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 structure. 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.
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