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

  title={A Tikhonov-based projection iteration for nonlinear Ill-posed problems with sparsity constraints},
  author={R. Ramlau and G. Teschke},
  journal={Numerische Mathematik},
  • R. Ramlau, G. Teschke
  • Published 2006
  • Mathematics, Computer Science
  • Numerische Mathematik
  • 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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