Phase Retrieval from Coded Diffraction Patterns

By E.J. Candes, Xiaodong Li, M. Soltanolkotabi. 2013

406 citations recorded by the source corpus.

This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can modulate the signal of interest and then collect the intensity of its diffraction pattern, each modulation thereby producing a sort of coded diffraction pattern. We show that PhaseLift, a recent convex programming technique, recovers the phase information exactly from a number of random modulations, which is polylogarithmic in the number of unknowns. Numerical experiments with noiseless and noisy data complement our theoretical analysis and illustrate our approach.

Subfields: Computer Vision and Pattern Recognition, Mathematical Physics, Radiation

View Paper: https://www.semanticscholar.org/paper/477bdb1fcc89ee345fe2d622c531273c088b94f3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

In Mathematical Physics

In Radiation

Citations in the corpus

Phase Retrieval Using Alternating Minimization (2013, background): “Recently, [34] establishes near-optimal statistical guarantees for PhaseLift under masked Fourier transform measurements.”
Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow (2016, methodology): “Other approaches rely on introducing redundancy into measuremen ts using for example, the short-time Fourier transform, or masks [27], [28].”
Learned D-AMP: Principled Neural Network based Compressive Image Recovery (2017, methodology): “We tested the algorithms with i.i.d. Gaussian measurements and with measurements from a randomly sampled coded diffraction pattern [44].”
An Overview of Low-Rank Matrix Recovery From Incomplete Observations (2016, background): “is analyzed in detail in [124], where the acquisition process consists of first modulating a signal with a small number of”
Phase Retrieval via Wirtinger Flow: Theory and Algorithms (2014, methodology): “We refer to the combination of these two steps, introduced in reverse order below, as the Wirtinger ﬂow (WF) algorithm.”
Low-rank Solutions of Linear Matrix Equations via Procrustes Flow (2015, background): “Subsequently, a series of papers (Candès & Recht, 2009; Gross, 2011; Recht, 2011; Candès et al., 2014) showed that trace minimization and related convex optimization approaches also work for other measurement ensembles such as those arising in matrix completion and related problems.”
Experimental robustness of Fourier Ptychography phase retrieval algorithms (2015, methodology): “These algorithms come with the significant advantage of rigorous mathematical guarantees [28] and were successfully applied to FPM data [27].”