<title>Uniform approximation of wavelet coefficients</title>

Abstract

Mallat's pyramid algorithm relates the scaling coefficients of a function at one level to the scaling and wavelet coefficients at lower levels. In practice, the scaling coefficients are estimated at some level m, and the algorithm is used to produce estimates of the scaling and wavelet coefficients at lower levels. Initial errors propagate to lower level estimates. this paper descries conditions under which this process generates estimates which are uniformly reliable at a particular level, and under which the errors at that level tend uniformly to zero as m increases.