Large-scale phase retrieval

High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information. In computational phase imaging, phase retrieval (PR) is required to reconstruct both amplitude and phase in complex space from intensity-only measurements. The existing PR algorithms suffer from the tradeoff among low computational complexity, robustness to measurement noise and strong generalization on different modalities. In this work, we report an efficient large-scale phase retrieval technique termed as LPR. It extends the plug-and-play generalized-alternating-projection framework from real space to nonlinear complex space. The alternating projection solver and enhancing neural network are respectively derived to tackle the measurement formation and statistical prior regularization. This framework compensates the shortcomings of each operator, so as to realize high-fidelity phase retrieval with low computational complexity and strong generalization. We applied the technique for a series of computational phase imaging modalities including coherent diffraction imaging, coded diffraction pattern imaging, and Fourier ptychographic microscopy. Extensive simulations and experiments validate that the technique outperforms the existing PR algorithms with as much as 17dB enhancement on signal-to-noise ratio, and more than one order-of-magnitude increased running efficiency. Besides, we for the first time demonstrate ultra-large-scale phase retrieval at the 8K level ($$7680\times 4320$$ 7680 × 4320 pixels) in minute-level time.

Phaseless Characterization of Compact Antenna Test Range via Improved Alternating Projection Algorithm

A practical compact antenna test range (CATR) requires good quiet zone quality for antenna characterization. This paper addresses the phase profile of the CATR quiet zone from the known intensity pattern of spatial domain and Fourier domain based on a combined alternating projection algorithm. The proposed algorithm is composed of Gerchberg–Saxton (GS) and Hybrid Input–Output (HIO) algorithms and the two algorithms with spatial phase perturbation (SPP) work collaboratively or independently under predesigned conditions. It is observed that the algorithm with random initial phase guess can always converge to an optimal solution by performing a series of hierarchical optimizations of the problem. The numerical results are in good agreement with simulated results in different frequency bands, overcoming the phase retrieval limitation of local convergence in the iterative process. Furthermore, to validate the effectiveness and robustness of the proposed procedure, the related discussions corresponding to different sampling areas in Fourier domain and different signal to noise ratios (SNRs) are given.

Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval

We present the convergence analysis of convex combination of the alternating projection and Douglas–Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are established by applying various schemes of numerical analysis and exploring both physical and mathematical characteristics of the phase retrieval problem. Numerical results demonstrate the advantages of the algorithm over the other widely known projection methods in practically relevant simulations.

Effect of varying Number of Spacing between Antenna Elements, Snapshots, SNR on AP ML, AP-SSF and ESPRIT Algorithm

The direction of arrival estimation is the main key problem in array signal processing. In this paper, the alternating projection maximum Likelihood (AP-ML), Alternating projection sub space framework (APSSF) and ESPRIT algorithm are studied. The simulation is performed in MATLAB for single and multiple sources. The effect of the varying number of spacing between antenna elements, number of snapshots and SNR are studied. The performance comparison shows that ESPRIT algorithm performs better as compared to the AP-ML and AP-SSF. Key-Words: - AP-ML, AP-SSF, Direction of Arrival, ESPRIT, Snapshots, SNR