Improved recovery guarantees for phase retrieval from coded diffraction patterns

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• 作者：D. Gross^a ; ^b ; F. Krahmer^c ; R. Kueng^d ; ^b ; ^a ; ^{richard.kueng@physik.uni-freiburg.de}
• 关键词：Compressed sensing ; Low rank matrix recovery ; Phase retrieval ; PhaseLift ; Masked Fourier measurements ; Coded diffraction patterns ; Golfing scheme
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：42
• 期：1
• 页码：37-64
• 全文大小：597 K
• 卷排序：42

文摘

In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex optimization. We provide recovery guarantees which require O(log2⁡d)O(log2⁡d) different diffraction patterns, thus improving on recent results by Candès et al. [1], which demand O(log4⁡d)O(log4⁡d) different patterns.