# A Tikhonov-based projection iteration for nonlinear Ill-posed problems with sparsity constraints

@article{Ramlau2006ATP, title={A Tikhonov-based projection iteration for nonlinear Ill-posed problems with sparsity constraints}, author={R. Ramlau and G. Teschke}, journal={Numerische Mathematik}, year={2006}, volume={104}, pages={177-203} }

In this paper, we consider nonlinear inverse problems where the solution is assumed to have a sparse expansion with respect to a preassigned basis or frame. We develop a scheme which allows to minimize a Tikhonov functional where the usual quadratic regularization term is replaced by a one-homogeneous (typically weighted ℓp) penalty on the coefficients (or isometrically transformed coefficients) of such expansions. For (p < 2), the regularized solution will have a sparser expansion with respect… CONTINUE READING

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