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abstract:
Ill-posed problems are problems in which the solution does not depend continuously on the data. In this talk we consider Tikhonov regularization of such problems, and especially focus on sparse regularization. By combining techniques from ill-posed problems and sparse recovery we show, that it it is possible to reconstruct the exact support of the unknown solution even for ill-posed problems. We illustrate our results on the ill-posed problem of digital particle holography. |
