prior...
We study compact operator equations with noisy data in Hilbert space. Instead of assuming that the e...
In the area of sparse recovery, numerous researches hint that non-convex penalties might induce bett...
There exists a vast literature on convergence rates results for Tikhonov regularized minimizers. We ...