Qiao, C.; Liu, S.; Wang, Y.; Xu, W.; Geng, X.; Jiang, T.; Zhang, J.; Meng, Q.; Qiao, H.; Li, D.; Dai, Q.

Single image super-resolution (SISR) neural networks for optical microscopy have shown great capability to directly transform a low-resolution (LR) into its super-resolution (SR) counterpart, enabling low-cost long-term live-cell SR imaging. However, when processing time-lapse data, current SISR models failed to exploit the important temporal dependencies between neighbor frames, inclined to generate temporally inconsistent results. Besides, SISR models are subject to inference uncertainty that is hard to accurately quantify, therefore it is difficult to determine to what extend can we trust the inferred SR images. Here, we first build a large-scale, high-quality dataset for the time-lapse image super-resolution (TISR) task, and conducted a comprehensive evaluation on two essential components, i.e., propagation and alignment mechanisms, of TISR methods. Second, we devised the deformable phase-space alignment (DPA) based TISR neural network (DPA-TISR), which adaptively enhances the cross-frame alignment in the phase domain and outperforms existing state-of-the-art TISR models. Third, we combined the Bayesian training scheme with DPA-TISR, dubbed Bayesian DPA-TISR, and designed an expected calibration error (ECE) minimization framework to obtain a well-calibrated confidence map along with each output SR image, which reliably implicates potential inference errors. We demonstrate that the Bayesian DPA-TISR achieves resolution enhancement by more than 2-fold compared to diffraction limits with high fidelity and temporal consistency, enabling confidence-quantifiable TISR in long-term live-cell SR imaging for various bioprocesses.