Steerlets: a novel approach to rigid-motion covariant multiscale transforms
Robert Azencott, Bernhard G. Bodmann, Manos Papadakis · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
We present steerlets, a new class of wavelets which allow us to define wavelet transforms that are covariant with respect to rigid motions in d dimensions. The construction of steerlets is derived from an Isotropic Multiresolution Analysis, a variant of a Multiresolution Analysis whose core subspace is closed under translations by integers and under all rotations. Steerlets admit a wide variety of design characteristics ranging from isotropy, that is the full insensitivity to orientations, to directional and orientational selectivity for local oscillations and singularities. The associated 2D or 3D-steerlet transforms are fast MRA-type of transforms suitable for processing of discrete data. The subband decompositions obtained with 2D or 3D-steerlets behave covariantly under the action of the respective rotation group on an image, so that each rotated steerlet is the linear combination of other steerlets in the same subband.