Wavelet Transforms in Image Processing

Abstract

This paper is designed to be partly tutorial in nature and partly a summary of recent work by the authors in applying wavelets to various image processing problems. The tutorial part describes the filter-bank implementation of the discrete wavelet transform (DWT) and shows that most wavelets which permit perfect reconstruction are similar in shape and scale. We then discuss an important drawback of these wavelet transforms, which is that the distribution of energy between coefficients at different scales is very sensitive to shifts in the input data. We propose the Complex Wavelet Transform (CWT) as a solution to this problem and show how it may be applied in two dimensions. Finally we give brief details of applications of the CWT to motion estimation and image de-noising. Keywords: Wavelets, complex wavelets, gabor filters, shift-invariance, motion estimation, image de-noising.