The picture on the right shows the second dyadic decomposition (SDD), which is also the frequency partitioning of curvelets. The SDD was invented by Charles Fefferman in 1973 to answer mathematical questions of boundedness of Bochner-Riesz summation multipliers (some convolution operators).
Next, we show examples of curvelets at different scales, both in space and frequency.
Finally, the picture on the right shows the second dyadic decomposition in three dimensions, which is also the frequency partitioning of 3d curvelets. All the pictures are taken from the paper Fast Discrete Curvelet Transforms and refer to the wrapping variant, complex-valued, and with curvelets at the finest scale.