1. Sparse signal recovery from phaseless measurements via hard thresholding pursuit.
- Author
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Cai, Jian-Feng, Li, Jingzhi, Lu, Xiliang, and You, Juntao
- Subjects
- *
ALGORITHMS , *COMPRESSED sensing - Abstract
In this paper, we consider the sparse phase retrieval problem, recovering an s -sparse signal x ♮ ∈ R n from m phaseless samples y i = | 〈 x ♮ , a i 〉 | for i = 1 , ... , m. Existing sparse phase retrieval algorithms are usually first-order and hence converge at most linearly. Inspired by the hard thresholding pursuit (HTP) algorithm in compressed sensing, we propose an efficient second-order algorithm for sparse phase retrieval. Our proposed algorithm is theoretically guaranteed to give an exact sparse signal recovery in finite (in particular, at most O (log m + log (‖ x ♮ ‖ 2 / | x min ♮ |)) steps, when { a i } i = 1 m are i.i.d. standard Gaussian random vector with m ∼ O (s log (n / s)) and the initialization is in a neighborhood of the underlying sparse signal. Together with a spectral initialization, our algorithm is guaranteed to have an exact recovery from O (s 2 log n) samples. Since the computational cost per iteration of our proposed algorithm is the same order as popular first-order algorithms, our algorithm is extremely efficient. Experimental results show that our algorithm can be several times faster than existing sparse phase retrieval algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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