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A Sample Efficient Alternating Minimization-Based Algorithm for Robust Phase Retrieval
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DOI：10.1109/TIT.2025.3609564.png)
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Abstract
En 中文
In this work, we study the robust phase retrieval problem where the task is to recover an unknown signal theta(& lowast; )is an element of R-d in the presence of potentially arbitrarily corrupted magnitude-only linear measurements. We propose an alternating minimization approach that incorporates an oracle solver for a non-convex optimization problem as a subroutine. Our algorithm guarantees convergence to theta(& lowast;) and provides an explicit polynomial dependence of the convergence rate on the fraction of corrupted measurements. We then provide an efficient construction of the aforementioned oracle under a sparse arbitrary outliers model and offer valuable insights into the geometric properties of the loss landscape in phase retrieval with corrupted measurements. Our proposed oracle avoids the need for computationally intensive spectral initialization, using a simple gradient descent algorithm with a constant step size and random initialization instead. Additionally, our overall algorithm achieves nearly linear sample complexity, O(d polylog(d)).
Keywords:
Phase measurement
Pollution measurement
Complexity theory
Convergence
Loss measurement
Minimization
Data collection
Vectors
Data models
Current measurement
Robust phase retrieval
signal recovery
nonconvex optimization with guarantees
Journal
I
IF:
2.9
Papers:
317
Citations:
0