Directional multidimensional monogenic signal analysis using shearlet monogenic transform

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. Shearlet transform combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data, which is optimally efficient in representing images containing edges. We construct a new shearlet monogenic analysis method using the monogenic and structure based method of the shearlet transform. The result is a representation which each decomposition component of shearlet transform is associated with local orientation, amplitude and phase, which are the AM/FM component of each characters. The new method is highly anisotropic at the fine scales and yields a well-interpretable amplitude/phase decomposition of the transform coefficients over all scales. We illustrate the specific feature extraction capabilities of the method. The results are directional and multidimensional characters of the original image.