We discuss first one effective and robust estimator of the local Hölder exponent called Average Cone Ratio (ACR), which makes use of a wavelet (or related x-let decompositon). Then we discuss the use of this local regularity estimator in three applications: noise reduction, signal classification and blur estimation. Even first-order statistics of ACR (e.g. using the center of gravity of its histogram) turns out to be very powerful in estimating parameters of image blur (like radius of defocus blur or standard deviation of Gaussian blur). It is interesting to explore how this metric could be used in modelling human perception of blur.