Improving the stability of phase retrieval algorithm in speckle autocorrelation imaging by Huber penalty sparsity constraint

• Published in: Optics communications Vol. 549; p. 129882
• Main Authors: Cui, Guangmang, He, Bintao, Shi, Shigong, Zhao, Jufeng, Xiang, Qinlei
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.12.2023
• Subjects: Huber penalty sparsity constraint; Hybrid input output algorithm; Local optimal solution; Memory effect; Speckle image; Huber penalty sparsity constraint; Local optimal solution; Hybrid input output algorithm; Speckle image; Memory effect
• ISSN: 0030-4018; 1873-0310
• DOI: 10.1016/j.optcom.2023.129882

One of the most widely used methods for reconstructing images through a scattering medium is the Hybrid Input Output (HIO) phase retrieval algorithm. However, the stability and noise robustness of the HIO method are poor, as they are affected by initial values and noise during the imaging process. This paper presents an optimized HIO phase retrieval algorithm that utilizes the Huber penalty as a sparsity constraint to effectively enhance the quality and stability of the reconstruction algorithm. The introduced constraint is designed to guide the iteration process away from local optimal solutions, ensuring superior recovery images even with random initial values. Additionally, an adaptive step size parameter is incorporated to control the iterations and convergence steps, resulting in stronger robustness against noise effects. Moreover, the error criterion for image restoration is defined as the sum of the Fourier transform amplitude of the gradient. Experimental results demonstrate that the proposed phase retrieval algorithm achieves superior quality in the recovered images, while significantly improving noise immunity and stability for randomly selected initial values. •The Huber penalty is introduced into the HIO phase retrieval algorithm as the sparsity constraint so as to reduce the dependence on the selection of initial values.•The error criterion value to assess the quality of the restored solution is introduced into the integrated phase retrieval process framework to control the number of iterations.•An adaptive step size in the iteration process is designed to strengthen the noise robustness of the algorithm.