We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.
|Publication status||Published - 22 May 2009|
|Event||International Conference on SAMPling Theory and Applications - Marseille, France|
Duration: 18 May 2009 → 22 May 2009
|Conference||International Conference on SAMPling Theory and Applications|
|Period||18/05/09 → 22/05/09|
Bibliographical note4 pages
- 65K10, 65N55, 65N21, 65Y05, 90C25, 52A41, 49M30, 49M27, 68U10
Fornasier, M., Langer, A., & Schönlieb, C-B. (2009). Domain decomposition methods for compressed sensing. Paper presented at International Conference on SAMPling Theory and Applications, Marseille, France.