The Continuous Wavelet Transform and the Wave Front Set
Jaime Navarro · University of North Texas Digital Library (University of North Texas) · 1993
In this paper I formulate an explicit wavelet transform that, applied to any distribution in S^1(R^2), yields a function on phase space whose high-frequency singularities coincide precisely with the wave front set of the distribution. This characterizes the wave front set of a distribution in terms of the singularities of its wavelet transform with respect to a suitably chosen basic wavelet.