Regularised, semi-local hurst estimation via generalised lasso and dual-tree complex wavelets

Semi-local Hurst estimation is considered for random fields where the regularity varies in a piecewise manner. The recently developed generalised lasso is exploited to propose a spatially regularised Hurst estimator. Dual-tree complex wavelets are used to formulate the usual log-spectrum regression problem and an interlaced penalty matrix is constructed to form a 2-d fused lasso constraint on the double-indexed parameters. We thus extend a regularity-based denoising approach and demonstrate the utility of our method with experiments.