  Multipath propagation in the interstellar medium distorts radio pulses, an
effect predominant for distant pulsars observed at low frequencies. Typically,
broadened pulses are analyzed to determine the amount of propagation-induced
pulse broadening, but with little interest in determining the undistorted pulse
shapes. In this paper we develop and apply a method that recovers both the
intrinsic pulse shape and the pulse broadening function that describes the
scattering of an impulse. The method resembles the CLEAN algorithm used in
synthesis imaging applications, although we search for the best pulse
broadening function, and perform a true deconvolution to recover intrinsic
pulse structre. As figures of merit to optimize the deconvolution, we use the
positivity and symmetry of the deconvolved result along with the mean square
residual and the number of points below a given threshold. Our method makes no
prior assumptions about the intrinsic pulse shape and can be used for a range
of scattering functions for the interstellar medium. It can therefore be
applied to a wider variety of measured pulse shapes and degrees of scattering
than the previous approaches. We apply the technique to both simulated data and
data from Arecibo observations.
