The monogenic curvelet transform

In this article, we reconsider the continuous curvelet transform from a signal processing point of view. We show that the analyzing elements of the curvelet transform, the curvelets, can be understood as analytic signals in the sense of the partial Hilbert transform. We then replace the usual curvelets by the monogenic curvelets, which are analytic signals in the sense of the Riesz transform. They yield a new transform, called the monogenic curvelet transform, which has the interesting property that it behaves at the fine scales like the usual curvelet transform and at the coarse scales like the monogenic wavelet transform. In particular, the new transform is highly anisotropic at the fine scales and yields a well-interpretable amplitude/phase decomposition of the transform coefficients over all scales.