  This paper is concerned with the inverse scattering problem by an unbounded
rough surface. A direct imaging method is proposed to reconstruct the rough
surface from the scattered near-field Cauchy data generating by point sources
and measured on a horizontal straight line segment at a finite distance above
the rough surface. Theoretical analysis of the imaging algorithm is given for
the case of a penetrable rough surface, but the imaging algorithm also works
for impenetrable surfaces with Dirichlet or impedance boundary conditions.
Numerical experiments are presented to show that the direct imaging algorithm
is fast, accurate and very robust with respect to noise in the data.
