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Inverse problems in spaces of measures

Kristian BrediesHanna Katriina Pikkarainen — 2013

ESAIM: Control, Optimisation and Calculus of Variations

The ill-posed problem of solving linear equations in the space of vector-valued finite Radon measures with Hilbert space data is considered. Approximate solutions are obtained by minimizing the Tikhonov functional with a total variation penalty. The well-posedness of this regularization method and further regularization properties are mentioned. Furthermore, a flexible numerical minimization algorithm is proposed which converges subsequentially in the weak* sense and with rate 𝒪( ...

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