In this paper, we show how to carry out a relatively more realistic and complete reconstruction of supernova neutrino spectra in the future large liquid-scintillator detectors, by implementing the method of singular value decomposition with a proper regularization. For a core-collapse supernova at a distance of $10~{\rm kpc}$ in the Milky Way, its $\overlineν^{}_e$ spectrum can be precisely determined from the inverse beta-decay process $\overlineν^{}_e + p \to e^+ + n$, for which a $20~{\rm kiloton}$ liquid-scintillator detector with the resolution similar to the Jiangmen Underground Neutrino Observatory (JUNO) may register more than 5000 events. We have to rely predominantly on the elastic neutrino-electron scattering $ν+ e^- \to ν+ e^-$ and the elastic neutrino-proton scattering $ν+ p \to ν+ p$ for the spectra of $ν^{}_e$ and $ν^{}_x$, where $ν$ denotes collectively neutrinos and antineutrinos of all three flavors and $ν^{}_x$ for $ν^{}_μ$ and $ν^{}_τ$ as well as their antiparticles. To demonstrate the validity of our approach, we also attempt to reconstruct the neutrino spectra by using the time-integrated neutrino data from the latest numerical simulations of delayed neutrino-driven supernova explosions.

26 pages, 6 figures, more discussions, final version in PRD