I want to perform total variation on wavelet domain/PCA domain. How can i proceed in this problem?

I have two problems. 1. smooth out texture regions, 2. Preserve edges of the objects in the image. So I intend to use wavelet domain/curvelet domain (preserve edges)then perform total variation (for image texture smoothing). But I don't know how to apply total variation (TV) on wavelet/curvelet domain.