Despite the prevalence of superresolution (SR) microscopy, quantitative live-cell SR imaging that maintains the completeness of delicate structures and the linearity of fluorescence signals remains an uncharted territory. Structured illumination microscopy (SIM) is the ideal tool for live-cell SR imaging. However, it suffers from an out-of-focus background that leads to reconstruction artifacts. Previous post hoc background suppression methods are prone to human bias, fail at densely labeled structures, and are nonlinear. Here, we propose a physical model-based Background Filtering method for living cell SR imaging combined with the 2D-SIM reconstruction procedure (BF-SIM). BF-SIM helps preserve intricate and weak structures down to sub-70 nm resolution while maintaining signal linearity, which allows for the discovery of dynamic actin structures that, to the best of our knowledge, have not been previously monitored.