AAAI Publications, Thirty-First AAAI Conference on Artificial Intelligence

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Fast Compressive Phase Retrieval under Bounded Noise
Hongyang Zhang, Shan You, Zhouchen Lin, Chao Xu

Last modified: 2017-02-13

Abstract


We study the problem of recovering a t-sparse real vector from m quadratic equations yi=(ai*x)^2 with noisy measurements yi's. This is known as the problem of compressive phase retrieval, and has been widely applied to X-ray diffraction imaging, microscopy, quantum mechanics, etc. The challenge is to design a a) fast and b) noise-tolerant algorithms with c) near-optimal sample complexity. Prior work in this direction typically achieved one or two of these goals, but none of them enjoyed the three performance guarantees simultaneously. In this work, with a particular set of sensing vectors ai's, we give a provable algorithm that is robust to any bounded yet unstructured deterministic noise. Our algorithm requires roughly O(t) measurements and runs in O(tn*log (1/epsilon)) time, where epsilon is the error. This result advances the state-of-the-art work, and guarantees the applicability of our method to large datasets. Experiments on synthetic and real data verify our theory.

Keywords


Phase Retrieval, Compressed Sensing, Sparsity

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