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Open AccessArticle

Numerical Analysis of Mask-Based Phase Reconstruction in Phaseless Spherical Near-Field Antenna Measurements

by Adrien A. Guth, Sakirudeen Abdulsalaam, Holger Rauhut and Dirk Heberling

Sensors 2025, 25(18), 5637; https://doi.org/10.3390/s25185637 - 10 Sep 2025

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Phase-retrieval problems are employed to tackle the challenge of recovering a complex signal from amplitude-only data. In phaseless spherical near-field antenna measurements, the task is to recover the complex coefficients describing the radiation behavior of the antenna under test (AUT) from amplitude near-field measurements. The coefficients refer, for example, to equivalent currents or spherical modes, and from these, the AUT’s far-field characteristic, which is usually of interest, can be obtained. In this article, the concept of a mask-based phase recovery is applied to spherical near-field antenna measurements. First, the theory of the mask approach is described with its mathematical definition. Then, several mask types based on random distributions,

ϕ

-rotations, or probes are introduced and discussed. Finally, the performances of the different masks are evaluated based on simulations with multiple AUTs and with Wirtinger flow as a phase-retrieval algorithm. The simulation results show that the mask approach can improve the reconstruction error depending on the number of masks, oversampling, and the type of mask. Full article

(This article belongs to the Special Issue Recent Advances in Antenna Measurement Techniques)

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22 pages, 638 KB

Open AccessArticle

Unfolded Algorithms for Deep Phase Retrieval

by Naveed Naimipour, Shahin Khobahi, Mojtaba Soltanalian, Haleh Safavi and Harry C. Shaw

Algorithms 2024, 17(12), 587; https://doi.org/10.3390/a17120587 - 20 Dec 2024

Viewed by 1542

Abstract

Exploring the idea of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements. In this paper, we approach the problem by proposing a hybrid model-based, data-driven deep architecture referred to as Unfolded Phase Retrieval (UPR), which exhibits significant potential in improving the performance of state-of-the-art data-driven and model-based phase retrieval algorithms. The proposed method benefits from the versatility and interpretability of well-established model-based algorithms while simultaneously benefiting from the expressive power of deep neural networks. In particular, our proposed model-based deep architecture is applied to the conventional phase retrieval problem (via the incremental reshaped Wirtinger flow algorithm) and the sparse phase retrieval problem (via the sparse truncated amplitude flow algorithm), showing immense promise in both cases. Furthermore, we consider a joint design of the sensing matrix and the signal processing algorithm and utilize the deep unfolding technique in the process. Our numerical results illustrate the effectiveness of such hybrid model-based and data-driven frameworks and showcase the untapped potential of data-aided methodologies to enhance existing phase retrieval algorithms. Full article

(This article belongs to the Special Issue Machine Learning for Edge Computing)

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17 pages, 10147 KB

Open AccessArticle

Fourier Ptychographic Neural Network Combined with Zernike Aberration Recovery and Wirtinger Flow Optimization

by Xiaoli Wang, Zechuan Lin, Yan Wang, Jie Li, Xinbo Wang and Hao Wang

Sensors 2024, 24(5), 1448; https://doi.org/10.3390/s24051448 - 23 Feb 2024

Viewed by 2107

Abstract

Fourier ptychographic microscopy, as a computational imaging method, can reconstruct high-resolution images but suffers optical aberration, which affects its imaging quality. For this reason, this paper proposes a network model for simulating the forward imaging process in the Tensorflow framework using samples and coherent transfer functions as the input. The proposed model improves the introduced Wirtinger flow algorithm, retains the central idea, simplifies the calculation process, and optimizes the update through back propagation. In addition, Zernike polynomials are used to accurately estimate aberration. The simulation and experimental results show that this method can effectively improve the accuracy of aberration correction, maintain good correction performance under complex scenes, and reduce the influence of optical aberration on imaging quality. Full article

(This article belongs to the Special Issue Deep Learning-Based Neural Networks for Sensing and Imaging)

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16 pages, 4262 KB

Open AccessArticle

Research of Phase Compensation Methods Based on the Median Reweighted Wirtinger Flow Algorithm

by Yang Cao, Zupeng Zhang, Xiaofeng Peng, Huaijun Qin and Wenqing Li

Photonics 2022, 9(9), 619; https://doi.org/10.3390/photonics9090619 - 30 Aug 2022

