Phase retrieval algorithms
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Ptychographic reconstructions: Wigner distribution deconvolution [25,159–165], non-linear optimization [9], ptychographic iterative engine [4,11,18,166,167], maximum-likelihood optimization [18,42,168], difference map [18,169], relaxed averaged alternating reflections [170], Douglas-Rachford algorithm [117,171], alternating direction methods of multipliers [172–176], stochastic proximal gradient descent [174,177,178], Gauss-Newton method with amplitude-based cost function [41], adaptive step size for gradient descent [179], Wirtinger gradient [99,180–185], convex relaxation [186], regularization via sparsity [146,187,188], noise modeling and denoising [181,185,189–191], low-rank recovery [192].
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System corrections and other extensions
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Correction for conventional ptychographic systems: Joint object-probe retrieval [9–11,31,193], state mixture decomposition [18,194–196], positional error correction [197–200], partial coherence correction [18,19,201,202], fly scan ptychography [203–207], optimization of probe overlapping area [208], angle calibration for the reflection configuration [209].
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Correction for Fourier ptychographic systems: LED intensity correction [210,211], joint sample-pupil recovery [12,13,81,150,152] LED alignment calibration and incident angle correction [37,41,117,211–218], correcting under- and over-exposed pixels [219], sample motion correction [220,221], stray light detection [222], vignetting effect [223], an open-source MATLAB application for correcting different system parameters [44], Miscalibration-tolerant multi-look FPM [224–226], pose correction for camera-scanning Fourier ptychography [227].
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Other extensions: Multiplexing algorithm [20,117,228], Multi-slice modeling [14–17,229–232], 3D diffraction tomography [49–52,65,71,93,233–236], super-resolution ptychography [23,96], autofocusing [60,237], parallel computation [238–240], GPU-based solver [239,241], correlation analysis for imaging through diffusing media [242–244], refraction index reconstruction to avoid phase wrapping [245], sub-pixel modeling [30,246], temporal correlation constraint for time-lapse experiment [64], high-dynamic range acquisition using a color camera [247], vectorial extensions for polarization-sensitive imaging [102,248–251].
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Neural network and related approaches
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Automatic differentiation (neural networks for modeling the forward imaging process): Recovering object and other system parameters for FPM [252–257] and for conventional ptychography [258–261].
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Optimizing the illumination strategy and other system parameters: Incorporating physical model for designing the coded illumination pattern [79,119,262–266], parameter refinement [267,268].
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Deep learning-based reconstruction: Image recovery from raw measurements via data-driven deep neural networks [114,148,225,269–275], physics-guided network [270,276].
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Post-reconstruction processing and analysis: Virtual staining and image translation [30,277–281], post-reconstruction cytometric analysis [60,264,265,282].
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