Using Tensor Products to Apply Wavelets to Images

Abstract

Previously we have used wavelets to analyze sound. We would also like to use them in a similar way to analyze images. In Chap. 8 we used the tensor product to construct two dimensional objects (i.e. matrices) from one-dimensional objects (i.e. vectors). Since the spaces in wavelet contexts are function spaces, we need to extend the strategy from Chap. 8 to such spaces. In this chapter we will start with this extension, then specialize to the resolution spaces V _m, and extend the DWT to images. Finally we will look at several examples.