Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy

The incremental gradient approaches, such as PIE and ePIE, are widely used in the field of ptychographic imaging due to their great flexibility and computational efficiency. Nevertheless, their stability and reconstruction quality may be significantly degraded when non-negligible noise is present in the image. Though this problem is often attributed to the non-convex nature of phase retrieval, we found the reason for this is more closely related to the choice of the step-size, which needs to be gradually diminishing for convergence even in the convex case. To this end, we introduce an adaptive step-size strategy that decreases the step-size whenever sufficient progress is not made. The synthetic and real experiments on Fourier ptychographic microscopy show that the adaptive step-size strategy significantly improves the stability and robustness of the reconstruction towards noise yet retains the fast initial convergence speed of PIE and ePIE. More importantly, the proposed approach is simple, nonparametric, and does not require any preknowledge about the noise statistics. The great performance and limited computational complexity make it a very attractive and promising technique for robust Fourier ptychographic microscopy under noisy conditions.