Since a different wavelet is computed for each offset volume, compensation is automatically done for offset-dependent bandwidth, scaling and tuning effects.
It is a two-dimensional wavelet transform which provides multiresolution, sparse representation, and useful characterization of the structure of an image.
Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations.
All wavelet transforms may be considered forms of time-frequency representation for continuous-time (analog) signals and so are related to harmonic analysis.