On Fienup Methods for Sparse Phase Retrieval
On Fienup Methods for Sparse Phase Retrieval
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DOI：
10.1109/tsp.2017.2780044
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发表时间：
2017-02
影响因子：
5.4
通讯作者：
Edouard Pauwels;A. Beck;Yonina C. Eldar;Shoham Sabach
中科院分区：
文献类型：
--
作者：
Edouard Pauwels;A. Beck;Yonina C. Eldar;Shoham Sabach
交替最小化或Fienup方法在相位恢复中具有悠久的历史。我们提供了新的见解，这些算法的经验和理论分析时，与傅立叶测量和凸先验相结合。特别是，我们表明，Fienup方法可以被视为执行交替最小化的正则化非凸最小二乘问题的振幅测量。此外，我们证明了在温和的额外的结构假设的先验（半代数性），信号估计序列具有光滑的收敛行为的非凸正则化最小二乘目标的临界点。最后，我们提出了一个扩展Fienup技术，基于投影梯度下降的解释和加速使用惯性项。我们的实验表明，这种修改结合了$\ell_1 $先验构成了稀疏相位检索的竞争力的方法。
Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex priors. In particular, we show that Fienup methods can be viewed as performing alternating minimization on a regularized nonconvex least-squares problem with respect to amplitude measurements. Furthermore, we prove that under mild additional structural assumptions on the prior (semialgebraicity), the sequence of signal estimates has a smooth convergent behavior toward a critical point of the nonconvex regularized least-squares objective. Finally, we propose an extension to Fienup techniques, based on a projected gradient descent interpretation and acceleration using inertial terms. We demonstrate experimentally that this modification combined with an $\ell _1$ prior constitutes a competitive approach for sparse phase retrieval.