Cited by 1 | Viewed by 2281

Abstract

An improved non-convex optimized phase recovery algorithm is used to compensate for wavefront aberrations caused by atmospheric turbulence and pointing errors in the vortex beam. The algorithm is divided into two parts: initialization and iteration. To reduce the effect of outliers, truncation rules are formulated in the initialization phase using the robustness of the sample median to obtain an initial value that is close to the global optimum. The relationship between the results of adjacent iterations is used in the iterations to calculate new weight coefficients, which are applied to the gradient descent to ensure the accuracy of the recovery results. Simulation experiments are carried out for different channel environments and different modes, and the results show that the improved phase recovery algorithm can accurately compensate for distorted wave fronts. The improved algorithm recovers the best results at different turbulence intensities and under the influence of different pointing errors. The recovered Strehl ratio can reach 0.9 and the mode purity can reach 0.92. Single-mode and multi-mode simulations were carried out, and the results show that the improved algorithm is effective and robust. Full article

(This article belongs to the Special Issue Application of Adaptive Optics Theory and Technology in Optical Wireless Communication)

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13 pages, 4494 KB

Open AccessFeature PaperArticle

Pixel Super-Resolution Phase Retrieval for Lensless On-Chip Microscopy via Accelerated Wirtinger Flow

by Yunhui Gao, Feng Yang and Liangcai Cao

Cells 2022, 11(13), 1999; https://doi.org/10.3390/cells11131999 - 22 Jun 2022

Cited by 26 | Viewed by 6368

Abstract

Empowered by pixel super-resolution (PSR) and phase retrieval techniques, lensless on-chip microscopy opens up new possibilities for high-throughput biomedical imaging. However, the current PSR phase retrieval approaches are time consuming in terms of both the measurement and reconstruction procedures. In this work, we present a novel computational framework for PSR phase retrieval to address these concerns. Specifically, a sparsity-promoting regularizer is introduced to enhance the well posedness of the nonconvex problem under limited measurements, and Nesterov’s momentum is used to accelerate the iterations. The resulting algorithm, termed accelerated Wirtinger flow (AWF), achieves at least an order of magnitude faster rate of convergence and allows a twofold reduction in the measurement number while maintaining competitive reconstruction quality. Furthermore, we provide general guidance for step size selection based on theoretical analyses, facilitating simple implementation without the need for complicated parameter tuning. The proposed AWF algorithm is compatible with most of the existing lensless on-chip microscopes and could help achieve label-free rapid whole slide imaging of dynamic biological activities at subpixel resolution. Full article

(This article belongs to the Collection Computational Imaging for Biophotonics and Biomedicine)

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20 pages, 4210 KB

Open AccessArticle

Phaseless Terahertz Coded-Aperture Imaging for Sparse Target Based on Phase Retrieval Algorithm

by Long Peng, Chenggao Luo, Bin Deng, Hongqiang Wang, Shuo Chen and Jun Dong

Sensors 2019, 19(21), 4617; https://doi.org/10.3390/s19214617 - 23 Oct 2019

Cited by 7 | Viewed by 3136

Abstract

Phaseless terahertz coded-aperture imaging (PL-TCAI) is a novel radar computational imaging method that utilizes the coded aperture and the incoherent detector array to achieve forward-looking and high-resolution imaging without relying on relative motion. In this paper, we propose a more reasonable and compact architecture for the PL-TCAI system and derive the imaging model of PL-TCAI based on the random frequency-hopping signal. Since most phase retrieval algorithms for PL-TCAI utilize only the intensity of echo signals to accurately reconstruct the target, excessive measurement samples are usually required. In order to reduce the number of measurement samples required for imaging, this paper proposes a sparse Wirtinger flow algorithm with optimal stepsize (SWFOS) by using the sparse prior of the target. The specific procedures of the SWFOS algorithm include the support recovery, initialization by truncated spectral method, iteration via gradient descent scheme, hard threshold operation, and stepsize optimization of iteration. Numerical simulations are performed, and the results show that the SWFOS algorithm not only has good performance for the PR problem, but can also sharply reduce the number of measurement samples required for imaging in the PL-TCAI system. Full article

(This article belongs to the Section Remote Sensors)

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