  This article present a new method to reconstruct slowly varying width defects
in 2D waveguides using one-side section measurements at locally resonant
frequencies. At these frequencies, locally resonant modes propagate in the
waveguide up to a "cut-off" position. In this particular point, the local width
of the waveguide can be recovered. Given multi-frequency measurements taken on
a section of the waveguide, we perform an efficient layer stripping approach to
recover shape variations slice by slice. It provides an L infinite-stable
method to reconstruct the width of a slowly monotonous varying waveguide. We
validate this method on numerical data and discuss its limits.
