  Giant pulses emitted by PSR B1937+21 are bright, intrinsically impulsive
bursts. Thus, the observed signal from a giant pulse is a noisy but direct
measurement of the impulse response from the ionized interstellar medium. We
use this fact to detect 13,025 giant pulses directly in the baseband data of
two observations of PSR B1937+21. Using the giant pulse signals, we model the
time-varying impulse response with a sparse approximation method, in which the
time dependence at each delay is decomposed in Fourier components, thus
constructing a wavefield as a function of delay and differential Doppler shift.
We find that the resulting wavefield has the expected parabolic shape, with
several diffuse structures within it, suggesting the presence of multiple
scattering locations along the line of sight. We also detect an echo at a delay
of about 2.4 ms, over 1.5 times the rotation period of the pulsar, which
between the two observations moves along the trajectory expected from geometry.
The structures in the wavefield are insufficiently sparse to produce a complete
model of the system, and hence the model is not predictive across gaps larger
than about the scintillation time. Nevertheless, within its range, it
reproduces about 75% of the power of the impulse response, a fraction limited
mostly by the signal-to-noise ratio of the observations. Furthermore, we show
that by deconvolution, using the model impulse response, we can successfully
recover the intrinsic pulsar emission from the observed signal.
