Computational Complexity of the Continuous Wavelet Transform in Two Dimensions
Romain Murenzi, Lance Kaplan, Jean-Pierre Antoine, Fernando A. Mujica · 1998
The two-dimensional continuous wavelet transform (CWT) is characterized by a rotation parameter, in addition to the usual translations and dilations. The CWT has been interpreted as space-frequency representation of two-dimensional signals, where the translation corresponds to the position variable, and the inverse of the scale and the rotation, taken together, correspond to the spatial-frequency variable. The integral of the CWT's squared modulus, with respect to all variables, gives the energy of the original signal. Therefore, an integration on a subset of the parameters gives an energy density in the remaining variables. This paper deals with the implementation of the two basic densities, that is, the position (or aspect-angle) and scale-angle densities. Introduction The 2D continuous wavelet transform (CWT) has been used by a number of authors, in a wide variety of physical problems [1]. It has also been applied in designing CWT-based algorithms for detection and recognition of ...