  High-frequency ultrasonic pulses at 36 MHz are used to measure velocity
profiles in a complex fluid sheared in the Couette geometry. Our technique is
based on time-domain cross-correlation of ultrasonic speckle signals
backscattered by the moving medium. Post-processing of acoustic data allows us
to record a velocity profile in 0.02--2 s with a spatial resolution of 40
$\mu$m over 1 mm. After a careful calibration using a Newtonian suspension, the
technique is applied to a sheared lyotropic lamellar phase seeded with
polystyrene spheres of diameter 3--10 $\mu$m. Time-averaged velocity profiles
reveal the existence of inhomogeneous flows, with both wall slip and shear
bands, in the vicinity of a shear-induced ``layering'' transition. Slow
transient regimes and/or temporal fluctuations can also be resolved and exhibit
complex spatio-temporal flow behaviors with sometimes more than two shear
bands.
