Bahcall, Neta A.Charlotte, WardKrishnaraj, Veena2026-07-082026-07-082026-04-27https://theses-dissertations.princeton.edu/handle/88435/dsp01h989r669cThe Rubin Observatory Legacy Survey of Space and Time (LSST) is projected to discover hundreds of gravitationally lensed Type Ia supernovae (glSNe), offering an unprecedented opportunity for time-delay cosmography and independent measurements of the Hubble constant. However, the majority of Rubin-discovered glSNe will be marginally resolved in ground-based imaging, making accurate deblending of the multiply-imaged supernovae from the foreground lens and host galaxy a critical challenge. We present a new framework to extract light curves of the multiply-imaged SNe from blended glSNe systems via joint forward modeling of multi-epoch, multi-band high-resolution space-based imaging and ground-based imaging using \texttt{Scarlet2}, combined with Gaussian Process time-delay inference using \texttt{GausSN}. Using pixel-level simulations of Rubin and Roman imaging of typical glSNe systems from the Goldstein et al. 2019 catalog across a range of angular separations, we quantify pipeline performance as a function of source blending and space-based follow-up availability. We find that Rubin-only observations are sufficient to recover time-delays with sub-day mean errors, outperforming configurations that include supplemental Roman epochs. SN image separations are recovered to $\sim 10^{-2}$ arcsecond precision even when sources are initialized with significant spatial offsets. These results suggest transient light curves, time-delays, and image positions can be extracted from Rubin data alone, while more accurate lens mass modeling can be performed separately using archival high-resolution imaging, reducing the need for prompt space-based follow-up and substantially increasing the number of systems suitable for time-delay cosmography.en-USPrinceton University Senior Theses