Inverse problems in spaces of measures
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 190-218.

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(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.

DOI : https://doi.org/10.1051/cocv/2011205
Classification : 65J20,  46E27,  49M05
Mots clés : inverse problems, vector-valued finite Radon measures, Tikhonov regularization, delta-peak solutions, generalized conditional gradient method, iterative soft-thresholding, sparse deconvolution
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     title = {Inverse problems in spaces of measures},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {190--218},
     publisher = {EDP-Sciences},
     volume = {19},
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     doi = {10.1051/cocv/2011205},
     zbl = {1266.65083},
     mrnumber = {3023066},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2011205/}
}
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Bredies, Kristian; Pikkarainen, Hanna Katriina. Inverse problems in spaces of measures. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 190-218. doi : 10.1051/cocv/2011205. http://www.numdam.org/articles/10.1051/cocv/2011205/

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