  We develop an algorithm for the computation of general Fourier integral
operators associated with canonical graphs. The algorithm is based on dyadic
parabolic decomposition using wave packets and enables the discrete approximate
evaluation of the action of such operators on data in the presence of caustics.
The procedure consists in the construction of a universal operator
representation through the introduction of locally singularity-resolving
diffeomorphisms, enabling the application of wave packet driven computation,
and in the construction of the associated pseudo-differential joint-partition
of unity on the canonical graphs. We apply the method to a parametrix of the
wave equation in the vicinity of a cusp singularity.
