Wavelet Transforms
Raghuveer Rao · 2002
Abstract In a 1984 paper, Grossman and Morlet investigated the problem of representing square‐integrable functions by using shifts and dilations of a single function called a wavelet. The motivation lay in the fact that there is evidence for the usefulness of such representations in analyzing seismic traces. Although earlier articles dealing with similar problems can be found, the Grossman–Morlet paper provides an integral transform along with conditions under which one can invert the transform. Thus was born the field of wavelet transforms. Subsequent developments in the field such as the formulation of discrete basis functions, the relationship to subband filtering, and the application to signal/image processing have contributed to widespread interest in the subject. The purpose of this article is to provide a short overview of wavelet transforms and their application to certain image processing problems.