  We define a new type of wavelet frame adapted to the study of wave equations,
that we call Minkowski curvelets, by reference to the curvelets introduced by
Cand\`es, Demanet and Donoho. These space-time, strongly anisotropic,
directional wavelets have a Fourier support which does not intersect the
light-cone; their maximal size is proportional to the inverse of the distance
to the light-cone. We show that the matrix of the Green kernel of the
Klein-Gordon operator on Minkowski space-time has a nearly exponential
off-diagonal decay in this basis.
