Improved Recovery Guarantees for Phase Retrieval from Coded Diffraction Patterns

@article{Gross2014ImprovedRG,
  title={Improved Recovery Guarantees for Phase Retrieval from Coded Diffraction Patterns},
  author={David Gross and Felix Krahmer and Richard Kueng},
  journal={ArXiv},
  year={2014},
  volume={abs/1402.6286}
}
Phase Recovery Guarantees From Designed Coded Diffraction Patterns in Optical Imaging
TLDR
It is established that the image reconstruction quality directly depends on the coded aperture structure; therefore, a design strategy is proposed and Experimental results show that the scene is successfully recovered by using designed coded apertures with up to 40% less measurements compared to non-designed ensembles.
Learning Illumination Patterns for Coded Diffraction Phase Retrieval.
TLDR
This paper learns illumination patterns to recover signals from coded diffraction patterns using a fixed-cost alternating minimization-based phase retrieval method and demonstrates that the proposed method provides near-perfect reconstruction using patterns learned with a small number of training images.
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TLDR
Numerical results show that the proposed coding elements are able to solve sparsity-based PR at any optical field under an admissible modulation and show the types of admissible coding elements that best estimate the support.
Data-Driven Illumination Patterns For Coded Diffraction Imaging
TLDR
This paper learns illumination patterns to recover signals from coded diffraction patterns using a fixed-cost alternating minimization-based phase retrieval method and demonstrates that the proposed method provides near-perfect reconstruction using patterns learned with a small number of training images.
The numerics of phase retrieval
TLDR
The past decade has witnessed a surge in the systematic study of computational algorithms for phase retrieval, and this paper will review recent advances from a numerical viewpoint.
Phase retrieval with PhaseLift algorithm
TLDR
This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years and establishes stable guarantees for measurements sampled from sufficiently random distribution.
Super-Resolution Phase Retrieval From Designed Coded Diffraction Patterns
TLDR
A super-resolution phase retrieval algorithm that minimizes a smoothed nonconvex least-squares objective function is proposed and results show that the proposed algorithm overcomes state-of-the-art methods in reconstructing the high-resolution image.
Algebraic theory of phase retrieval
The phase retrieval problem first arose in the early 20th century from work on X-ray crystallography. In the last century, X-ray crystallography has developed into the leading method to elucidating
Phase Retrieval via Wirtinger Flow: Theory and Algorithms
TLDR
This paper develops a nonconvex formulation of the phase retrieval problem as well as a concrete solution algorithm that is shown to rigorously allow the exact retrieval of phase information from a nearly minimal number of random measurements.
Solving Phase Retrieval with a Learned Reference
TLDR
This paper proposes a proposed method for phase retrieval via unrolled network and learned reference that provides near-perfect recovery at fixed (small) computational cost and compared with standard Fourier phase retrieval methods.
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Phase Retrieval from Coded Diffraction Patterns
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TLDR
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