The ill-posed problem of solving linear equations in the space of vector-valued finiteRadon measures with Hilbert space data is considered. Approximate solutions are obtainedby minimizing the Tikhonov functional with a total variation penalty. The well-posednessof this regularization method and further regularization properties are mentioned.Furthermore, a flexible numerical minimization algorithm is proposed which convergessubsequentially in the weak* sense and with rate 𝒪(n-1) in terms of the functional values. Finally, numerical results for sparsedeconvolution demonstrate the applicability for a finite-dimensional discrete data spaceand infinite-dimensional solution space.
