
Reshaped Wirtinger Flow and Incremental Algorithm for Solving Quadratic System of Equations
We study the phase retrieval problem, which solves quadratic system of e...
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Misspecified Nonconvex Statistical Optimization for Phase Retrieval
Existing nonconvex statistical optimization theory and methods crucially...
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DOLPHIn  Dictionary Learning for Phase Retrieval
We propose a new algorithm to learn a dictionary for reconstructing and ...
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Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow
This paper considers the noisy sparse phase retrieval problem: recoverin...
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Structured signal recovery from quadratic measurements: Breaking sample complexity barriers via nonconvex optimization
This paper concerns the problem of recovering an unknown but structured ...
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Fast signal recovery from quadratic measurements
We present a novel approach for recovering a sparse signal from crossco...
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QuantizationAware Phase Retrieval
We address the problem of phase retrieval (PR) from quantized measuremen...
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Robust Wirtinger Flow for Phase Retrieval with Arbitrary Corruption
We consider the phase retrieval problem of recovering the unknown signal from the magnitudeonly measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow, to jointly estimate the unknown signal and the sparse corruption. We show that our proposed algorithm is guaranteed to converge linearly to the unknown true signal up to a minimax optimal statistical precision in such a challenging setting. Compared with existing robust phase retrieval methods, we improved the statistical error rate by a factor of √(n/m) where n is the dimension of the signal and m is the sample size, provided a refined characterization of the corruption fraction requirement, and relaxed the lower bound condition on the number of corruption. In the noisefree case, our algorithm converges to the unknown signal at a linear rate and achieves optimal sample complexity up to a logarithm factor. Thorough experiments on both synthetic and real datasets corroborate our theory.
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