Phase unwrapping is an indispensable step in recovering the true phase from a modulo-2π phase. Conventional phase unwrapping methods suffer from error propagation under severe noise. In this Letter, we propose an iterative framework for robust phase unwrapping with high fidelity. The proposed method utilizes the transport-of-intensity equation to solve the phase unwrapping problem with high computational efficiency. To further improve reconstruction accuracy, we take advantage of non-local structural similarity using low-rank regularization. Meanwhile, we use an adaptive iteration strategy that dynamically and automatically updates the denoising parameter to avoid over-smoothing and preserve image details. A set of simulation and experimental results validates the proposed method, which can provide satisfying results under severe noise conditions, and outperform existing state-of-the-art phase unwrapping methods with at least 6 dB higher peak SNR (PSNR).