Fast adaptive expansions in local trigonometric bases

Abstract

Smooth local trigonometric bases along with wavelet packet bases have provided a natural setup for the best basis algorithm of Coifman and Wickerhauser. We consider a best basis algorithm for local trigonometric bases with a cost function that only depends on the local behavior of the signal near the points where the local trigonometric functions overlap. The benefit is that the complexity of the algorithm is much lower than using a standard cost function in the best basis algorithm. We compare the performance of the algorithm to the best basis algorithm using an ℓ 1-norm as cost function on several test signals.