Extracting the rich quasi-normal mode spectrum in the gravitational-wave ringdown signals poses data analysis challenges, partly due to the need to isolate the ringdown phase from the preceding inspiral and merger phases. A variety of data analysis strategies have been developed to address this issue, including the gating and inpainting technique to single out the ringdown contribution. In this talk, I will introduce a novel data analysis formalism that integrates information from the pre-ringdown as an informed prior for ringdown by gating and inpainting. Thanks to the recent theoretical progress on calculating the quadratic modes coupling ratio, we focus on the GW250114 ringdown phase and theoretically computes the contribution from quadratic modes. I will also discuss the evidence of detecting quadratic modes in GW250114.