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Tikhonov regularization with a stabilizer being the sum of total variation and the norm of space  L  p [ a ;  b ] (1 &lt; p ≤ ∞) is considered. For one-dimensional case we prove that, along with the convergence of regularized solutions, in  L  p  we have uniform convergence over intervals where the solution to be found is continuous. Results of numerical experiments on reconstruction of model solutions, differing in smoothness, of the one-dimensional first-kind Fredholm integral equation are reported.

Tikhonov regularization with nondifferentiable stabilizing functionals