Multispectral geospatial image sets retain the scene’s spatial and spectral information. To jointly use both of them for analysis purposes, we propose to extend the concept of wavelet packets, by introducing a new integrated multispectral entropy function. Each spectral band is individually decomposed by the wavelet packets transform, and then the entropy term is jointly guided by information f...

This article studies change-points of a function for noisy data observed from a transformation of the function. The proposed method uses a wavelet-vaguelette decomposition to extract information about the wavelet transformation of the function from the data and then detect and estimate change-points by the wavelet transformation. Asymptotic theory for the detection and estimation is established...

We present an application of wavelet theory in partial differential equations. We study the wavelet fundamental solutions to the heat equation. The heat evolution of an initial wavelet state is called a heatlet. Like wavelets for the L space, heatlets are ``atomic'' heat evolutions in the sense that any general heat evolution can be ``assembled'' from a heatlet according to some simple rules. W...

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory—including some new extensions for fractional orders—in a se...