  We present an improvement on the signal-to-background of single-beam coherent
anti-Stokes Raman scattering (SB-CARS) spectroscopy measurements for systems
employing ultrafast supercontinuum sources based on all-normal dispersion
photonic crystal fibers. Improvements to the signal-to-background arise in the
use of a new pulse-reconstruction algorithm based on temporal ptychography,
I$^2$PIE. A simple SB-CARS strategy is used to measure the spectrum of
para-xylene, where the supercontinuum pulses used are compressed using
multiphoton intrapulse interference phase scan (MIIPS) and, for the first time
to the best of our knowledge, I$^2$PIE using the same single-beam setup. With
the I$^2$PIE implementation, the signal-to-background is improved by nearly a
factor of 4 in comparison with MIIPS. More notably, the integrated SB-CARS
spectral intensity is increased by a factor of 6.5.
