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| Content Provider | Springer Nature Link |
|---|---|
| Author | Tasche, Manfred Langemann, Dirk |
| Copyright Year | 2009 |
| Abstract | Let $$\mathcal {S}(\mathbb {R})$$ be the Schwartz space of all complex–valued, rapidly decreasing functions. Let $$f \in \mathcal {S}(\mathbb {R})$$ be an interpolating function with the Fourier transform $$\hat {f}$$ . In this paper, we consider the following phase retrieval problem: Recover f, if only finitely many values of |f| and $$|\hat {f}|$$ are given. This problem leads to a well structured nonlinear system. The solution of the nonlinear system is an ill–posed inverse problem which we solve by iteratively regularized Gauss–Newton method. Applying a new multilevel strategy, we construct sufficiently good initial guesses. We close with some numerical tests for undisturbed and noisy data, which illustrate the performance of our method. |
| Ending Page | 340 |
| Page Count | 8 |
| Starting Page | 333 |
| File Format | |
| ISSN | 14226383 |
| e-ISSN | 14209012 |
| Journal | Results in Mathematics |
| Issue Number | 3 |
| Volume Number | 53 |
| Language | English |
| Publisher | Birkhäuser-Verlag |
| Publisher Date | 2009-06-29 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Systems of equations Inverse problems rapidly decreasing interpolating function multilevel strategy Mathematics iteratively regularized Gauss–Newton method Phase reconstruction |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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