Multidimensional Wavelets and Applications
Yves Nievergelt · Birkhäuser Boston eBooks · 1999
This chapter extends Haar’s wavelets from one-dimensional arrays to multidimensional grids of data, for instance, encodings of photographs, scatter plots, or geographical measurements. Some of the logical derivations involve matrix algebra. For two-dimensional wavelets, encodings can consist of matrices, indexed by rows from top to bottom, and by columns from left to right. Corresponding to the index of the rows, the first coordinate axis runs from top to bottom; similarly, corresponding to the index of the columns, the second coordinate axis runs from left to right. Such an indexing scheme amounts to a rotation of the usual mathematical axes by one quarter of a turn clockwise, as shown in Figure 2.1. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.