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

Voir la notice de l'article provenant de la source Numdam

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 : 10.1051/cocv/2011205
Classification : 65J20, 46E27, 49M05
Keywords: inverse problems, vector-valued finite Radon measures, Tikhonov regularization, delta-peak solutions, generalized conditional gradient method, iterative soft-thresholding, sparse deconvolution 
@article{COCV_2013__19_1_190_0,
     author = {Bredies, Kristian and Pikkarainen, Hanna Katriina},
     title = {Inverse problems in spaces of measures},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {190--218},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {1},
     year = {2013},
     doi = {10.1051/cocv/2011205},
     mrnumber = {3023066},
     zbl = {1266.65083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011205/}
}
TY  - JOUR
AU  - Bredies, Kristian
AU  - Pikkarainen, Hanna Katriina
TI  - Inverse problems in spaces of measures
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2013
SP  - 190
EP  - 218
VL  - 19
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011205/
DO  - 10.1051/cocv/2011205
LA  - en
ID  - COCV_2013__19_1_190_0
ER  - 
%0 Journal Article
%A Bredies, Kristian
%A Pikkarainen, Hanna Katriina
%T Inverse problems in spaces of measures
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2013
%P 190-218
%V 19
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011205/
%R 10.1051/cocv/2011205
%G en
%F COCV_2013__19_1_190_0
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

Cité par Sources :