Non-convex Sparse Regularization
نویسنده
چکیده
We study the regularising properties of Tikhonov regularisation on the sequence space l 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 solution of operator equations with sparsity constraints. Assuming a linear growth of the penalty term at zero, we prove the sparsity of all regularised 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. These results in particular cover non-convex lp regularisation with 0 < p < 1. MSC: 65J20,47A52;
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