کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898184 | 1631323 | 2018 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The discrete sign problem: Uniqueness, recovery algorithms and phase retrieval applications
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper we consider the following real-valued and finite dimensional specific instance of the 1-D classical phase retrieval problem. Let FâRN be an N-dimensional vector, whose discrete Fourier transform has a compact support. The sign problem is to recover F from its magnitude |F|. First, in contrast to the classical 1-D phase problem which in general has multiple solutions, we prove that with sufficient over-sampling, the sign problem admits a unique solution. Next, we show that the sign problem can be viewed as a special case of a more general piecewise constant phase problem. Relying on this result, we derive a computationally efficient and robust to noise sign recovery algorithm. In the noise-free case and with a sufficiently high sampling rate, our algorithm is guaranteed to recover the true sign pattern. Finally, we present two phase retrieval applications of the sign problem: (i) vectorial phase retrieval with three measurement vectors; and (ii) recovery of two well separated 1-D objects.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 45, Issue 3, November 2018, Pages 463-485
Journal: Applied and Computational Harmonic Analysis - Volume 45, Issue 3, November 2018, Pages 463-485
نویسندگان
Ben Leshem, Oren Raz, Ariel Jaffe, Boaz Nadler,