Inverse problems in spaces of measures
نویسندگان
چکیده
The ill-posed problem of solving linear equations in the space of vector-valued finite Radon measures with Hilbert-space data is considered. The well-posedness of regularization by minimizing the Tikhonov functional is established and further regularization properties are studied. In particular, the convergence rate of O(δ) for the Bregman distance under a source condition is obtained. Furthermore, a flexible numerical minimization algorithm is proposed which converges subsequentially in the weak* sense and with O(n−1) in terms of the functional values. Finally, numerical results for sparse deconvolution demonstrate the applicability for a finite-dimensional discrete data space and infinite-dimensional solution space.
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