Toward robust super-resolution imaging: A low-rank approximation approach for pattern-illuminated Fourier ptychography

Pattern-illuminated Fourier ptychography (piFP) is an elegant combination of structured illumination imaging and a Fourier ptychographic algorithm with the ability to image beyond the diffraction limit of the employed optics. Artifact-free piFP super-resolution reconstruction requires a high level of stability in the illumination pattern. However, unpredictable pattern variation occurs in the presence of environment perturbation, intensity fluctuation, and pointing instability at the source, leading to declines in image reconstruction quality. To address this issue, we present an efficient and robust piFP algorithm based on low-rank approximation (LRA-piFP), which relaxes the requirement for the stability of illumination patterns. This LRA-piFP method can model frame-wise pattern variation during a full scan, thus improve the reconstruction quality significantly. We take numerical simulations and proof-of-principle experiments with both long-range imaging and microscopy for demonstrations. Results show that the LRA-piFP method can handle different kinds of pattern variation and outperforms other state-of-the-art techniques in terms of reconstruction quality and resolution improvement. Our method provides effective experimental robustness to piFP with a natural algorithmic extension, paving the way for its application in both macroscopic and microscopic imaging.