A Theory for Multiresolution Signal Decomposition: The Wavelet Representation

Abstract-Multiresolution representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions 2 ’ + ’ and 2jcan be extracted by decomposing this signal on a wavelet orthonormal basis of L*(R”). In LL(R), a wavelet orthonormal basis is a family of functions ( @ w (2’ ~-n)),,,“jEZt, which is built by dilating and translating a unique function t+r (xl. This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on…