Fig. 1. Schematic of FPM experimental setup and principle^[6]. (a) Physical map of FPM system; (b) schematic of the working process of FPM; (c) overlappled frequency domain sub-apertures; (d) LED array oblique light illumination; (e) LED array sequential lighting process

Fig. 2. Simulated high-resolution images and pupil functions. (a) Ideal high-resolution amplitude; (b) ideal high-resolution phase; (c) pupil function amplitude; (d) pupil function phase

Fig. 3. High-resolution amplitude and phase images are reconstructed by several typical sequential methods. (a) Traditional G-S method; (b) EPRY method; (c) sequential Gauss-Newton method

Fig. 4. Images reconstructed by global gradient descent method with variable step-size update strategy. (a) (b) Reconstructed amplitude and phase images by update step-size dichotomy; (c) (d) reconstructed amplitude and phase images by update step-size Newton method; (e) (f) amplitude and phase of pupil function recovered by update step-size dichotomy; (g) (h) amplitude and phase of pupil function recovered by update step-size Newton method

Fig. 5. Error measurement index curves of each reconstruction algorithm. (a) Curve of amplitude relative error measurement index; (b) curve of phase relative error measurement index; (c) curve of cost function error measurement index

Fig. 6. High-resolution amplitude images reconstructed by each reconstruction algorithm and error measurement curve. (a) G-S method; (b) EPRY method; (c) sequential Gauss-Newton method; (d) global Newton with update step-size dichotomy method; (e) global Newton with update step-size Newton method; (f) error measurement curve

Fig. 7. Amplitude and phase images reconstructed by each sequential method. (a) G-S method; (b) EPRY method; (c) sequential Gauss-Newton method

Fig. 8. Images restored by global variable step-size algorithm and error measurement curve. (a) (b) Amplitude and phase images reconstructed by global gradient descent update step-size dichotomy; (c) (d) amplitude and phase images reconstructed by global Newton updating step-size Newton method; (e) error measurement curve corresponding to each reconstruction algorithm