Directional Wavelet Analysis with Fourier-Type Bases for Image Processing

Abstract

Motivated by the fact that in natural images, there is usually a presence of local strongly oriented features such as directional textures and linear discontinuities, a representation which is both well-localised in frequency and orientation is desirable to efficiently describe those oriented features. Here we introduce a family of multiscale trigonometric bases for image processing using Fourier-type constructions, namely, the multiscale directional cosine transform and the multiscale Fourier transform. We also show that by seeking an adaptive basis locally, the proposed bases are able to capture both oriented harmonics as well as discontinuities, although the complexity of such adaptiveness varies significantly. We conducted denoising experiments with the proposed bases and the results show great promise of the proposed directional wavelet bases.