VOW: Variance-Optimal Wavelets for the Steerable Pyramid

We study the issue of localization in the context of isotropic wavelet frames. We define a variance-type measure of localization and propose an algorithm based on calculus of variations to minimize this criterion under the constraint of a tight wavelet frame. Based on these calculations, we design the variance-optimal wavelet (VOW). Finally, we demonstrate the advantage of better localization in a practical image-processing task.