Variance based uncertainty principles and minimum uncertainty samplings

Following an analysis of “local minima” of such an uncertainty measure, in this letter we introduce minimum uncertainty samplings. Denoting the transformation group with G, these samplings lead to lattices gm(m∈M) with gm∈G such that, starting from a function f, the total uncertainty of the function system {fgm}m∈M has the lowest possible value under some given constraints (here fgm denotes the function transformed with gm). We apply this construction to, e.g., wavelet transforms and related techniques like shearlets.