On phase retrieval via matrix completion and the estimation of low rank PSD matrices
arXiv:1907.09537 · doi:10.1088/1361-6420/ab4e6d
Abstract
Given underdetermined measurements of a Positive Semi-Definite (PSD) matrix of known low rank , we present a new algorithm to estimate based on recent advances in non-convex optimization schemes. We apply this in particular to the phase retrieval problem for Fourier data, which can be formulated as a rank 1 PSD matrix recovery problem. Moreover, we provide theory for how oversampling affects the stability of the lifted inverse problem.
References in corpus (13)
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
- Phase Retrieval via Wirtinger Flow: Theory and Algorithms
- High-resolution ab initio three-dimensional X-ray diffraction microscopy
- A unified evaluation of iterative projection algorithms for phase retrieval
- Relaxed Averaged Alternating Reflections for Diffraction Imaging
- An algebraic characterization of injectivity in phase retrieval
- A Field Guide to Forward-Backward Splitting with a FASTA Implementation
- Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
- On convexification/optimization of functionals including an l2-misfit term
- An unbiased approach to compressed sensing
- Numerical methods for phase retrieval
- Bias Reduction in Compressed Sensing
- An unbiased approach to low rank recovery