Sparse Affine Sampling: Ambiguity-Free and Efficient Sparse Phase Retrieval

Ming-Hsun Yang; Y.-W. Peter Hong; Jwo-Yuh Wu

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Sparse Affine Sampling: Ambiguity-Free and Efficient Sparse Phase Retrieval

机译：Sparse Affine Sampling: Ambiguity-Free and Efficient Sparse Phase Retrieval

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Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine measurements to achieve ambiguity-free signal reconstruction. The proposed method relies on two-stage approach that consists of support identification followed by the exact recovery of nonzero signal entries. In the noise-free case, perfect support identification using a simple counting rule is guaranteed subject to a mild condition on the signal sparsity, and subsequent exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed approach is then extended to two noisy scenarios, namely, sparse noise (or outliers) and non-sparse bounded noise. For both cases, perfect support identification is still ensured under mild conditions on the noise model, namely, the support size for sparse outliers and the power of the bounded noise. Under perfect support identification, exact signal recovery can be achieved using a simple majority rule for the sparse noise scenario, and reconstruction up to a bounded error can be achieved using linear least-squares (LS) estimation for the non-sparse bounded noise scenario. The obtained analytic performance guarantee for the latter case also sheds light on the construction of the sensing matrix and bias vector. In fact, we show that a near optimal performance can be achieved with high probability by the random generation of the nonzero entries of the sparse sensing matrix and bias vector according to the uniform distribution over a circle. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme.

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来源
《IEEE Transactions on Information Theory》 |2022年第11期|7604-7626|共23页
作者
Ming-Hsun Yang; Y.-W. Peter Hong; Jwo-Yuh Wu;
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作者单位

Department of Communication Engineering, National Central University, Taoyuan, Taiwan;

Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan;

Department of Electrical and Computer Engineering, Institute of Communications Engineering, and the College of Electrical Engineering, National Yang Ming Chiao Tung University, Hsinchu, Taiwan;

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正文语种英语
中图分类通信;
关键词
Sensors; Noise measurement; Signal reconstruction; Sparse matrices; Phase measurement; Channel estimation; Extraterrestrial measurements;

Sparse Affine Sampling: Ambiguity-Free and Efficient Sparse Phase Retrieval

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