کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599694 1631146 2014 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Phase retrieval from very few measurements
ترجمه فارسی عنوان
بازیابی فاز از چند اندازه گیری
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper focuses on completely determining signals with as few intensity measurements as possible, and on efficient phase retrieval algorithms from such measurements. For the case of complex M  -dimensional signals, we construct a measurement ensemble of size 4M−44M−4 which yields injective intensity measurements; this is conjectured to be the smallest such ensemble. For the case of real signals, we devise a theory of “almost” injective intensity measurements, and we characterize such ensembles. Later, we show that phase retrieval from M+1M+1 almost injective intensity measurements is NPNP-hard, indicating that computationally efficient phase retrieval must come at the price of measurement redundancy.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 449, 15 May 2014, Pages 475–499
نویسندگان
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