Shear Smoothlet -- Anisotropic Multiscale Functions for Adaptive Representation of Images

Smoothlet transform is an adaptive geometric multiscale representation for image approximation. It is an isotropic block oriented image analysis algorithm, one function is defined in each block, the function has characterized by location, scale, orientation, curvature and blur which can obtain an efficient representation of an image. However, Smoothlet does not take the anisotropic feature of blocks into account. In this paper, a special class of functions called Shear Smoothlet is proposed. Shear Smoothlet has considered the anisotropic characteristic of blocks themselves according to introducing shear operation before executing Smoothlet transform to an image. Final reconstructed images are obtained by calculating the average of all reconstructed images based on Shear Smoothlet transform in each direction. Experimental results including visual quality and peak signal to noise radio both verify the effectiveness of the algorithm proposed in this paper.