Fig. 1. Flowchart of alternating projection algorithms. (a) GS algorithm; (b) input-output algorithm; (c) output-output algorithm; (d) hybrid input-output algorithm

Fig. 2. FPM reconstruction using AP algorithm^[25].^{(a) FPM system structure; (b) FPM imaging model; (c) strength constraints imposed by AP algorithm in solution space; (d) AP solving FPM process}

Fig. 3. Applications of FPM technique^[25]. (a) Quantitative phase imaging of blood smear; (b) phase images of live HeLa cell; (c) phase images of mitosis and apoptosis events of live HeLa cell captured by annular illumination FPM at a frame rate of 25 Hz; (d) reconstruction of three-dimensional refractive index of HeLa cells by FPM; (e) topographic map of a 3D surface via FP technology

Fig. 4. CDI techniques and reconstruction algorithms^[30]. (a) Plane-wave CDI; (b) Bragg CDI; (c) ptychographic CDI; (d) Fresnel CDI; (e) reflection CDI; (f) flowchart of alternating-projection-based CDI reconstruction algorithm

Fig. 5. Applications of CDI technique^[30]. (a) 3D mass density distribution of an unstained yeast spore cell; (b) 3D image of an unstained human chromosome; (c) reconstruction of an unstained herpesvirus virion; (d) quantitative 3D measurement of osteocyte; (e) representative diffraction pattern of a giant mimivirus particle; (f) 3D reconstruction of a mimivirus; (g) diffraction pattern of a nanocrystal; (h) electron density map of 2mFo-DFc

Fig. 6. Framework of DIP algorithm. (a) Principle of DIP; (b) common CNN structure; (c) UNet structure; (d) deep decoder structure

Fig. 7. Results of DIP algorithm and comparisons with other algorithms in each task. (a) Inpainting^[31]; (b) diffraction imaging^[51]; (c) phase unwarpping^[63]

Fig. 8. Framework and applications of the PnP-GAP optimization. (a) Diagram of plug-and-play optimization framework based on GAP; (b) (c) comparison of large-scale snapshot compressive imaging and Fourier ptychographic microscopy between plug-and-play optimization and other methods, respectively^[6,90]

Fig. 9. Fusion process of living glioblastoma observed by using plug-and-play optimization framework based on GAP^[6]