PhaseMax: Convex Phase Retrieval via Basis Pursuit
By Tom Goldstein, Christoph Studer. 2016
291 citations recorded by the source corpus.
We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods that use semidefinite relaxation and lift the phase retrieval problem to a higher dimension, PhaseMax is a “non-lifting” relaxation that operates in the original signal dimension. We show that the dual problem to PhaseMax is basis pursuit, which implies that the phase retrieval can be performed using algorithms initially designed for sparse signal recovery. We develop sharp lower bounds on the success probability of PhaseMax for a broad range of random measurement ensembles, and we analyze the impact of measurement noise on the solution accuracy. We use numerical results to demonstrate the accuracy of our recovery guarantees, and we showcase the efficacy and limits of PhaseMax in practice.
Subfields: Computer Vision and Pattern Recognition, Radiation
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In Computer Vision and Pattern Recognition
In Radiation
- Lenka Zdeborov'a
- Florent Krzakala
- Cong Ma
- Yuejie Chi
- Tom Goldstein
- Yuxin Chen
- Kaizheng Wang
- Sundeep Rangan
Citations in the corpus
- Visualizing the Loss Landscape of Neural Nets (2017, background): “In fact, the expected cosine similarity between Gaussian random vectors in n dimensions is roughly √ 2/(πn) ([12], Lemma 5).”
- Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution (2017, background): “Another convex program PhaseMax [5,41,50,53] operates in the natural parameter space via linear programming, provided that an anchor vector is available.”
- Optimal errors and phase transitions in high-dimensional generalized linear models (2017, methodology): “Our comparison with the performance of a state-of-the-art algorithm PhaseMax [85] suggests that also for this simple benchmark there is room for improvement in term of matching the performance of GAMP.”