Phase Retrieval via Sparse Perturbed Amplitude Flow.

Saved in:

Bibliographic Details
Title:	Phase Retrieval via Sparse Perturbed Amplitude Flow.
Authors:	Lan Li¹ lanli@xsyu.edu.cn, Xiaoya Liu² 2015573234@qq.com, Xiaoyan Liu³ liuxiaoyan@xsyu.edu.cn, Yulong Mao² 1141628827@qq.com
Source:	IAENG International Journal of Applied Mathematics. Jul2025, Vol. 55 Issue 7, p2033-2041. 9p.
Subjects:	Absolute value, Smoothness of functions, Algorithms, Signals & signaling, Speed
Abstract:	Phase retrieval refers to reconstruct signal phase information only from acquired intensity or amplitude information. As the problem is underdetermined, its solution space admits multiple solutions. Additionally, the non-smooth absolute value term of the loss function may negatively impact the numerical results of Amplitude Flow. To address this issue, we propose a sparse perturbed based smooth loss function and is termed the Sparse Perturbed Amplitude Flow (SPAF) algorithm. The approach effectively constrains the signal solution space, reduces the number of required measurements. And mitigates the instability caused by near-zero of absolute value term that can lead to abrupt gradient changes. First, the initial value of the SPAF algorithm is obtained by sparse orthogonal initialization, then the exact solution is obtained after a series of hard thresholding iterations. Finally, the global convergence of the SPAF algorithm is also demonstrated. The SPAF algorithm does not require any truncation and reweighting process. Therefore, it is straightforward to achieve outstanding performance for both real and complex signals. Substantial tests confirm that the proposed algorithm significantly surpasses other state-of-the-art methods in recovery efficiency and convergence speed. [ABSTRACT FROM AUTHOR]
	Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database:	Engineering Source

Description
Abstract:	Phase retrieval refers to reconstruct signal phase information only from acquired intensity or amplitude information. As the problem is underdetermined, its solution space admits multiple solutions. Additionally, the non-smooth absolute value term of the loss function may negatively impact the numerical results of Amplitude Flow. To address this issue, we propose a sparse perturbed based smooth loss function and is termed the Sparse Perturbed Amplitude Flow (SPAF) algorithm. The approach effectively constrains the signal solution space, reduces the number of required measurements. And mitigates the instability caused by near-zero of absolute value term that can lead to abrupt gradient changes. First, the initial value of the SPAF algorithm is obtained by sparse orthogonal initialization, then the exact solution is obtained after a series of hard thresholding iterations. Finally, the global convergence of the SPAF algorithm is also demonstrated. The SPAF algorithm does not require any truncation and reweighting process. Therefore, it is straightforward to achieve outstanding performance for both real and complex signals. Substantial tests confirm that the proposed algorithm significantly surpasses other state-of-the-art methods in recovery efficiency and convergence speed. [ABSTRACT FROM AUTHOR]
ISSN:	19929978