Lebesgue-type partitions of unity for operator localization

Michael P. Lamoureux, Gary F. Margrave

Partitions of unity (POUs) that track geological features give an effective means to reduce computational complexity in time-frequency methods. Such methods typically localize operators using windowed Fourier transforms to implement Gabor multipliers or more general pseudodifferential operators. We give a description of a method to create nonuniform partitions of unity and show the approximations obtained by these non-uniform versions are as good as the uniform method, while reducing complexity and numerical errors due to window edge artifacts. This windowing is a key step in Gabor decon and Gabor wavefield extrapolation.